Year 12 Revision Guide - St John's Grammar School€¦ · • Simple Interest • Compound Interest...

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Year 12 Revision Guide

This guide provides an outline of course content for the upcoming November examinations. It can be

used in two ways:

1. To assist in your final preparation for November SACE examinations. Your teachers assist you

in planning your revision according to the structure of the examination paper and topics

examined. You can then use this guide to assist you in preparation for examination sessions.

2. As an ongoing revision resource to be used as part of your weekly revision routines. For

some courses these guides also provide an overview of content for the subject including

non-examined topics; this may be used as an ongoing guide for weekly revision across the

duration of the year, in conjunction with regular classroom exercises and Canvas resources

provided by your teachers.

How to use this resource:

• This guide contains revision materials for all Year 12 subjects with an examination. You need

to identify which pages/sections are relevant to the subjects you have studied.

• Start by familiarising yourself with the topic list and course content outlined in each guide.

Then objectively highlight which content you are confident/familiar with, and which you

need to focus on.

• You can then use this guide to help you plan your revision over the coming weeks. You can

speak with your teachers, Home Group teacher or Head of House if you need assistance with

this.

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Year 12, 2019

Subject group Subjects Page # Mathematics Mathematics Essential

Mathematics General Mathematical Methods Specialist Mathematics

3

Sciences Biology Physics Chemistry Psychology

28

Physical Education Physical Education 72 English English Literary Studies 80 Humanities Geography

Modern History 81

Languages Chinese (background speakers)

85

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Revision Guide: Year 12, Essential Mathematics, Measurement

Timing Term 2 Week 4

New Knowledge and Understanding

• Conversions: linear unit metric conversions. Discuss link between metric and imperial units and conversions

• Perimeter: calculations of simple and composite shapes.

• Conversions: metric area unit conversions and between metric and imperial units (e.g. km2 to Ha, etc.)

• Calculations of area.

• Regular and irregular triangles, quadrilaterals, sectors, circles and composites of these shapes.

• Irregular non-polygonal shapes: use Simpson’s rule to calculate irregular areas (with curved outlines) e.g. fish ponds, garden beds, golf greens, dams.

Text reference Exercises 2A, 2B, 2C, 2D, 2E, 2F.1, 2F.2 pp 36-59.

Term 2 Week 5 • Calculation of surface area of cubes, prisms, pyramids, and spheres

• Simple composites of these.

• Conversions: units of mass, volume, and capacity

• Calculations: volume of cubes, prisms, pyramids, cones, and spheres

• Density: Units, e.g. g/cm3

• Calculations: Use density to determine volume or mass of a specified material.

Exercises 5A.1, 5A.2, 5B.1, 5B.2, 5C, 5D.1, 5D.2, 5E pp 98-119.

Term 2 Week 6 • Calculating lengths of missing sides:

• Pythagoras Theorem

Exercises 4B, 4C, 4D pp 82-93.


• Right-angled triangle trigonometric ratios – sine, cosine and tangent

Exercises 6A, 6B, 6C.1, 6C.2, 6D pp 124-136.


• Non right-angled triangles: sine and cosine rules.

• Calculating unknown angles using sine and cosine rules.

Exercises 7A, 7B.1, 7B.2,7C.1, 7C.2, 7D pp 140-150.

Use of Specific Mathematical Notation and Formulae Students should be familiar with different measurements of area, such as square metres, square kilometres, hectares, and acres, and conversion of metric units of area to imperial measures of area. Students will be expected to know the area formulae for the following shapes: • triangle • square • rectangle • parallelogram • trapezium • circle • sector of a circle Students will be expected to know Simpson’s rule

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Students will be expected to know the following surface area formulae for solids: • cubes • rectangular-based prisms • triangular-based prisms • cylinders. Where the surface area of pyramids, cones or spheres are required to be calculated in an examination, the formulae will be provided. Right-angled triangles - consider the use of Pythagoras’ theorem, sine, cosine, and tangent ratios to find the lengths of missing sides of right-angled triangles. • Use the concepts angle of elevation and angle of depression. • Construct diagrams displaying information provided about angles of elevation and/or depression • Use these in solving problems The sine rule and cosine rule - to allow for angles of non-right-angled triangles. • Use them to find the lengths of missing sides of non-right-angled triangles. These calculations require the use of electronic technology.

Use of Electronic Technology • Calculations of sides for Pythagoras’ theorem using squared and square root buttons.

• Trigonometry functions – Sin, Cos, Tan for finding sides and angles.

• The sine rule and cosine rule to find the lengths of missing sides of non-right-angled triangles. These calculations require the use of electronic technology.

Revision Guide: Year 12, Essential Mathematics, Investments and Loans



• Simple Interest

• Compound Interest formula & different compounding periods.

• Electronic technology

• Variable interest rates

Text reference Exercises 13A, 13B.1, 13B.2, 13B.3 pp 308-319.

Term3 Week 2 • Future Value Annuities – starting with nothing

• Future Value Annuities – starting with an initial investment.

• Tax

• Inflation

• Superannuation

Exercises 13C.1, 13C.2, 13D.1, 13D.2, 13E pp 320-334.

Term 3 Week 3 • Reducing Balance Loans

• Home Loans

• Strategies to minimise interest – making larger payments per period

• Strategies to minimise interest – making more frequent repayments

• Strategies to minimise interest – reducing the term of the loan

• Strategies to minimise interest – making lump sum payments

Exercises 14A, 14B, 14C.1, 14C2, 14C.3, 14C.4 pp 340-354.

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Term 3 Week 4 • Comparing Loans

Exercise 14D pp 354-355.

Use of Specific Mathematical Notation, Terminology and Formulae Consideration of earning money through investing a lump sum into an account should include both simple and compound interest calculations. The focus is on rearranging the simple interest formula to find all of the variables. Students will be expected to know the simple interest and compound interest formulae; Interest rate terminology: variable rates and fixed rates. Students will be expected to know impact of taxation on investment earnings and calculations of inflation leading to the factors that diminish the value of investment earning. The mathematics is used in calculating future value annuities: • Future value • The regular deposit • The number of periods • The interest rate • The interest earned by the annuity investment • Assumptions made in long-term annuity calculations Applications of future value annuities • Long-term investments • Superannuation What may impact on the earnings of the future value annuity: • Taxation of interest earned • Inflation Mathematics is used in calculating the cost of a loan: • Present value • The regular payment • The number of periods • The interest rate • The interest paid • Assumptions made in long-term annuity calculations How you can determine the most appropriate loan option: • Charges on loan accounts • Comparison rates (no calculations required)

Use of Electronic Technology • The graphics calculator TVM or Financial function is utilised to allow easy investigation of problems

requiring the range of variables to be found for compound interest problems.

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Revision Guide: Year 12, Essential Mathematics, Statistics



• Sampling

• Sources of errors in surveys

• Sampling methods

• Displaying data

Text reference Exercises 11A.1, 11A.2, 11A.3, 11B pp 246-257.

Term3 Week 6 • Measuring the centre of data

• The mean and median of grouped data

• Measuring the spread of data

• Standard deviation

Exercises 11C.1, 11C.2, 11D.1, 11D.2 pp 257-267.

Term 3 Week 7 • Back-to-back stem plots

• Parallel box plots

Exercises 11E, 11F pp 268-275.

Term 3 Week 8 • Correlation

• Measuring Correlation

• The coefficient of determination r

Exercise 12A, 12B.1, 12B.2 pp 282-293.

Term 3 Week 9 • Line of Best Fit by eye

• Least Squares Regression Line

Exercise 12C, 12D pp 294-301.

Use of Specific Mathematical Notation, Terminology and Formulae What a sample is and what the purpose of sampling is: • Census • Population • Sample • Survey What some methods of sampling are: • Simple random • Stratified, including appropriate calculation • Systematic • Self-selected What are the advantages and disadvantages of each sampling method? How bias can occur in sampling: • Faults in the process of collecting data

• Errors in surveys: sampling errors measurement errors coverage errors non-response error The influence sample size has on the reliability of findings: • Sample mean compared with population mean

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How we compare two or more distributions: • Calculation of measures of central tendency and spread The effect of outliers on the distributions. The types of representation which are most suitable for comparing two or more distributions: • Stem-and-leaf plots • Box-and-whisker diagrams Is there a linear relationship between two variables: • Dependent and independent variable • Patterns and features of scatter plots • Description of association — direction, form, and strength • Causality between variables How the degree of linear relationship between two variables can be established: • Pearson’s correlation coefficient When it is appropriate to draw a least squares regression line: • Coefficient of determination ( 2 r ) • Least squares regression line (‘line of best fit’) How the least squares regression line may be used. How outliers affect the degree of linear relationship and the least squares regression line.

Use of Electronic Technology • The graphics calculator Statistics function is utilised.

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Revision Guide: Year 12, General Mathematics, Statistical Models

Timing

Term 2 Week 3


• Explanatory and response variables (independent and

dependent variables)

• Scatter plots

• Analysing correlation by looking at direction, linearity,

strength.

• The effects of outliers

• Understanding of Causality

Text reference

Exercises 4B Q1,3,4,5,6

Term 1 Week 4 • Correlation coefficients: Pearson’s Coefficient (r) and

Coefficient of Determination (r2) ( calculation is done

using technology )

• Least Squares Regression Line (LSRL): finding the line

in the form of a +bx and understanding the

mathematical & real-life application of a and b

• Prediction using Interpolation and extrapolation from

LSRL.

• Reliability of prediction using Interpolation and

Extrapolation

4C.1* Q2,

4 GC,

6 & 7 by hand

4C.2 all

4D Page 92 - discuss

4E* Q4-7

Term 2 Week 5 • Residual plots: concepts of residual plots; generating

a residual plot using technology and analysing

residual plots.

• Understand that the residual plot is another

technique to confirm if the linear model is accurate

for the set of data being analysed (besides the r

value)

• Exponential regression: writing the equation of an

Exponential Model in the form of abx.

understanding the mathematical & real-life application

of a and b

4F.1* all

4F.2* Q1-3,4,6

4G* all

Term 2 Week 6 • Normal Distribution:

• Properties of the bell-shaped curve

• 68%-95%-99.7% properties

• Finding probabilities of both integral and non-integral

standard deviations from the mean.

5A*Q1,2,3,4,6,7,8,9,

11,12

5B* Q1, 2, 3, 4, 6, 7, 9, 10, 11

Term 2 Week 7 • Inverse normal problems 5C* all

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Use of Specific Mathematical Notation

Graphing skills with axes labels.

Notation for equation of LSRL and Exponential Regressions.

Normal Distribution notation for Ncd and Inverse Normal

Use of Electronic Technology

• Calculations by using tables in STAT mode of graphics calculator to find r, r2, scatter plots, residual plots,

equation for LSRL and Exponential Model, Ncd and Inverse Normal functions

• Using the GRAPH mode of the graphics calculator to plot graphs and finding y value for a given x value

• Ncd, Npd, r, residual plots, LSRL,

Key Prerequisite Knowledge

• Understanding the key components for an equation of a linear model y= mx + b and the significance

of m and b to the model

Revision Guide: Year 12, General Mathematics, Financial Models

Timing

Term 3 Week 1


Models for Savings:

• Basic Simple Interest using I = Pin

• Compound Interest Investment accounts using

technology: TVM/Financial Mode on calculator.

• Familiarity with finding a missing information in investment; n, I

, Pv, Fv or PMT when the other key information is provided

• Calculating future-value annuities - Future value; The regular

deposit; The number of periods, The interest rate, The value of

the accumulating savings after a given period, Total interest

earned

Text reference

7AQ1-4

7B.3 Q1-8

7C.1 1-12

7C.2 1-6

Term 3 Week 2 • Comparing different investment options using Effective interest

rates (with technology: EFF)

• Calculating the after-tax return on an investment when a

marginal tax or when a salary per annum is provided

• Calculating real rate of return of an investment due to inflation

• Superannuation: Looking at calculating

a. the amount contributed per month, per quarter or per year.

b. Amount of withdrawal per period from pension funds

7D 1-8

7E.1 1-10

7E.2 1-8

7F 1-11

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c. Effect of inflation on amount of withdrawal per

period OR the duration (n) a pension fund can last for

Term 3 Week 3 &

4

Models for Borrowing: All done with technology

• Reducing balance loans: Familiarity with finding missing

information in a loan scenario: n, I , Pv, Fv or PMT; when the

other key information is provided

Strategies to reduce the amount of interest paid on a loan. Finding the

effect of:

• Making larger repayments per period

• Making more frequent repayments

• Reducing the term of the loan

• Changing interest rates

• Paying a lump sum off the principal owing

• Using offset accounts

8A 3, 5 -9

8B 1-8

8C.1 Q1-3

8C.2 Q1-2

Term 3 Week 5 • Comparison interest rates between financial institutions

with/without monthly fee ; establishment fee.

• Interest only loans and sinking funds

8C.3 Q1-4

8C.4 Q1-3

8C.5 Q1-3

8C.6 Q1-4

8D Q1-6

8E 1-5

Chapter reviews 7B & 8A

&8B


Correct rounding off when dealing with loan and investments for number of months and amount owing


• Calculations using Financial mode of graphics calculator to find n, Pv, Fv, PMT and EFF


• Understanding the key concepts of number of months in a year, number of weeks in year and number of

fortnights in a year.

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Revision Guide: Year 12, General Mathematics, Discrete Models

Timing

Term 3 Week 7


• Creating a precedence table that indicates which other jobs

must be completed before a given job can start.

• Drawing a network from a given precedence table or a table

which is generated based on job completion requirements

• Dummy Link(s):

a. using ‘dummy’ arcs in the network to show a given

precedence correctly (e.g. when job E requires

both A and B to be complete, but job C requires only B to be

complete).

b. Being able to identify from a given precedence table the jobs

which will have a dummy link incorporated.

c. Correctly showing the dummy link by using dotted/dashed

line with an arrow indicating the flow of a job in the

network.

Text reference

12A.1 (supplement with

extra questions from

Nelson 12 General or any

other resources)

12A.2

Term 3 Week 8 • Completing a forward and backward scan of a network. Using

this to

a. Find the earliest and latest starting times for individual tasks

b. Find the Critical Pathway in a network:

c. Determine the shortest time in which a complex task can be

completed and identify the critical components of that task.

• Slack/Float time:

a. Calculating the amount of leeway available in the starting

time for a given job in the network, and what happens if time

for a specific job is shortened or lengthened.

b. Discussion of leeway (or slack time) over sections of the

network not on the critical path

• Discuss the reasonableness of a results and any limitations to

the model in the context of the problem if certain jobs in a

network have the time allocated increased or decreased.

12A.3(supplement with

extra questions from

Nelson 12 General or any

other resources )

Term 3 Week 9 • Using the Hungarian algorithm technique to find optimum

solution of an assignment problem. This could be for

a. A minimizing problem; Finding minimum time; minimum

cost etc

b. A maximizing problem: Finding maximum profit

12B.2

12B.3

12B.4

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• Applying Hungarian algorithm when Working with non-

square arrays

• Considering the effects of changes to the original conditions

• Interpreting multiple solutions


• none


• Addition and Subtraction

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Revision Guide: Year 12, Mathematics Methods, Differential Calculus

Timing: Term 1 Week 1

New Knowledge and Understanding • Differentiate functions from first principles using the

theory of limits.

• Use simple rules to differentiate polynomials and power functions.

Text reference Ex 2A EX2B

Term 1 Week 2 • Apply the Chain Rule, Product Rule and Quotient Rule to differentiate more complex functions.

Exercises Ex 2C, 2D and 2E

Term 1 Week 3

• Find the derivative of exponential functions.

• Find the derivative of trig functions.

• Find Second derivatives.

Exercises Ex 2F Ex 2H Ex 2I

Term 1 Week 4

• Find the equations of tangents and normal.

• Determine intervals for which functions are increasing or decreasing.

• Locate and classify stationary points .

• Locate classify points of inflection .

• Use sign diagrams to describe the behaviour of functions.

• Understand the relationship between graphs of f(x) f’(x) and f’’(x) including being able to sketch one of these functions given the other(s).

Exercises Ex 3A Ex 3B Ex 3C Ex 3D.1 Ex 3D.2


• Limit notation must be used consistently e.g. 𝑓′(𝑥) = limℎ→0

𝑓(𝑥+ℎ)−𝑓(𝑥)

ℎ

• Use of 𝑓′(𝑥) or 𝑑𝑦

𝑑𝑥 should be consistent throughout a problem.

• Where answers are rounded 3 significant figures should be used.

• Use brackets to clarify working e.g.: sin(3𝑥 + 2)

• (𝑠𝑖𝑛𝑥)2 should be abbreviated to 𝑠𝑖𝑛2𝑥. Apply this to all trig functions

Use of Electronic Technology • Graphing on graphics calculator is expected in order to classify functions and their features. Full mastery

of the view window function is expected

Key Prerequisite Knowledge • Manipulation of algebraic fractions including addition, subtraction, multiplication, division and

simplification.

• Simplification of surds

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Revision Guide: Year 12, Mathematics Methods, Logarithmic Functions



• Know how to use logarithms for solving exponential equations.

• Given 𝑎𝑥 = 𝑏then 𝑥 = 𝑙𝑜𝑔𝑎𝑏 leading to 𝑦 = 𝑒𝑥 then 𝑥 = 𝑙𝑜𝑔𝑒𝑦 = ln𝑦

• Apply log laws to solve equations and simplify expressions.

Text reference Exercises Ex 1B2, 1B3 and 1B4 & A.2 Ex 4B Qu 3,4,5. Log Scales Investigation pg 20.

Term 3 Week 2 • Use the properties of Log functions and their graphs to model problems.

Demonstrate knowledge of:

• The graph of 𝑦 = ln𝑥 and its properties.

• The graph of functions in the form 𝑦 = 𝑘ln(𝑏𝑥 +𝑐).

• The relationship between the graphs of 𝑦 =ln𝑥and 𝑦 = 𝑒𝑥 .

Ex 1C Selected questions from QU 2- 15 Pg. 16 addresses the concept of inverses.

Term 3 Week 3 • Be able to find the derivatives of 𝑦 = ln𝑥 and 𝑦 =ln𝑓(𝑥)

• Know that ∫1

𝑥𝑑𝑥 = ln𝑥 + 𝑐 provided 𝑥is positive.

• Problem solve using the derivatives of logarithmic functions.

• Understand basic applications of logarithmic functions.

Derivatives Ex 2G Tangents & Normals Ex 3A Qu 7 b, d. Qu 8, 16 Increasing/Decreasing Ex 3B Qu 3 h, l, 7 e, g Stationary Points Ex 3C Qu 6, 10, 11. Inflections 3D1 Qu 8, 9 Kinematics Ex 3E, Qu 7, 10 Optimisation Ex 3G Qu 4 Applications Ex 3F Qu 8

Use of Electronic Technology • Be able to graph and carry out calculations using log functions

• It may be useful to be able to be able to carry out calculations with bases other than 10 or “e”. Look for the 𝑙𝑜𝑔𝑎𝑏 function in the Casio catalogue of functions.

Revision Guide: Year 12, Mathematics Methods, Continuous Random Variables

and the Normal Distribution.



• Identify discrete and continuous random variables.

• Identify and use probability density functions and their graphs.

• Calculate the mean

𝐸(𝑥) = ∫ 𝑥𝑓(𝑥)𝑑𝑥∞

−∞and the.....

Text reference Ex 8A, 8B1, 8B2

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• standard deviation 𝜎 = √∫ [𝑥 − 𝐸(𝑥)]2𝑓(𝑥)𝑑𝑥∞

−∞

Term 3 Week 5 and 6 • Describe the key properties of normal distributions.

• Make use of the probability density function

𝑓(𝑥) =1

𝜎√2𝜋𝑒

−1

2(𝑥−𝜇

𝜎)2

• Use electronic technology to calculate proportions, probabilities, and the upper or lower limit of a certain proportion.

• Use the fact that the standard normal distribution has mean 𝜇 = 0 and s.d. = 𝜎 = 1. to solve problems

• Standardise a normal distribution using 𝑍 =𝑋−𝜇

𝜎.

• Find unknown values of mean 𝜇 and 𝜎 given specific probabilities.

Ex 8C, 8D, 8E, 8F1, 8F2

Use of Specific Mathematical Notation: Important

• Use �̅� and s for sample mean and sample standard deviation. (Sample Statistics) • Use 𝜇 and 𝜎 for population mean and population standard deviation (Population Parameters)

Use of Electronic Technology • Make extensive use of Normal Cumulative Distribution (NCD) and Inverse Normal calculator functions

• Normal Point Distribution (NPD) can be use to sketch distributions

• Integrate functions on the calculator to save time and solve “1 mark” questions.

Revision Guide: Year 12, Mathematics Methods, Sampling and Confidence

Intervals



• Calculate sample statistics such as a sample means and sample sums.

• Know that 𝑆𝑛 is the outcome of adding n independent observations of X.

• Know that 𝑋𝑛̅̅̅̅ is the outcome of averaging n

independent observations of X.

• Know that if 𝑋~𝑁(𝜇, 𝜎) then 𝑆𝑛~𝑁(𝑛𝜇, 𝜎√𝑛)and

𝑋𝑛̅̅̅̅ ~𝑁 (𝜇,

𝜎

√𝑛) provided𝑛 is sufficiently large.

• Understand and be able to apply the Central Limit Theorem.

• Know that If 𝑋~𝑁(𝜇, 𝜎) then �̅�~𝑁 (𝜇,𝜎

√𝑛) for a

sample size 𝑛. Due to the Central limit theorem.

• Know that sample means are continuous random variables.

• Understand that the distribution of sample means (Taken from any distribution) will be approximately

normal for a sufficiently large sample. �̅�~𝑁 (𝜇,𝜎

√𝑛)

Text reference Exercises Ex 9A, 9B, 9C

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Term 3 Week 8

• Understand that a confidence interval can be created around the sample mean that may contain the population mean.

• Know that if �̅� is the sample mean then the

confidence interval is �̅� − 𝑧𝑠

√𝑛≤ 𝜇 ≤ �̅� + 𝑧

𝑠

√𝑛,

where 𝑧 is determined by the confidence level that the interval will contain the population mean.

• Construct confidence intervals

• Calculate the sample size needed to obtain a confidence interval of specified width

• Use confidence intervals to assess claims.

Exercises Ex 9D1, 9D2, 99D3

Term 3 Week 9

• Understand the concept of a population proportion 𝑝and be able to identify related problems.

• Know that sample proportion �̂� =𝑋

𝑛 is a discrete

random variable with a mean 𝑝 and standard

deviation √𝑝(1−𝑝)

𝑛.

• Know that as the sample size increases the distribution of�̂� becomes more like a normal distribution.

• Understand that a confidence interval can be created around the sample proportion that may contain the population proportion.

• Know that if �̂� is the sample mean then the confidence interval is:

�̂� − 𝑧√𝑝(1−𝑝)

𝑛≤ 𝑝 ≤ �̂� + 𝑧√

𝑝(1−�̂�)

𝑛, where 𝑧 is

determined by the confidence that the interval will contain the population mean.

Exercises Ex 9E, 9F1, 9F2, 9F3

Use of Specific Mathematical Notation: Important • Use �̅� and s for sample mean and sample standard deviation. (Sample Statistics)

• Use 𝜇 and 𝜎 for population mean and population standard deviation (Population Parameters

Use of Electronic Technology • Make extensive use of Normal Cumulative Distribution (NCD) and Inverse Normal calculator functions

• Use graphics Calculator to calculate Confidence Intervals for population means and population

proportions.

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Revision Guide: Year 12, Mathematics Methods, Discrete Random Variables


New Knowledge and Understanding • Classify random variables as continuous or discrete.

• Identify discrete probability functions given that the sum of all probabilities must equal 1.

• Display discrete probability distributions as tables or graphs

• Identify uniform and non-uniform discrete random variables.

• Find the median and mode of a discrete Distribution

Text reference Exercises 7A & 7B p.184-191

Term 1 Week 7 • Estimate probabilities of discrete random variables.

• Calculate the expected value and understand its purpose in estimating the centre of the distribution and the sample mean.

• Calculate the standard deviation and understand its purpose in measurement of the spread of the distribution.

Exercises 7C.1,2,3, 7D & 7E p.192-193

Term 1 Week 8 • Understand that Bernoulli variables are discrete random variables with only two outcomes.

• Apply the Bernoulli distribution 𝑝(𝑥) = 𝑝𝑛(1 − 𝑝)1−𝑛 to calculate probability.

• Calculate the mean, 𝑝 and standard deviation,√𝑝(1 − 𝑝)

of a Bernoulli distribution.

Exercises 7F

Term 1 Week 8 & 9 • Identify The binomial random variables and the binomial distributions.

• Calculate the mean 𝑛𝑝 and the standard deviation

√𝑛𝑝(1 − 𝑝)

• Model scenarios using the binomial distribution.

• Finding binomial probabilities using:

• 𝑝(𝑋 = 𝑘) = 𝐶𝑘𝑛𝑝𝑘𝑝𝑛−𝑘 and electronic technology.

• Describe the shape of the binomial distributions for large values of 𝑛.

Exercises 7G.1,2,3

Use of Specific Mathematical Notation • The probability that a Variable X takes value x is denoted by P(X = x)

• A random variable X with possible values: 𝑥1, 𝑥2, 𝑥3, ……… . 𝑥𝑛has associated probabilities 𝑝1, 𝑝2, 𝑝3, ……… . 𝑝𝑛

• Use and understand summation notation E.g. : ∑ 𝑝𝑖 =𝑝1 + 𝑝2 + 𝑝3 + ⋯…+ 𝑝4 = 1𝑛𝑖=1

• Expected value is denoted by 𝐸(𝑋) where 𝐸(𝑋) = µ

• Population standard deviation is denoted by 𝜎 and variance by 𝜎2

Use of Electronic Technology • Calculations of 𝐸(𝑋)and 𝜎 using tables in STAT mode of graphics calculator.

• Binomial point distribution (Bpd) calculations in STAT mode of graphics calculator.

• Binomial cumulative distribution (Bcd) calculations in STAT mode of graphics calculator.

Key Prerequisite Knowledge • P(A or B) = P(A)+P(B) , P(A and B) = P(A) × P(B)

• Probability calculations involving independent and non-independent events using Tree Diagrams.

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Revision Guide: Year 12, Mathematics Methods, Applications of Differential

Calculus


Review of Prerequisite Knowledge

• Understand the definitions of the general sine and cosine functions in relation to the unit circle

• Sketch trig functions in a given interval

• Solve trig functions, finding multiple solutions in a given interval

Text reference Exercises Ex 1D + Year 11 text.

Term 1 Week 10 & 11


• Apply differential calculus to solve linear motion problems involving displacement, velocity, speed and acceleration.

• Draw motion diagrams

Exercises Ex 3E

Term 2 Week 1 • Identify and calculate rates of change to solve problems in a variety of real-world contexts.

Ex 3F

Term 2 Week 2 • Optimise a variable to find the maximum or minimum of a function in a variety of real-world contexts

• Use sign diagrams to test optimal solutions

Ex 3G

Term 2 Week 3 • Apply knowledge of differential calculus to construct functions (Roller Coaster Track Investigation)


• Use s(t), v(t), a(t) to represent displacement, velocity and acceleration functions.

• s’(t) = v(t) and s’’(t) = v’(t) = a(t)


• Graphing on graphics calculator is expected in order to classify functions and their features. Full mastery of the view window function is expected


• Manipulation of algebraic fractions including addition, subtraction, multiplication, division and simplification.

• Simplification of surds

Revision Guide: Year 12, Mathematics Methods, Integral Calculus

Timing: Term 2 Week 5 & 6


• Estimate the area under a curve using the lower and upper rectangles method or other known area facts.

• Find antiderivatives by first differentiating a function

• Apply the rules for integration for constants, power, exponential trig and reciprocal* functions.

• Know that:

1. ( ) ( ) ( )d

b

a

f x x F b F a= −

2. ( )d 0

a

a

f x x =

3. ( ) ( ) ( )d d d

b c c

a b a

f x x f x x f x x+ =

Text reference Exercises Ex 4A.1 & A.2 Ex 4B Ex 4D Ex 4E.1 & E.2

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4. ( ) ( ) d

b

a

f x g x x−

Term 2 Week 7 & 8 • Integrate functions of the form 𝑓(𝑎𝑥 + 𝑏)

• Calculate Definite Integrals ad relate to the fundamental theorem of calculus.

• Calculate areas under curves

• Know that: When ( )f x is a continuous negative function

the exact area of the region between the curve ( )y f x=

and the x-axis over the interval a x b is given by:

( )db

a

f x x−

• Calculate areas between to curves

• Apply integration to displacement, velocity acceleration problems.

• Us the fact that when the rate of change of a quantity is graphed against the elapsed time, the area under the curve is the total change in the quantity

Ex 4F Ex 4G Ex 5A + Investigation 1 p. 132 Ex 5B Ex 5C.3 Ex 5D

Use of Specific Mathematical Notation • Pay attention to use of square brackets in the notation of definite Integrals

Use of Electronic Technology • Carry out integration using the integration function on the calculator

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Revision Guide: Year 12, Specialist Mathematics, Induction


New Knowledge and Understanding • Be able prove by induction conjectures that involve

(i) Sums (ii) Products (iii) Divisibility (iv) Matrices (v) Trigonometry

• Understanding the concept and significance of: (i) The proposition (Initial statement) (ii) The test or base case (iii) The inductive step (iv) The concluding statement of proof

• Understand the complete argument such that if we let there be associated with each positive integer n, a proposition ( )P n then:

If ( )1P is true, and for all k, ( )P k is true implies ( )1P k + is

true, then ( )P n is true for all positive integers.

Text reference Exercises 1A & 1B p. 11-18

Use of Specific Mathematical Notation • Use P(n) or 𝑃𝑛 to define the proposition.

• The summation symbol ∑ is not required in exams but should be understood in order to interpret the textbook.

• The product symbol ∏ is not required in exams but should be understood in order to interpret the textbook.

Use of Electronic Technology • NA – The SAT will be a non-calculator paper. However, calculators are allowed in the exam for general

arithmetic.

Key Prerequisite Knowledge • Arithmetic and Geometric Sequences

• Index Laws

• Matrix Multiplication

• Trigonometric Identities (See supplied Exam Formula Sheet)

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Revision Guide: Year 12, Specialist Mathematics, Complex Numbers


New Knowledge and Understanding • Be able to express complex numbers in cartesian form.

• Identify the real and imaginary parts of a complex number

• Calculate the modulus and argument.

• Describe sets of points in the complex plane such as lines circular regions.

• Represent complex numbers on an Argand diagram

• Carry out vector addition of complex numbers

• Use rays from the origin to represent complex numbers (covered in Ex3E of the old text.)

Text reference Exercises 4A & 4B p. 84-89

Term 1 Week 3 & 4

• Convert complex numbers from cartesian to polar form

• Know properties of complex numbers

( )11 2

2

ciscis

cis

= −

• Carry out multiplication of complex numbers and in particular

by 𝑟𝑐𝑖𝑠𝜃.

• Identify dilations by r

• Identify rotations by 𝜃

• Prove and use De Moivre’s Theorem

• Solve De Moivre Theorem problems involving positive and negative powers

Exercises 4C.1 - 4C.2 p. 90-94 4C.3 p.95-97 Exercise 4E p.100 - 103

Term 1 Week 5 & 6

• Make connection with induction topic

• Prove:

( )1 2 1 2cis cis .cis cisn n + + =

• Represent geometrically

• Apply the triangle Inequality for the sum of the lengths of complex numbers e.g. |𝑧1 +𝑧2| ≤ |𝑧1| + |𝑧2|

• Use geometrical interpretation of equations and inequalities.

• Identify regions Circles, lines, rays and other regions

USE Old Text Exercise 2E

Term 1 Week 7

• Solve z =cn with c complex.

• Solve Roots of unity problems z =1n

• Represent nth roots of unity on an Argand Plane

• Find the sum of roots by vector addition – construction of an n-gon.

Exercise 4F.1 -4F.2 p. 104-107

Use of Specific Mathematical Notation • Use 𝑧 rather than z* to represent a complex conjugate.

• Use 𝑐𝑖𝑠𝜃 to represent 𝑐𝑜𝑠𝜃 + 𝑖𝑠𝑖𝑛𝜃

• Label axes of Argand diagram as Real (Re) and Imaginary (Im) not x and y.

Use of Electronic Technology • Be able to convert complex numbers between cartesian and polar form

( )1 2 1 2cis .cis cis = +

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Revision Guide: Year 12, Specialist Mathematics, Polynomials


New Knowledge and Understanding • Expand Polynomials

• Find Roots Zeroes and factors with and without technology

• Equate coefficients when one factor is given, to further factorise a polynomial.

• Carry out the long division algorithm on polynomials

Text reference Exercises Ex 2B Briefly Ex 2C & 2D.1, 2D.2 p.24-32 2D.3 is optional

Term 1 Week 9

• Prove and apply the factor and remainder theorems

• Factorise real cubics and quartics using complex roots and their conjugates.

• Understand and apply the fundamental theorem of algebra

• Factorise

Exercises Ex 2E,2F and 2G p. 36-41

Use of Specific Mathematical Notation • Use 𝑧 rather than z* to represent a complex conjugate.

• Write statements in the form: 𝑃(𝑥)

𝑎𝑥+𝑏= 𝑄(𝑥) +

𝑅

𝑎𝑥+𝑏 (or equivalent)

where 𝑎𝑥 + 𝑏 is the divisor, 𝑄(𝑥)is the quotient and R is the remainder

Use of Electronic Technology • Be able to use calculator to located zeroes and roots from graphs.

• Use Long division program/algorithm to check algebraic solutions.

Key Prerequisite Knowledge • Expand and factorise quadratics

• Finding a quadratic equation from the sum, α + β and product, α β of its roots

• Quadratic theory – (Apply the quadratic formula to find roots)

• Equate coefficients to find unknowns.

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Revision Guide: Year 12, Specialist Mathematics, Functions and Graphs

Timing: Term 1 Week 10 &11

New Knowledge and Understanding • Consider composite functions and the requirements on

domain and range relationships.

• Determine a composite function 𝑓 ∘ 𝑔(𝑥) given 𝑓(𝑥) and 𝑔(𝑥) and define correctly the domain and range of such a function

• Determine if a function is one to one. I.e. know that:

𝑓(𝑎) = 𝑓(𝑏) only when 𝑎 = 𝑏

• Use the vertical and horizontal line test

• Know that a function has an inverse if it is one to one.

• Find the inverse of a one to one function and graph the inverse.

• Understand the connection between inverse functions and symmetry in the line y = x

Text reference Exercises Ex 3A p.56-58 Ex 3B p.58-64

Term 2 Week 1 & 2

• Be able to discuss and draw asymptotic behaviour of functions.

• Understand how the graph of a function is related to the graph of the reciprocal function.

• Discuss and graph reciprocal functions 1

𝑓(𝑥) where 𝑓(𝑥) is

linear quadratic or trigonometric.

• Understand the properties and be able to draw ration function where both the numerator and denominator have a degree of up to 2 and have real zeros.

• Understand the relationship between absolute functions and their graphs.

• Understand the relationship between the graphs of 𝑓(𝑥), 𝑓(|𝑥|)𝑎𝑛𝑑|𝑓(𝑥)|

• Understand the properties and be able to graph arcsine, arccosine and arctangent functions

Exercises Ex 3C & 3D p.65-68 Ex 3E p.68-71 + Investigation 4 p. 68 & 5 p.70 Ex 3F.1 & 3F.2 Investigation 1 p. 64-65

Use of Specific Mathematical Notation • 1-1 means a one to one function.

• Use 𝑓 ∘ 𝑔(𝑥) notation instead of 𝑓(𝑔(𝑥)).

• Use 𝑓−1(𝑥) to represent the inverse of a function.

• In this topic |𝑥| represents the absolute value of x and should be confused with the determinant in the vectors topic.

• Asymptotes should be represented with dotted lines and labelled eg y = 3 or x = -2

• Where more than one graph is required on the same axes labelling must be clear as to which function is which.

Use of Electronic Technology • Extensive use of graphing functions as described above on the graphics calculator is expected

including full mastery of the View window and G-Solve functions.

Key Prerequisite Knowledge • Asymptotes of reciprocal and rational functions

• Know that 𝑒𝑥 and 𝑙𝑛𝑥 are inverse functions. Apply this knowledge to find inverses of similar composite functions

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Revision Guide: Year 12, Specialist Mathematics, Vectors in 3 Dimensions


New Knowledge and Understanding • Use understanding of vectors in 2D (learned in Year 11) to

develop ideas in 3D. Key Ideas Include being able to: a) Carry out basic vector operations such as addition and

scalar multiplication in base unit vector and component form.

b) Apply vector algebra rules c) Find a vector between two points d) Identify parallel vectors e) Calculate the scalar product (dot product) of two vectors f) Identify perpendicular vectors g) Calculate the angle between two vectors

Text reference Exercises (Quick!) Ex 5B p.115 Ex 5C p.118 Ex 5D p.119 Ex 5E p.122 Ex 5F p.126 Ex 5G.1 & 5G.2 p.128-130.

Term 2 Week 3 & 4

• Calculate the vector product of two vectors to find a perpendicular vector

• Find the direction and length of a × b

• Use the cross product to calculate areas of triangles 1

2|𝒂 × 𝒃|

and parallelograms |𝒂 × 𝒃|

• Find vector equations for lines in 3 dimensions and understand their non-uniqueness

• Convert equations of lines in 3D between vector, parametric and cartesian forms

• Calculate the angle between two lines.

• Find the shortest distance from a point to a line

Exercises Ex 5I.1 & 5I.2 Ex 6A Ex 6B Ex 6C Ex 6E

Term 2 Week 5 & 6

• Identifying relationships between lines in 3D such as parallel coincident, intersecting, coplanar or skew.

• Calculate the shortest distance between two lines

• Develop equations of a plane in parametric and cartesian from (Vector form is not required)

• Find the equation of a plane from its normal vector and a point in the plane (Example 17)

• Find where lines intersect planes (Example 19)

• Find the shortest distance from a point to a plane (Example 20) and the shortest distance between two planes using the formula

• Find the point on a given plane (foot) closest to a point in space. (Example 21) Qu 17 -20 p. 174 are essential

• Find the distance between a line and a plane. (Not between two planes)

• Find the angles between to planes

Exercises Ex 6G.2 + p. 163 of old text Ex 6G.3 Ex 6H also use p.164 of old book + p.170 -175 of new Ex 6I p. 176 - 178

Term 2 Weeks 7 and 8

• Apply elementary techniques to solve 3 by 3 systems of equations.

• Interpret unique solutions, no solutions and infinitely many solutions in terms of their geometrical meaning

• Use vector proofs to establish geometric facts for example: parallelism, perpendiculars, diagonal bisection, midpoints

Ex 6J and 6K p.178-184 Ex 5H p. 132

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Use of Specific Mathematical Notation • Use a for a

• Position vector a = 𝑂𝐴⃑⃑⃑⃑ ⃑

• Base unit vector form: a = pi + qj + rk

• Component form: a = [ p, q, r ]. Vectors will not appear in columns in the exam

Use of Electronic Technology • Programs may be used to calculate vector cross product and scalar dot product but knowledge of

the algorithms is also essential

Key Prerequisite Knowledge • The triangle inequality

• Basic vector operations and vector equality problem solving

• Use of Pythagoras to calculate magnitude (Distance Formula)

• Determinants

• Area formula for a triangle 𝐴 =1

2𝑎𝑏𝑠𝑖𝑛𝜃

• Solving simultaneous equations

Revision Guide: Year 12, Specialist Mathematics Integration Techniques and

Applications


New Knowledge and Understanding • Carry out integration of trigonometric and composite

functions.

• Use identities to simplify integrals of squared trigonometric functions.

• Use partial fractions for integrating simple rational functions.

• Establish and use ∫1

𝑥𝑑𝑥 = ln|𝑥| + 𝑐, for 𝑥 ≠ 0.

Text reference Exercises Ex 7A Use Q 12 Emphasises trig relationship

Term 3 Week 3

• Use inverse trigonometric functions to enable integration of certain functions.

• Integrate expressions of the form ±1

√𝑎2−𝑥2 ,

𝑎

𝑎2+𝑥2

Exercises Ex 7B Note: do NOT do Q9 (a) or (f) they are not mathematically possible.

Term 3 Week 4

• Use substitution 𝑢 = 𝑔(𝑥) to integrate expressions of

the form 𝑓(𝑔(𝑥))𝑔′(𝑥)

Exercises Ex7C1 (Q 10 is beyond the course) Ex 7C2 Integration by substitution

Term 3 Week 5 & 6

• Carry out integration by parts

∫𝑓′(𝑥)𝑔(𝑥)𝑑𝑥 = 𝑓(𝑥)𝑔(𝑥) − ∫𝑓(𝑥)𝑔′(𝑥)𝑑𝑥.

• Calculate areas between curves.

• Calculate volumes of revolution about the x-axis and about the y-axis.

Exercises Ex 7D, 7E, 7F.1, 7F.2

Use of Electronic Technology • Discerning use of the graphics calculator to find definite integrals is expected.

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• ( )2 1sin 1 cos2

2x x= − ,

• ( )2 1cos 1 cos2

2x x= + , 2 21 tan secx x+ =

• Rational Expressions

For example:

Verify that ( )( )

1 1 3

2 1 2 1x x x x

−− =

+ − + −

and hence find 2

1d

2x

x x+ −

Revision Guide: Year 12, Specialist Mathematics, Rates of Change and Differential

Equations.

Timing Term 3 Week 1 (possibly one lesson of Week 2- Started at this time as it is relevant to the folio task). Followed up when working on folio task. Tested with Integration SAT 5 in 2019


• Recognise curves are traced out by a moving point ( ) ( )( )x t y t, in which the functions ( )x t

and ( )y t are polynomials of degree 1 to 3?

• Convert to cartesian form by eliminating the parameter.

• Consider examples of applications to: a. uniform motion:

𝑥(𝑡) = 𝑥0 + 𝑎𝑡, 𝑦(𝑡) = 𝑦0 + 𝑏𝑡. b. Non- uniform motion

For example: objects in free flight:

𝑥(𝑡) = 𝑥0 + 𝑎𝑡, 𝑦(𝑡) = 𝑦0 + 𝑏𝑡 −1

2𝑔𝑡2

• Use vector representations:

0 0 0 0x ta y tb x y t a b+ + = +, , , .

• The velocity vector, 𝑣 = [𝑥′(𝑡), 𝑦′(𝑡)], is always tangent to the curve traced out by a moving point.

• The speed of the moving point is the magnitude

of the velocity vector, that is, √𝑥′2(𝑡) + 𝑦′2(𝑡) =

√𝑣 • 𝑣 • Find the arc length along parametric curve using

𝑙 = ∫ √𝑣 • 𝑣𝑏

𝑎𝑑𝑡.

• Sketch graphs of parametric functions

Text reference Exercises Ex 9A, 9B, 9C Ex 9D only if used for folio task. 9E.1, 9E.2, 9F

Use of Electronic Technology • Draw Parametric graphs in the graphics calculator

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• The chain rule 𝑦′(𝑡) = 𝑓′(𝑥(𝑡)) × 𝑥′(𝑡) shows that 𝑑𝑦

𝑑𝑥=

𝑑𝑦

𝑑𝑡÷

𝑑𝑥

𝑑𝑡

Revision Guide: Year 12, Specialist Mathematics, Rates of Change and Differential

Equations.



• Carry out implicit differentiation

• Finding gradients of curves in implicit form.

• Derivation of the derivative of the natural log function

• Understand the relationship between the rates of change of two related functions of time? (Related Rates)

• Identify related rate problems and form differential equations by differentiating with respect to time.

Text reference Exercises Ex 8A, 8B

Term 3 Week 8

• Solve differential equations of the form 𝑑𝑦

𝑑𝑥= 𝑓(𝑥)

(Simple Integration)

• Solve differential equations of the form 𝑑𝑦

𝑑𝑥= 𝑓(𝑥)𝑔(𝑦)

(Separable)

• Examine Slope Fields of first-order differential equations

• Reconstruct a graph from a slope field

Exercises Ex 8C, 8D, 8E and 8F.

Term 3 Week 9

• Formulate differential equations in contexts where rates are involved.

• Form models using separable differential equations.

• Form models using the logistic differential equation.

Exercises Ex 8G and 8H (Exercises 8G and 8H are not in the course)

Use of Electronic Technology • Reconstruct a slope field using graphics software.

Key Prerequisite Knowledge • Knowledge of all integration techniques taught in the Mathematical Methods and Specialist

Mathematics topics is expected.

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Content guide: Stage 2 Biology - Semester 1 & 2

Science Understanding - Topic 1: DNA and proteins

DNA stores and transmits genetic information; it functions in the same way in all living things.

DNA is a helical double-stranded molecule.

In eukaryotes, DNA is bound to proteins in linear chromosomes, which are found in the nucleus.

DNA is unbound and circular in the cytosol of prokaryotes and in the mitochondria and chloroplasts of

eukaryotes.

● Compare chromosomes in prokaryotes and eukaryotes.

Replication of DNA allows for genetic information to be inherited.

Base-pairing rules and method of DNA replication are universal.

● Describe the structural properties of the DNA molecule, including:

o nucleotide composition and pairing

o the weak bonds between strands of DNA, allow for replication.

● Explain the importance of complementary base pairing (A–T and C–G).

● Describe and represent the process of semi-conservative replication of DNA.

A gene consists of a unique sequence of nucleotides that codes for a functional

protein or an RNA molecule.

● Distinguish between exons and introns as coding and non-coding segments of DNA found in genes in eukaryotes.

● Describe how both exons and introns are transcribed but only the information contained in exons is translated to form a polypeptide in eukaryotes.

Protein synthesis involves transcription of a gene into messenger RNA (mRNA), and translation of mRNA into an

amino acid sequence at the ribosomes. In eukaryotic cells, transcription occurs in the nucleus.

● Describe and illustrate the role of DNA, mRNA, transfer RNA (tRNA), ribosomal RNA (rRNA) in transcription and translation.

● Describe the relationship between DNA and RNA codons, anticodons, and amino acids.

● Differentiate between coding (gene) and template strands.

The folding of a polypeptide to form a protein with a unique three-dimensional shape is determined by its

sequence of amino acids.

● Describe the factors that determine the primary, secondary, tertiary, and quaternary structure of proteins.

Proteins are essential to cell structure and function.

Examples of proteins with specific shapes

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include enzymes, some hormones, receptor proteins, and antibodies.

● Explain why the three-dimensional shape of a protein is critical to its function.

Enzymes are specific for their substrate and increase reaction rates by lowering activation energy.

● Describe the induced-fit model of enzyme–substrate binding.

Enzymes have specific functions and are affected by factors including:

– temperature

– pH

– presence of inhibitors.

The rate of an enzyme-controlled reaction is affected by:

– concentrations of reactants

– concentration of the enzyme.

The phenotypic expression of genes depends on factors controlling transcription and translation. These include

the products of other genes and the environment.

Cellular differentiation associated with tissue growth and development is controlled by gene expression.

● Recognise that cytosine nucleotides in DNA can be methylated and this alters gene expression.

Epigenetic changes can lead to differences between identical siblings and clones.

Epigenetic changes may cause human diseases.

● Explain how epigenetic modifications in genes that control cell division, such as changes in DNA methylation, can lead to cancer.

Changes in the DNA sequence are called ‘mutations’.

Mutations in genes and chromosomes can result from errors in DNA replication or cell division, or from damage

by physical or chemical factors in the environment.

Mutation rate can be increased by:

– ionising radiation

– mutagenic chemicals

– viruses.

● Explain how inheritable mutations can lead to changes in the characteristics of the descendants. ● Compare the different potential consequences of mutations in germ cells and somatic cells.

DNA can be extracted from cells.

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Modern techniques can be used to analyse even small amounts of DNA.

Segments of DNA can be multiplied using the polymerase chain reaction (PCR).

● Describe PCR, including the roles of

– heating and cooling

– primers

– free nucleotides

– heat-resistant enzymes.

The base sequence of DNA can be

determined by electrophoresis.

● Describe electrophoresis.

The results may be displayed in an electropherogram.

● Interpret electropherograms that illustrate DNA sequences.

DNA sequencing enables mapping of species’ genomes.

The results of electrophoresis can be used to construct DNA profiles. They may be displayed in an

electropherogram or in a table of data.

DNA profiling identifies the unique genetic makeup of individuals.

● Interpret electropherograms and tables of data that illustrate DNA profiles. ● Explain how differences in DNA fragments, identified by DNA profiling, can be used; for example, in forensic

science. ● Discuss the ethical, economic, and cultural issues related to the collection of genetic information.

Biotechnology can involve the use of bacterial enzymes, plasmids, and viruses as vectors, and yeasts. Techniques

include gel electrophoresis, bacterial transformations, electroporation, microinjection, and PCR.

● Describe how particular genes can be selected using probes and removed using restriction enzymes. ● Describe how selected genes can be transferred between species. ● Describe how CRISPR can be used to edit and/or transfer genes. ● Discuss the design of new proteins and their uses.

Science Understanding - Topic 2: Cells

The cell theory unifies all living things.

The cell membrane separates the cell cytoplasm from its surroundings and controls the exchange of materials,

including nutrients and wastes, between the cell and its environment.

● Describe and represent the fluid mosaic model of the cell membrane.

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The major types of cell are

– prokaryotic

– eukaryotic.

Prokaryotic and eukaryotic cells have many features in common, which is a reflection of their common

evolutionary past.

● Compare prokaryotic and eukaryotic cells with respect to their:

– size

– internal organisation

– shape and location of chromosomes.

Prokaryotes only exist as single cells.

Eukaryotic cells have specialised organelles which facilitate biochemical processes.

● Represent the structure and describe the function of:

– nucleus

– nucleolus

– mitochondrion

– chloroplast

– vacuole/vesicle

– Golgi body

– endoplasmic reticulum (rough and smooth)

– ribosome

– lysosome

– cytoskeleton.

● Compare the structures of plant and animal cells.

Cells require inputs of suitable forms of energy, including light energy or chemical energy in complex molecules.

● Distinguish between autotrophs and heterotrophs.

The sun is the main source of energy for life.

● Recognise that photosynthesis is important in the conversion of light energy into chemical energy, as illustrated by the following equation:

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Energy transformations occur within all living cells.

● Explain how most autotrophs and heterotrophs transform chemical energy for use through aerobic respiration, as illustrated by the following equation:

● Explain that fermentation is an anaerobic alternative to aerobic respiration:

– in plants and yeast:

– in animals:

● Compare the amount of energy released through aerobic respiration and fermentation (anaerobic respiration).

● Recognise that energy is required to break chemical bonds and energy is released when new bonds are formed.

● Describe the formation of ATP from ADP and Pi.

● Explain how the conversion of ATP to ADP and Pi releases energy for some metabolic reactions.

In order to survive, cells require an input of matter, including gases, simple nutrients, and ions, and the removal

of wastes.

● Compare the inputs and outputs of autotrophic and heterotrophic cells.

Substances move in and out of cells by processes such as:

– diffusion

– facilitated diffusion

– osmosis

– active transport

– endocytosis

– exocytosis.

● Explain how the structure of a membrane facilitates different processes of movement through it.

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● Explain how the exchange of materials across membranes is affected by factors including:

– surface-area-to-volume ratio of the cell

– concentration gradients

– the physical and chemical nature of the materials being exchanged.

Cell metabolism is critical to the survival of cells.

Biochemical processes in the cell are influenced by the nature and arrangement of internal membranes and the

presence of specific enzymes.

● Explain how the structure of internal membranes of mitochondria and chloroplasts facilitates some biochemical processes.

● Explain that in a metabolic pathway:

– there are many regulated steps

– each step loses some energy as heat

– some steps produce intermediate compounds

– specific enzymes are required at each step.

● Biochemical processes in the cell are influenced by environmental factors.

Chemicals can interfere with cell metabolism.

● Discuss possible benefits and/or harmful effects of chemicals that human beings use.

Cells arise from pre-existing cells, and cell division leads to an increase in cell number.

Cell division in somatic cells is different from the cell division that produces gametes from germ-line cells.

Continuity of life requires the replication of genetic material and its transfer to the next generation through

processes including binary fission, mitosis, meiosis, and fertilisation.

● Explain why the amount of DNA in a cell doubles before division.

The products of binary fission and mitotic division have the same number and type of chromosomes as the

parent.

● Recognise, describe, and represent the process of binary fission in prokaryotic cells.

● Recognise, describe, and represent the process of mitosis in eukaryotic cells.

● Compare the products of binary fission and mitotic division.

Diploid cells contain pairs of homologous chromosomes. Haploid cells have one chromosome from each

homologous pair.

● Recognise, describe, and represent the process of meiosis in eukaryotic cells.

● Explain why the products of meiosis are haploid cells and contain a single set of chromosomes.

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● Explain the importance of crossing over and independent assortment in meiosis.

● Explain that fertilisation restores the diploid number.

● Compare the products of mitotic and meiotic cell division.

● Compare the sources and degree of genetic variation of the products of asexual and sexual reproduction.

Cell division may be regulated by internal and external factors.

The cell produces gene products that regulate the cell cycle.

● Describe the stages in the cell cycle (including checkpoints).

● Explain that hormones may regulate cell division.

Carcinogens upset the normal controls of cell division by causing mutations in key regulatory genes.

Human beings culture cells for a variety of purposes.

● Describe techniques of cell culture, and discuss the applications and limitations of contemporary examples.

Science Understanding - Topic 3: Homeostasis

Organisms survive most effectively within their tolerance limits. Factors for which organisms have tolerance limits

include:

– body temperature

– water availability

– blood glucose level

– carbon dioxide concentration in the blood and tissues.

There are impacts on an organism when conditions fall outside its tolerance limits.

Organisms detect and respond to changes in the internal and external environment.

Homeostasis depends on the set of detections and responses that maintain a relatively constant internal

environment in the human body. This ensures the optimum conditions for the body to function.

In human beings, homeostasis depends on the functioning of the nervous and endocrine systems.

Homeostasis involves a stimulus–response and negative feedback model.

• Describe the role of sensory receptors.

• Describe the role of effectors.

• Explain the stimulus–response model.

• Recognise that in negative feedback the response inhibits the initial stimulus.

The nervous system is composed of the central nervous system and the peripheral nervous system.

• Compare the structure and function of sensory neurons, interneurons, and motor neurons.

• Describe the structure of a nerve pathway from receptor to effector.

• Describe the role of synapses and neurotransmitters.

• Describe the role and pathway of reflex responses.

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The endocrine system releases hormones that are peptides, proteins, or steroids.

Hormones travel to target sites via the blood.

Hormones can alter the metabolism of target cells, tissues, or organs.

• Compare the action of insulin and glucagon in blood sugar regulation.

• Describe how diabetes can result from a hormonal imbalance.

• Describe the action of thyroid stimulating hormone and thyroxine in metabolism.

• Describe the role of antidiuretic hormone (ADH) in osmoregulation.

• Discuss links between osmoregulation, blood volume, and blood pressure.

Hormonal responses are stimulated by either the nervous system or other hormonal messages.

• Describe the role of adrenaline in the ‘fight or flight’ response.

Describe the role of thyroid-stimulating hormone in the production of thyroxine.

The nervous system and endocrine system function independently or together to achieve homeostasis.

• Compare the action of the nervous and endocrine systems.

• Explain how the nervous and endocrine systems work independently or together to: – control body temperature – enable osmoregulation – maintain blood sugar level – monitor pH in the brain to maintain a constant carbon dioxide level in the blood.

Science Understanding - Topic 4: Evolution

Evidence shows that life has existed on Earth for around 3.5 billion years, during which time it has diversified.

Existing cells are the products of evolution.

Membranes may have formed spontaneously and the first simple cells may have used RNA as genetic

information. Ribozymes may have played a role in this development.

• Describe the possible roles of RNA and ribozymes in the first simple cells.

There is evidence that prokaryotic cells existed before eukaryotic cells.

• Describe this evidence, including fossil evidence.

• Explain how the ancestry of most existing eukaryotic cells probably involved endosymbiotic events.

Comparative genomics provides evidence for evolution and helps establish the likely evolutionary relationship

between different species.

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• Describe techniques for obtaining evidence including: – sequencing of common proteins (e.g. cytochromes) – DNA–DNA hybridization – DNA sequencing.

Phylogenetic tree diagrams represent evolutionary relationships.

• Draw and analyse simple phylogenetic tree diagrams to represent evolutionary relationships.

Mutations accumulate over time and the rate of mutation is relatively constant over time. This enables it to be

used as a ‘clock’.

More closely related species have fewer differences in their DNA sequences and have separated more recently

from a common ancestor than distantly related species.

Different criteria are used to define a species depending on the mode of reproduction.

A species that reproduces sexually can be defined by the ability of its members to actually or potentially

interbreed to produce fertile offspring.

Other criteria used to define a species include:

– morphological similarity – biochemical similarity – sharing a common gene pool.

Reproductive isolating mechanisms act to maintain distinct species.

• Describe pre-zygotic (prevention of zygote formation) mechanisms including: – temporal isolation – behavioural isolation – mechanical isolation – gamete isolation.

• Describe post-zygotic (prevention of fertile hybrids) mechanisms including: – hybrid inviability – hybrid sterility.

Mutation is a permanent change in the sequence of DNA nucleotides and is the ultimate source of genetic

variation in a species.

In a species that reproduces sexually there are additional sources of genetic variation.

• Explain the sources of genetic variation in a species that reproduces sexually.

A gene pool comprises all the genetic information in an interbreeding population.

• Recognise that a large gene pool indicates considerable genetic diversity and is found in populations that are more likely to survive selection pressures.

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Natural selection is a process in which organisms that are better adapted to their environment are more likely to

survive and produce offspring.

• Explain how natural selection results in evolution by causing a change in the frequency of alleles in a population.

Evolutionary changes are affected by other factors besides selection, including:

– sexual reproduction – genetic drift.

Speciation may result from an accumulation of genetic changes influenced by different selection pressures or

genetic drift in geographically isolated populations.

• Describe the process of speciation due to physical separation (allopatric speciation).

• Compare allopatric and sympatric speciation.

Similar selection pressures in different environments may lead to convergent evolution.

• Recognise and give examples of convergent evolution.

When new niches become available to a species, for example as a result of succession or following an

environmental change, different selection pressures may lead to divergent evolution or adaptive radiation.

• Recognise and give examples of adaptive radiation.

• Describe the process of succession.

Species or populations that have a reduced genetic diversity have a higher risk of extinction.

• Give examples of species with low genetic diversity.

Human activities can create new and significant selection pressures on a gene pool, leading to species extinction.

• Give examples of human activities that lead to climate or environmental change.

• Describe how these activities have caused or may threaten the extinction of species.

Maintaining biodiversity is an ethical issue with long-term biological and/or environmental consequences.

• Recognise that humans have an obligation to prevent species extinction.

Science as a Human Endeavour

Learn the names and of the four key concepts of science as a human endeavor (SHE):

● Communication and Collaboration

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o Science is a global enterprise that relies on clear communication, international conventions, and review and verification of results.

o Collaboration between scientists, governments, and other agencies is often required in scientific research and enterprise.

● Development

o Development of complex scientific models and/or theories often requires a wide range of evidence from many sources and across disciplines.

o New technologies improve the efficiency of scientific procedures and data collection and analysis. This can reveal new evidence that may modify or replace models, theories, and processes.

● Influence

o Advances in scientific understanding in one field can influence and be influenced by other areas of science, technology, engineering, and mathematics.

o The acceptance and use of scientific knowledge can be influenced by social, economic, cultural, and ethical considerations.

● Application and Limitation

o Scientific knowledge, understanding, and inquiry can enable scientists to develop solutions, make discoveries, design action for sustainability, evaluate economic, social, cultural, and environmental impacts, offer valid explanations, and make reliable predictions.

o The use of scientific knowledge may have beneficial or unexpected consequences; this requires monitoring, assessment, and evaluation of risk, and provides opportunities for innovation.

o Science informs public debate and is in turn influenced by public debate; at times, there may be complex, unanticipated variables or insufficient data that may limit possible conclusions.

Develop and apply an understanding of the complex ways in which science interacts with society, and investigate

the dynamic nature of biological science, according to the four key concepts of SHE.

Science Inquiry Skills

Results of investigations are represented in a well-organised way to allow them to be interpreted.

● Represent results of investigations in appropriate ways, including: o use of appropriate SI units, symbols

o construction of appropriately labelled tables

o drawing of graphs: linear, non-linear, lines of best fit

o use of significant figures.

Scientific information can be presented using different types of symbols and representations.

● Select, use, and interpret appropriate representations, including: o mathematical relationships, such as ratios o diagrams o equations

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to explain concepts, solve problems, and make predictions.

● Analysis of the results of investigations allows them to be interpreted in a meaningful way. o Analyse data, including:

▪ identification and discussion of trends, patterns, and relationships ▪ interpolation/extrapolation where appropriate.

Critical evaluation of procedures and data can determine the meaningfulness of the results.

● Identify sources of uncertainty, including: o random and systematic errors o uncontrolled factors.

● Evaluate reliability, accuracy, and validity of results, by discussing factors including: o sample size o precision o resolution of equipment o random error o systematic error o factors that cannot be controlled.

Conclusions can be formulated that relate to the hypothesis or inquiry question.

● Select and use evidence and scientific understanding to make and justify conclusions. ● Recognise the limitations of conclusions. ● Recognise that the results of some investigations may not lead to definitive conclusions.

Effective scientific communication is clear and concise.

● Communicate to specific audiences and for specific purposes using: o appropriate language o terminology o conventions.

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Content guide: Stage 2 Chemistry

Blue font = covered in Semester 1. Black font = covered in Semester 2.

Science Understanding - Topic 1: Monitoring the Environment

Some gases in the atmosphere, called ‘greenhouse gases’, keep the Earth’s atmosphere warmer than it would

be without these gases. This is known as the ‘greenhouse effect’.

• Describe the action of the common greenhouse gases, carbon dioxide and methane, to maintain a steady

temperature in the Earth’s atmosphere.

Anthropogenic increases in greenhouse gases disrupt the thermal balance of the atmosphere.

• Explain the warming associated with global climate change and its consequences for the environment.

Ocean acidification is caused by the ocean absorbing higher levels of carbon dioxide from the atmosphere.

• Describe and write equations to show how carbon dioxide lowers the pH of the oceans.

• Calculate the pH of solutions given the concentration of H+ or OH–, and vice versa.

The skeletons and shells of many marine organisms are made of calcium carbonate and are vulnerable to

dissolution at low pH.

• Write equations for carbonates reacting in acidic conditions.

Nitrogen oxides are formed in high-temperature engines and furnaces.

• Write equations for the formation of nitrogen oxides NO and NO2.

Nitrogen oxides and ozone are pollutants in the troposphere that are associated with photochemical smog.

• Describe and write equations showing the role of nitrogen oxides in the formation of ozone in the

troposphere.

• Describe the harmful effects of nitrogen oxides and ozone in the troposphere.

• Describe and write equations showing how catalytic converters reduce the quantities of nitrogen oxides

generated by motor vehicles.

Concentrations can be described by using a number of standard conventions.

• Calculate concentration and interconvert units, including: mol L 1, g L 1, %w/v, ppm, and ppb.

• Apply SI prefix conventions to quantities.

Knowledge of the mole ratios of reactants can be used in quantitative calculations.

• Perform stoichiometric calculations when given the reaction equation and the necessary data.

A titration can be used to determine the concentration of a solution of a reactant in a chemical reaction.

• Describe and explain the procedure involved in carrying out a titration, particularly rinsing glassware and

determining the end-point.

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• Determine the concentration of a solution of a reactant in a chemical reaction by using the results of a

titration.

Chromatography techniques, including thin layer chromatography (TLC), gas chromatography (GC), high-

performance liquid chromatography (HPLC), and ion chromatography (IC), involve the use of a stationary phase

and a mobile phase to separate the components of a mixture.

The rate of movement of the components is caused by the differences between the strengths of the

interactions between atoms, molecules, or ions in the mobile and stationary phases.

• Predict the relative rates of movement of components along a stationary phase on the basis of their polarities

and charge, given the structural formulae or relative polarities of the two phases.

Data from chromatography techniques can be used to determine the composition and purity of substances.

• Calculate and apply RF values and retention times in the identification of components in a mixture.

Ion chromatography (also known as ion exchange chromatography) is used to remove either cations or anions

from a mixture by replacing them with ions of another type.

• Explain, using equilibrium principles, how ions attached to the surface of a resin can be exchanged with ions in

aqueous solution.

Flame tests and atomic absorption spectroscopy (AAS) are analytical techniques that can be used to identify

elements; these methods rely on electron transfer between atomic energy levels.

• Write the electron configuration using subshell notation of an atom or monatomic ion of any of the first 38

elements in the periodic table.

• Explain the effect of the absorption or emission of radiation on the electron configuration of electrons in

atoms or ions.

The wavelengths of radiation emitted and absorbed by an element are unique to that element and can be used

to identify its presence in a sample.

• Explain why some wavelengths of radiation emitted and absorbed by an element are unique to that element.

Atomic absorption spectroscopy is used for quantitative analysis.

• Explain the principles of atomic absorption spectroscopy in identifying elements in a sample.

• Describe the construction and use of calibration graphs in determining the concentration of an element in a

sample.

Science Understanding - Topic 2: Managing Chemical Processes

The rates of a reaction at different times can be compared by considering the slope of a graph of quantity or

concentration of reactant or product against time.

• Draw and interpret graphs representing changes in quantities or concentration of reactants or products

against time.

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Rates of reaction can be influenced by a number of factors, including the presence of inorganic and biological

catalysts (enzymes).

• Predict and explain, using collision theory, the effect on rates of reaction due to changes in:

concentration

temperature

pressure (for reactions involving gases)

surface area

the presence of a catalyst.

Energy profile diagrams can be used to represent the relative enthalpies of reactants and products, the

activation energy, and the enthalpy change for a chemical reaction.

Draw and interpret energy profile diagrams.

Chemical systems may be open or closed.

Over time, reversible chemical reactions carried out in a closed system at fixed temperature eventually reach a

state of chemical equilibrium.

The changes in concentrations of reactants and products, as a system reaches equilibrium, can be represented

graphically.

• Draw and interpret graphs representing changes in concentrations of reactants and products.

The position of equilibrium in a chemical system at a given temperature can be indicated by a constant, Kc,

related to the concentrations of reactants and products.

• Write Kc expressions that correspond to given reaction equations for homogeneous equilibrium systems.

• Undertake calculations involving Kc and initial and/or equilibrium quantities of reactants and products for

homogeneous equilibrium systems.

The final equilibrium concentrations, and hence position of equilibrium, for a given reaction depend on various

factors.

• Predict and explain, using Le Châtelier’s principle, the effect on the equilibrium position of a system of a

change in the:

concentration of a reactant or product

overall pressure of a gaseous mixture

temperature of an equilibrium mixture for which the H value for the forward or back reaction is specified.

• Predict the change that occurred in a system, or whether a reaction is exothermic or endothermic, given the

effect of the change on the equilibrium position of the system.

Designing chemical-synthesis processes involves constructing reaction pathways that may include more than

one chemical reaction.

The steps in industrial chemical processes can be conveniently displayed in flow charts.

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• Interpret flow charts and use them for such purposes as identifying raw materials, chemicals present at

different steps in the process, waste products, and by-products.

Industrial processes are designed to maximise profit and to minimise impact on the environment.

• Explain how certain reaction conditions represent a compromise that will give maximum yield in a short time.

• Explain the impact of increases in temperature and pressure on manufacturing conditions and costs, and on

the environment.

• Explain how use of a catalyst may benefit both the manufacturer and the environment.

Science Understanding - Topic 3: Organic and Biological Chemistry

Organic compounds can be represented by molecular and structural formulae.

• Determine the molecular formula of an organic compound given its extended, condensed, or skeletal

structural formula.

Organic compounds are named systematically to provide unambiguous identification.

Condensation reactions occur when two organic molecules combine to form a larger molecule, also releasing

another small molecule, such as water.

The physical properties of organic compounds are influenced by the molar masses of the molecules, and the

number and polarity of functional groups.

• Predict, explain, and compare the melting points, boiling points, and solubilities in water and in non-polar

solvents of organic compounds, given their structural formulae.

Alcohols are classified as primary, secondary, or tertiary.

• Identify, name systematically, and draw structural formulae of alcohols containing:

up to eight carbon atoms in the main chain, with side chains limited to a maximum of two carbon atoms

one or more hydroxyl groups.

Primary, secondary, and tertiary alcohols behave differently with oxidising agents.

• Describe how primary and secondary alcohols can be distinguished from tertiary alcohols by their reaction

with acidified dichromate solution.

• Predict the structural formula(e) of the product(s) of oxidation of a primary or secondary alcohol, given its

structural formula.

Aldehydes and ketones are produced by the oxidation of the corresponding primary and secondary alcohols

respectively.

• Identify, name systematically, and draw structural formulae of aldehydes and ketones containing:


one or more aldehyde or ketone groups.

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Aldehydes can be readily oxidised; ketones cannot.

• Draw the structural formula of the oxidation product of a given aldehyde in either acidic or alkaline

conditions.

• Describe how acidified dichromate solution and Tollens reagent (ammoniacal silver nitrate solution) can be

used to distinguish between aldehydes and ketones.

Carbohydrates are naturally occurring sugars and their polymers. They are defined as either polyhydroxy

aldehydes or polyhydroxy ketones, or substances that form these compounds on hydrolysis.

• Given its structural formula, determine whether a molecule is a carbohydrate.

Disaccharides and polysaccharides are produced by the condensation of monosaccharide units linked in chains

by covalent bonds.

• Write molecular formulae for glucose, and for disaccharides and polysaccharides, based on glucose

monomers.

• Draw the structural formulae of the monosaccharide(s), given the structural formula of a disaccharide.

• Identify the repeating unit and draw the structural formula of the monomer, given the structural formula of a

section of a polysaccharide.

In aqueous solution there is an equilibrium between a ring form and a chain form of glucose.

• Explain the ability of glucose to react as an aldehyde when in chain form but not when in ring form.

Carboxylic acids can be produced by the oxidation of aldehydes or primary alcohols.

• Identify, name systematically, and draw structural formulae of carboxylic acids containing:


one or two carboxyl groups.

Carboxylic acids are weak acids and, to a small extent, ionise in water.

• Write equations for the reactions of carboxylic acids with bases, including hydroxides, carbonates, and

hydrogen carbonates, to form carboxylate salts, and describe changes that accompany these reactions.

• Explain why sodium and potassium carboxylate salts are more soluble in water than their parent carboxylic

acids.

Amines are classified as primary, secondary, or tertiary.

• Identify, name systematically, and draw structural formulae of primary amines containing:


one or more amino groups.

Amines act as bases.

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• Draw the structural formula of the protonated form of an amine, given the structural formula of its molecular

form, and vice versa.

• Explain why the protonated form of an amine is more soluble in water than its parent molecular amine.

Carboxylic acids undergo condensation reactions with alcohols to form esters.

• Identify, name systematically, and draw structural formulae of methyl and ethyl esters of acids containing up

to eight carbon atoms in the main chain, with side chains limited to a maximum of two carbon atoms.

• Draw the structural formula of the ester that could be produced by the condensation reaction between a

carboxylic acid and an alcohol, given their structural formulae or vice versa.

• Draw the structural formula of a polyester, given the structural formula(e) of the monomer(s) or vice versa.

Condensation reactions are slow at 25°C.

• Explain the use of heating under reflux, and the use of a trace of concentrated sulfuric acid in the laboratory

preparation of esters.

Esters may be hydrolysed under acidic or alkaline conditions.

• Identify the products of acidic or alkaline hydrolysis of an ester or polyester, given the appropriate structural

formula.

Carboxylic acids undergo condensation reactions with amines to form amides.

• Draw the structural formula of the amide formed from a carboxylic acid and an amine, given their structural

formulae or vice versa.

• Draw the structural formula of a polyamide, given the structural formula(e) of the monomer(s) or vice versa.

Amides may be hydrolysed under acidic or alkaline conditions.

• Identify the products of acidic or alkaline hydrolysis of an amide or polyamide, given the appropriate

structural formula.

Edible oils and fats are esters of propane-1,2,3-triol (glycerol) and various carboxylic acids.

• Draw the structural formula of an edible oil or fat, given the structural formula(e) of the carboxylic acid(s)

from which it is derived.

Triglycerides can be hydrolysed to produce propane-1,2,3-triol and various carboxylic acids.

• Identify and draw the structural formulae of the alcohol and acid(s) from which a triglyceride is derived, given

its structural formula.

Triglycerides may be saturated or unsaturated.

• Describe and explain the use of a solution of bromine or iodine to determine the degree of unsaturation of a

compound. Draw the structural formula of the reaction product.

• Explain how the degree of unsaturation causes differences in the melting points of edible oils and fats.

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Liquid triglycerides can be converted into triglycerides of higher melting point.

• Explain the role of pressure, temperature, and a catalyst in the hydrogenation of liquid triglycerides to form

triglycerides of higher melting point.

Alkaline hydrolysis of triglycerides produces carboxylate ions, which have both hydrophilic and hydrophobic

regions.

• Explain how such particles form micelles in solutions.

• Explain how micelles can dissolve and move non-polar substances through an aqueous medium or vice versa.

Proteins are polymers of amino acids.

Amino acids contain a carboxyl group and an amino group.

• Write the general formula of amino acids and recognise their structural formulae.

Amino acids have both acidic and basic properties.

• Draw the structural formula of the product formed when an amino acid self-ionises, given its structural

formula.

Amino acids can undergo condensation to form protein chains.

The amide groups within proteins are also known as ‘peptide links’.

• Draw the structural formula of a section of a protein chain that could be formed from amino acids, given their

structural formulae or vice versa.

The unique spatial arrangement of a protein depends on secondary interactions between sections of the chain

and, in aqueous environments, between the chain and water.

• Identify where secondary interactions can occur, given the structural formula of a section of a protein chain.

The biological function of a protein is a consequence of its spatial arrangement.

• Explain why the biological function of a protein (e.g. an enzyme) may be affected by changes in pH and

temperature.

Science Understanding - Topic 4: Managing Resources

Photosynthesis and respiration are important processes in the cycling of carbon and oxygen on Earth.

In photosynthesis the light energy absorbed by chlorophyll is stored as chemical energy in carbohydrates such

as glucose.

• Describe and write the equation for photosynthesis.

The chemical energy present in carbohydrates can be accessed by respiration and combustion.

• Describe and write the equation for the aerobic respiration of glucose.

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Fossil fuels (coal, petroleum, and natural gas) have been formed over geological time scales by anaerobic

decomposition of dead organisms. They are considered to be non-renewable because reserves are depleted

more quickly than they are formed.

Carbon-based fuels provide energy and are feedstock for the chemical industry.

• Discuss the advantages and disadvantages of using carbon-based fuels as sources of heat energy, compared

with their use as feedstock.

Renewable energy is generated over time scales of years to decades, from sources that are replenished much

more quickly than fossil fuels.

• Identify bioethanol, biodiesel, sunlight, and wind as renewable energy sources.

• Compare the contributions of fossil fuels to global warming with those from renewable energy sources.

Biofuels are produced by present-day biological processes.

• Identify bioethanol and biodiesel as biofuels.

• Describe the production, from biological materials, of ethanol and biodiesel, including the writing of chemical

equations for the reactions involved.

• Explain how fossil fuels contribute more than biofuels to global warming.

The complete combustion of fuels containing carbon and hydrogen produces carbon dioxide and water and

energy.

• Write thermochemical equations for the complete combustion of fuels in which the only products are carbon

dioxide and water.

Incomplete combustion, producing carbon (soot) and carbon monoxide, is more likely with longer-chain carbon-

based fuels.

• Explain why incomplete combustion is more likely with longer-chain carbon-based fuels than with shorter

chains.

• Discuss the undesirable consequences of incomplete combustion.

The energy released in combustion of fuels can be determined experimentally.

• Use experimental data to determine the enthalpy of combustion of a fuel.

• Undertake thermochemical calculations involving enthalpy changes and temperature changes of a specified

mass of water given the necessary data.

Fuels, including fossil fuels and biofuels, can be compared in terms of their energy output and the nature of

products of combustion.

• Calculate the quantities of heat evolved per mole, per gram, and per litre (for liquids) for the complete

combustion of fuels.

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• Compare fuels given appropriate data.

Although most electricity is generated using fuels to drive steam turbines, electrical energy can be also be

generated using photovoltaic cells (known as solar cells) and directly from oxidation of fuels using galvanic cells.

• Explain the advantages and disadvantages of direct electricity generation (photovoltaic and fuel cells)

compared to using steam turbines.

Fuel cells, including flow cells, are galvanic cells in which the electrode reactants are available in continuous

supply.

• State the advantages and disadvantages of fuel cells compared with other galvanic cells.

• Identify the anode and cathode and their charges, as well as the direction of ion and electron flow, in a fuel

cell, given sufficient information.

• Write electrode half-equations for a fuel cell given sufficient information.

• Discuss the advantages of flow cells compared with other fuel cells.

Water from different sources is treated with different methods depending on its origin and intended use.

Suspended matter is commonly removed from water by flocculation, followed by sedimentation and filtration.

The surface of fine silicate and aluminosilicate particles in clays is negatively charged and can be flocculated into

larger particles by the addition of salts containing highly charged cations such as aluminium ions or polymers.

• Explain the use of aluminium ions and polymers in flocculating clay particles suspended in water.

Hard water contains high concentrations of Ca2+ and Mg2+ ions. Hard water renders soaps less effective and

causes build-up of precipitates.

Natural and modified zeolites can be used in the purification and softening of water, through the exchange of

cations.

• Explain the use of zeolites in water softeners.

Reverse osmosis is a filtration technique whereby water is forced, under pressure, through a semi-permeable

membrane.

• Explain how reverse osmosis produces potable water from saline water.

Desalination is a process used to remove minerals from saline water to produce fresh potable water. Reverse

osmosis and thermal distillation are two widely used methods for desalination.

• Describe the disadvantages of using desalination for the production of potable water.

Hypochlorous acid, chlorine, and hypochlorites are oxidisers used for water disinfection.

• Explain the effect of pH on the equilibrium between chlorine and water, and hydrochloric acid and

hypochlorous acid.

Plants require nutrients, which they obtain from the soil.

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• Explain why plants need soil nutrients in soluble form.

Soil productivity is related to the availability of plant nutrients, which need to be replenished naturally or by the

addition of fertilisers.

Nitrogen, phosphorus, and potassium are the major nutrients that plants require from the soil.

• Explain how natural processes (including lightning, nitrogen-fixing bacteria, and decay) replenish soil nitrogen.

• Explain why fertilisers are required to improve the productivity of some soils.

Excess nitrogen and phosphorus can be leached from soils and can cause eutrophication in water bodies.

• Explain the process and consequences of eutrophication.

Silicon dioxide, silicates, and aluminosilicates are important components of rocks and soils.

• Write the formula of the anion given the formula of a silicate or aluminosilicate.

Cations adsorbed on the surface of soil silicates and aluminosilicates are in equilibrium, and can be exchanged

with, the cations in soil water, which are available as sources of plant nutrients.

Soil silicates and aluminosilicates are able to adsorb H+ and release cations.

• Explain how cations on the surface of soil silicates and aluminosilicates become available to plants.

Nutrient cations on the surface of soil silicates and aluminosilicates are replaced if the concentrations of H+ or

Na+ in soil water become too high.

• Explain how acidic or saline conditions (i.e. high concentrations of H+ or Na+) deplete the nutrient value of

soils.

Polymers are produced from monomers by addition or condensation reactions.

• Identify whether a molecule could undergo polymerisation, given its structural formula and, if so, the type of

polymerisation.

• Identify a polymer as being the product of an addition polymerisation or a condensation polymerisation, given

its structural formula.

• Identify the repeating unit of a polymer, given its structural formula.

The production of synthetic polymers allows the manufacture of materials with a diverse range of properties.

• Discuss the advantages and disadvantages of synthetic polymers.

• Compare the effects of heating on thermoplastic and thermoset polymers.

Organic polymers can have different properties, such as rigidity, depending on the monomers and the degree of

cross-linking between chains.

• Compare the physical properties of polymers with different degrees of cross-linking and secondary

interactions between polymer chains.

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Polymers can be made from fossil resources or from renewable materials.

• Discuss the advantages and disadvantages of making polymers from fossil resources or from renewable

materials.

Some polymers are biodegradable — being able to be broken down by microorganisms and other living things.

• Explain why some polymers are biodegradable but others are not.

• Explain the advantages of polymers being biodegradable.

The occurrence of metals in combined or uncombined form in the Earth’s crust is related to the reactivity of the

metal.

The production of some metals requires the conversion of minerals to a form suitable for reduction.

• Explain, with the aid of equations, the methods designed for the conversion of a mineral to a metal, given

sufficient information.

The method used in the reduction stage in the production of a metal is related to the reactivity of the metal and

the availability of energy.

Given the position of a metal in the activity series of metals:

• Predict whether the metal is likely to occur in nature in a combined or uncombined form.

• Predict and explain the likely method of reduction of the metal compound, including electrolysis of the molten

compound, electrolysis of an aqueous solution of the metal compound, and use of carbon as a reducing agent.

• Explain the benefits of one method of reduction compared with another, given relevant information.

Electrolytic cells are used to produce required substances.

• Identify the anode and cathode and their charges, as well as the direction of ion and electron flow in an

electrolytic cell, given sufficient information.

• Write electrode half-equations for an electrolytic cell, given sufficient information.

There is a finite amount of materials on Earth. Materials that can be recycled reduce the amount of new

materials that need to be produced from the Earth’s crust.

• Explain the advantages of recycling materials.

Some objects are difficult to recycle.

• Explain the difference in the ease of recycling thermoplastic and thermoset polymers.

Composite materials comprise two or more constituent materials to produce a material with properties

different from the individual components.

• Explain the advantages of using composite materials.

• Explain the difficulties associated with recycling materials and objects comprising two or more different

materials with different properties.

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Learn the names and of the four key concepts of science as a human endeavour (SHE):


o Science is a global enterprise that relies on clear communication, international conventions, and

review and verification of results.

o Collaboration between scientists, governments, and other agencies is often required in scientific

research and enterprise.

● Development

o Development of complex scientific models and/or theories often requires a wide range of evidence

from many sources and across disciplines.

o New technologies improve the efficiency of scientific procedures and data collection and analysis.

This can reveal new evidence that may modify or replace models, theories, and processes.

● Influence

o Advances in scientific understanding in one field can influence and be influenced by other areas of

science, technology, engineering, and mathematics.

o The acceptance and use of scientific knowledge can be influenced by social, economic, cultural, and

ethical considerations.


o Scientific knowledge, understanding, and inquiry can enable scientists to develop solutions, make

discoveries, design action for sustainability, evaluate economic, social, cultural, and environmental

impacts, offer valid explanations, and make reliable predictions.

o The use of scientific knowledge may have beneficial or unexpected consequences; this requires

monitoring, assessment, and evaluation of risk, and provides opportunities for innovation.

o Science informs public debate and is in turn influenced by public debate; at times, there may be

complex, unanticipated variables or insufficient data that may limit possible conclusions.

Develop and apply an understanding of the complex ways in which science interacts with society, and

investigate the dynamic nature of chemistry according to the four key concepts of SHE.


Scientific methods enable systematic investigation to obtain measurable evidence.

● Deconstruct a problem to determine the most appropriate method for investigation.

● Design investigations, including:

o a hypothesis or inquiry question

o types of variables

– dependent

52 | P a g e

– independent

– factors held constant (how and why they are controlled)

– factors that may not be able to be controlled (and why not)

o materials required

o the method/procedure to be followed

o the type and amount of data to be collected

o identification of ethical and safety considerations.


● Represent results of investigations in appropriate ways, including:

o use of appropriate SI units, symbols





● Select, use, and interpret appropriate representations, including:

o mathematical relationships, such as ratios

o diagrams

o equations


● Analysis of the results of investigations allows them to be interpreted in a meaningful way.

o Analyse data, including:

▪ identification and discussion of trends, patterns, and relationships

▪ interpolation/extrapolation where appropriate.


● Identify sources of uncertainty, including:

o random and systematic errors

o uncontrolled factors.

● Evaluate reliability, accuracy, and validity of results, by discussing factors including:

53 | P a g e

o sample size

o precision

o resolution of equipment

o random error

o systematic error

o factors that cannot be controlled.


● Select and use evidence and scientific understanding to make and justify conclusions.

● Recognise the limitations of conclusions.

● Recognise that the results of some investigations may not lead to definitive conclusions.


● Communicate to specific audiences and for specific purposes using:

o appropriate language

o terminology

o conventions.

54 | P a g e

Content guide: Stage 2 Physics - Semester 1

Science Understanding

Topic 1: Projectile Motion

Uniformly accelerated motion is described in terms of relationships between measurable scalar and vector quantities,

including displacement, speed, velocity, and acceleration.

Motion under constant acceleration can be described quantitatively using the following formulae:

• 0v v at= +

• 2

01

2s v t at= +

• 2 2

0 2v v as= + .

Projectile motion can be analysed quantitatively by treating the horizontal and vertical components of the motion

independently.

• Construct, identify, and label displacement, velocity, and acceleration vectors.

• Use vector addition and subtraction to calculate net vector quantities.

• Resolve velocity into vertical and horizontal components, using cosHv v = and sinVv v = for the horizontal

and vertical components respectively.

• Determine the velocity at any point, using trigonometric calculations.

An object experiences a constant gravitational force near the surface of the Earth, which causes it to undergo uniform

acceleration.

• Explain that, in the absence of air resistance, the horizontal component of the velocity is constant.

The motion formulae are used to calculate measurable quantities for objects undergoing projectile motion.

• Calculate the time of flight when a projectile is launched horizontally.

• Calculate the time of flight and the maximum height for a projectile when the launch height is the same as the

landing height.

• Calculate the horizontal range of a projectile when it is launched horizontally or when the launch height is the

same as the landing height (or the flight time is given).

• Explain qualitatively that the maximum range occurs at a launch angle of 45° for projectiles that land at the same

height from which they were launched.

• Describe the relationship between launch angles that result in the same range.

• Describe and explain the effect of launch height, speed, and angle on the time of flight and the maximum range of

a projectile.

Analyse multi-image representations of projectile paths.

When a body moves through a medium such as air, the body experiences a drag force that opposes the motion of the

body.

• Explain the effects of speed, cross-sectional area of the body, and density of the medium on the drag force on a

moving body.

• Explain that terminal velocity occurs when the magnitude of the drag force results in zero net force on the moving

body.

• Describe situations such as skydiving and the maximum speed of racing cars where terminal velocity is achieved.

• Describe and explain the effects of air resistance on the vertical and horizontal components of the velocity,

maximum height, and range of a projectile.

55 | P a g e

• Describe and explain the effects of air resistance on the time for a projectile to reach the maximum height or to

fall from the maximum height.

Subtopic 1.2: Forces and Momentum

Momentum is a property of moving objects and is defined as the product of the mass and the velocity of the object. It is

conserved in an isolated system and may be transferred from one object to other objects when a force acts over a time

interval.

Kinetic energy is a property of moving objects, and is given by the formula 212

=KE mv

Newton’s Second Law of Motion can be expressed as two formulae, F ma= andp

Ft

= , where p mv= is the

momentum of the object.

• Derive p

Ft

= by substituting the defining formula for acceleration

va

t

=

into Newton’s Second Law of

Motion, F ma= , for particles of fixed mass. (The net force, F , and hence the acceleration, a, are assumed to be

constant. Otherwise, average or instantaneous quantities apply.)

• Draw vector diagrams in which the initial momentum is subtracted from the final momentum, giving the change in

momentum, p .

• Solve problems (in both one dimension and two dimensions) using the formulae F ma= , p

Ft

= , 21

2=KE mv

and p mv= .

Newton’s Third Law of Motion, 1 2F F= − , in conjunction with the Second Law expressed in terms of momentum, implies

that the total momentum of a system of two interacting particles, subject only to the force of each one on the other, is

conserved.

• Derive a formula expressing the conservation of momentum for two interacting particles by substituting

1 21 2 1 2 .

p pF F F F

t t

= = = −and into

• Use the law of conservation of momentum to solve problems in one and two dimensions.

• Analyse multi-image representations to solve conservation of momentum problems, using only situations in which

the mass of one object is an integral multiple of the mass of the other object(s). The scale of the representations

and the flash rate can be ignored.

The conservation of momentum can be used to explain the propulsion of spacecraft, ion thrusters, and solar sails.

• Use the conservation of momentum to describe and explain the change in momentum and acceleration of

spacecraft due to the emission of gas particles or ionised particles.

• Use the conservation of momentum to describe and explain how the reflection of particles of light (photons) can

be used to accelerate a solar sail.

• Use vector diagrams to compare the acceleration of a spacecraft, using a solar sail where photons are reflected

with the acceleration of a spacecraft, and using a solar sail where photons are absorbed.

56 | P a g e

Subtopic 1.3: Circular Motion and Gravitation

An object moving in a circular path at a constant speed undergoes uniform circular motion. This object undergoes

centripetal acceleration, which is directed towards the centre of the circle.

The magnitude of the centripetal acceleration is constant for a given speed and radius and is given by 2v

ar

= .

The formula 2 r

vT

= relates the speed, v, to the period, T, for an object undergoing circular motion with radius, r.

• Solve problems involving the use of the formulae 2v

ar

= , 2 r

vT

= , and F ma= .

• Use vector subtraction to show that the change in the velocity, v , and hence the acceleration, of an object over

a very small time interval is directed towards the centre of the circular path.

On a flat curve, the friction force between the tyres and the road causes the centripetal acceleration. To improve safety,

some roads are banked at an angle above the horizontal.

• Draw a diagram showing the force vectors (and their components) for a vehicle travelling around a flat curve and

around a banked curve.

• Explain how a banked curve reduces the reliance on friction to provide centripetal acceleration.

Objects with mass produce a gravitational field in the space that surrounds them.

An object with mass experiences a gravitational force when it is within the gravitational field of another mass.

Gravitational field strength, g, is defined as the net force per unit mass at a particular point in the field.

This definition is expressed quantitatively as F

gm

= , hence it is equal to the acceleration due to gravity. The magnitude of

the acceleration due to gravity at the surface of the Earth is 9.80 m s–2.

• Explain that the acceleration of a projectile is always downwards and independent of its mass.

All objects with mass attract one another with a gravitational force; the magnitude of this force can be calculated using

Newton’s Law of Universal Gravitation.

Every particle in the universe attracts every other particle with a force that is directly proportional to the product of the

two masses and inversely proportional to the square of the distance between them.

The force between two masses, 1 2m mand , separated by distance, r, is given by:

1 22

m mF G

r=

• Solve problems using Newton’s Universal Law of Gravitation.

• Use proportionality to discuss changes in the magnitude of the gravitational force on each of the masses as a

result of a change in one or both of the masses and/or a change in the distance between them.

• Explain that the gravitational forces are consistent with Newton’s Third Law.

Use Newton’s Law of Universal Gravitation and Second Law of Motion to calculate the value of the acceleration

due to gravity, g, on a planet or moon.

Many satellites orbit the Earth in circular orbits.

• Explain why the centres of the circular orbits of Earth satellites must coincide with the centre of the Earth.

• Explain that the speed, and hence the period, of a satellite moving in a circular orbit depends only on the radius of

the orbit and the mass of the central body (m2) about which the satellite is orbiting and not on the mass of the

satellite.

57 | P a g e

• Derive the formula GM

vr

= for the speed, v, of a satellite moving in a circular orbit of radius, r, about a

spherically symmetric mass, M, given that its gravitational effects are the same as if all its mass were located at its

centre.

Kepler’s Laws of Planetary Motion describe the motion of planets, their moons, and other satellites.

Kepler’s First Law of Planetary Motion: All planets move in elliptical orbits with the Sun at one focus.

Kepler’s Second Law of Planetary Motion: The radius vector drawn from the Sun to a planet sweeps equal areas in equal

time intervals.

• Describe Kepler’s first two Laws of Planetary Motion.

• Use these first two Laws to describe and explain the motion of comets, planets, moons, and other satellites.

Kepler’s Third Law of Planetary Motion shows that the period of any satellite depends upon the radius of its orbit.

For circular orbits, Kepler’s Third Law can be expressed as: 2

2 34T r

GM

= .

• Derive: 2

2 34T r

GM

= .

• Solve problems involving the use of the formulae 2GM r

v vr T

= =, , and

22 34

T rGM

= .

• Explain why a satellite in a geostationary orbit must have an orbit in the Earth’s equatorial plane, with a relatively

large radius and in the same direction as the Earth’s rotation.

• Explain the differences between polar, geostationary, and equatorial orbits. Justify the use of each orbit for

different applications.

Perform calculations involving orbital periods, radii, altitudes above the surface, and speeds of satellites, including

examples that involve the orbits of geostationary satellites.

Subtopic 1. 4: Relativity

Motion can only be measured relative to an observer; length and time are relative quantities that depend on the observer’s

frame of reference.

Observations of objects travelling at very high speeds cannot be explained by Newtonian physics. Einstein’s Theory of

Special Relativity predicts significantly different results to those of Newtonian physics for velocities approaching the speed

of light.

The Theory of Special Relativity is based on two postulates:

• that the speed of light in a vacuum is an absolute constant

• that the laws of physics are the same in all inertial reference frames.

In relativistic mechanics, there is no absolute length or time interval.

Two events that appear simultaneous for a stationary observer may not be for an observer in motion.

At relativistic speeds, time intervals in moving frames of reference are dilated when observed from a stationary reference

frame according to 0t t= where 2

2

1

1v

c

=

−

, is the Lorentz factor, 0t , is the time interval in the moving frame of

reference and t is the time interval in the stationary observer’s frame of reference.

• Solve problems using 0t t= and the Lorentz factor formula.

• Explain the effects of time dilation on objects moving at relativistic speeds.

58 | P a g e

Some subatomic particles exist in the laboratory for very short time periods before decaying. These same particles are

detected as part of cosmic ray showers in the atmosphere, travelling at relativistic speeds close to the speed of light.

Time dilation effects allow these particles to travel significant distances without decay.

• Given the laboratory lifetime of a subatomic particle and its relativistic speed:

• calculate time dilation factors.

• using calculations, compare the distance travelled by subatomic particles when incorporating relativistic effect.

An object moving at relativistic speeds always appears shorter to an observer in a stationary frame of reference, and the

length is given by: 0ll

= , where 0l is the length in the moving object’s frame of reference and l is the length in the

stationary observer’s frame of reference.

• Solve problems using 0ll

= .

• Explain the effects of length contraction on objects moving at relativistic speeds.

The magnitude of the relativistic momentum of a moving object is given by op m v= , where om is the mass of the object in

the frame of reference where the object is stationary and v is the speed of the object.

• Solve problems using op m v= .

• Explain why masses moving at relativistic speeds are unable to reach the speed of light.

Topic 2: Electricity and Magnetism

Electrostatically charged objects exert forces upon one another; the magnitude of these forces can be calculated using

Coulomb’s Law.

• Solve problems involving the use of: 1 22

0

1

4

q qF

r= .

• Using proportionality, discuss changes in the magnitude of the force on each of the charges as a result of a change

in one or both of the charges and/or a change in the distance between them.

• Explain that the electric forces are consistent with Newton’s Third Law.

When more than two point charges are present, the force on any one of them is equal to the vector sum of the forces due

to each of the other point charges.

• Use vector addition in one dimension or two dimensions with right-angled, isosceles, or equilateral triangles to

calculate the magnitude and direction of the force on a point charge due to two other point charges.

Point charges and charged objects produce electric fields in the space that surrounds them. A charged object in an electric

field experiences an electric force.

The direction and number of electric field lines per unit area represent the direction and magnitude of the electric field.

• Sketch the electric field lines:

o for an isolated positive or negative point charge and for two point charges

o between and near the edges of two finite oppositely charged parallel plates.

A positively charged body placed in an electric field will experience a force in the direction of the field; the strength of the

electric field is defined as the force per unit charge.

• Solve problems involving the use of: E F q= .

• Using Coulomb’s Law, derive the formula: 2

0

1

4

qE

r= .

59 | P a g e

Solve problems using: 2

0

1

4

qE

r= ,

for one or two point charges in one or two dimensions.

There is no electric field inside a hollow conductor of any shape, provided that there is no charge in the cavity.

• Sketch the electric field produced by a hollow spherical charged conductor.

Electric fields are strongest near sharp points on conductors. These fields may be large enough to ionise the polar and non-

polar molecules in the air near the sharp points, resulting in charge movement away from the conductor. This is called a

‘corona discharge’.

• Sketch the electric field produced by a charged pear-shaped conductor.

• Describe how the electric field near sharp points may ionise the air.

Subtopic 2.2: Motion of charged particles in electric fields

Electric fields store electric potential energy.

When a charged body moves or is moved from one point to another in an electric field and its potential energy changes,

work is done on or by the field.

The electric potential difference, V , between two points is the work done per unit charge on a small positive test charge

moved between the points, provided that all other charges remain undisturbed.

The electronvolt ( )eV is a unit of measurement which describes the energy carried by a particle. It is the work done when

an electron moves through a potential difference of 1 volt.

• Solve problems involving the use of W q V= .

• Convert energy from joules into electronvolts and vice versa.

The magnitude of the electric field (away from the edges) between two oppositely charged parallel plates a distance d

apart, where V is the potential difference between the plates, is given by the formula: V

Ed

= .

• Solve problems involving the use of V

Ed

= .

The force on a charged particle moving in a uniform electric field is constant in magnitude and direction, thus producing a

constant acceleration.

• Derive the formula qE

am

= for the acceleration of a charged particle in an electric field.

• Solve problems using qE

am

= and the motion formulae for the movement of charged particles parallel or

antiparallel to a uniform electric field.

• Describe the motion of charged particles parallel or antiparallel to a uniform electric field.

In a cyclotron, the electric field in the gap between the dees increases the speed of the charged particles.

• Describe how an electric field between the dees can transfer energy to an ion passing between them.

• Describe how ions could be accelerated to high energies if they could be made to repeatedly move across an

electric field.

• Calculate the energy transferred to an ion each time it passes between the dees.

• Explain why the ions do not gain kinetic energy when inside the dees.

When a charged particle moves at an angle to the uniform electric field the component of the velocity perpendicular to the

field remains constant.

60 | P a g e

• Compare the motion of a projectile in the absence of air resistance with the motion of a charged particle in a

uniform electric field.

• Solve problems for the motion of charged particles that enter a uniform electric field perpendicular to the field.

• Solve problems for the motion of charged particles that enter a uniform electric field at an angle to the field where

the displacement of the charged particle parallel to the field is zero.

Sub Topic 2.3: Magnetic Fields

Magnetic fields are associated with moving charges, such as charges in an electric current.

Current-carrying conductors produce magnetic fields; these fields are utilised in solenoids.

Magnetic field lines can be used to represent the magnetic field. The direction of the magnetic field depends on the

direction of the moving charge that is producing the magnetic field.

The magnitude of magnetic field strength, B, at any point is represented by the number of lines crossing a unit area

perpendicular to the field in the vicinity of the point.

• Sketch and/or interpret the magnetic field lines produced by an electric current flowing in a straight conductor, a loop, and a solenoid.

The magnitude of the magnetic field strength in the vicinity of a current-carrying conductor is given by 0

2

IB

r

= , where r is

the radial distance to the conductor and 7 10 2.00 102

TmA

− −= .

Solve problems involving the use of 0

2

IB

r

= .

Sub Topic 2.4 Motion of Charged Particles in Magnetic Fields

Magnets, magnetic materials, moving charges, and current-carrying conductors experience a force in a magnetic field.

The force on a current element that is parallel or antiparallel to a magnetic field is zero.

The magnetic force on a moving charged particle depends on both the magnitude and the direction of the velocity of the

moving charge.

The direction of the force on a current-carrying conductor or an individual charged particle moving at any angle to a

uniform magnetic field depends on the direction of the magnetic field and the direction of charge movement.

• Determine the direction of one of:

• force

• magnetic field

• charge movement

given the direction of the other two.

• Solve problems involving the use of sinF IlB = for a current-carrying conductor and sinF qvB = for a moving

charged particle.

A charged particle moving at right angles to a uniform magnetic field experiences a force of constant magnitude at right

angles to the velocity. The force changes the direction but not the speed of the charged particle and hence the particle

moves with uniform circular motion.

• Explain how the velocity dependence of the magnetic force on a charged particle causes the particle to move with uniform circular motion when it enters a uniform magnetic field at right angles.

• Derive mv

rqB

= for the radius r of the circular path of an ion of charge q and mass m that is moving with speed v at

right angles to a uniform magnetic field of magnitude B.

61 | P a g e

• Solve problems involving the use of mv

rqB

= .

Cyclotrons are used to accelerate ions to high speed. Radioisotopes used in medicine and industry may be produced from

collisions between high-speed ions and nuclei.

The magnetic field within the dees of a cyclotron causes the charged particles to travel in a circular path, so that they

repeatedly pass through the electric field.

• Describe the nature and direction of the magnetic field needed to deflect ions into a circular path in the dees of a

cyclotron.

• Derive the formula 2 m

TqB

= for the period T of the circular motion of an ion, and hence show that the period is

independent of the speed of the ion.

• Derive the formula 2 2 2

2K

q B rE

m= for the kinetic energy KE of the ions emerging at radius r from a cyclotron.

• Use the formula 2 2 2

2K

q B rE

m= to show that KE is independent of the potential difference across the dees and,

for given ions, depends only on the magnetic field and the radius of the cyclotron.

• Solve problems involving the use of 2 m

TqB

= and

2 2 2

2K

q B rE

m=

Sub Topic 2.5 Electromagnetic Induction

Magnetic flux (Φ) is defined as the product of magnetic field strength (B) and the area perpendicular to the magnetic field (

A⊥). Hence: .BA⊥ =

• Solve problems involving the use of .BA⊥ =

Electromagnetic induction is the process in which a changing magnetic flux induces a potential difference in a conductor.

The induced potential difference is referred to as an electromotive force ( )emf .

The changing magnetic flux is due to relative movement of the conductor or variation of the magnetic field strength.

Faraday’s Law states that the induced emf is equal to the rate of change of the magnetic flux. Lenz’s Law states that the

direction of a current created by an induced emf is such that it opposes the change in magnetic flux producing the emf.

Hence: emft

= .

For N conducting loops the induced emf is given by Ν

emft

= .

• Solve problems involving the induction of an emf in a straight conductor.

• Solve problems involving the induction of an emf in N conducting loops.

• Use the law of conservation of energy to explain Lenz's Law.

• Use Lenz’s Law to determine the direction of the current produced by the induced emf.

• Use Lenz's Law to explain the production of eddy currents.

Topic 3 Light and Atoms

Oscillating charges produce electromagnetic waves of the same frequency as the oscillation; electromagnetic waves cause

charges to oscillate at the frequency of the wave.

• Use the frequency of oscillation of the electrons in the transmitting and receiving antennae to explain the

transmission and reception of radio or television signals.

62 | P a g e

Electromagnetic waves are transverse waves made up of mutually perpendicular, oscillating electric and magnetic fields.

• Relate the orientation of the receiving antenna to the plane of polarisation of radio or television waves.

The speed of a wave, its frequency, and its wavelength are related through the formula v f = .

• Solve problems using v f = .

Monochromatic light is light composed of a single frequency. Most light sources emit waves that radiate in all directions

away from the source.

Coherent wave sources are wave sources that maintain a constant phase relationship with each other.

• Describe what is meant by two wave sources being in phase or out of phase.

• Explain why light from an incandescent source is neither coherent nor monochromatic.

When two or more electromagnetic waves overlap, the resultant electric and magnetic fields at a point can be determined

using the principle of superposition.

When the waves at a point are in phase, ‘constructive interference’ occurs.

When the waves at a point are out of phase, ‘destructive interference’ occurs.

Use the principle of superposition to describe and represent constructive and destructive interference.

For two monochromatic sources in phase, the waves at a point some distance away in a vacuum:

• constructively interfere when the path difference from the sources to the point is m

• destructively interfere when the path difference from the sources to the point is ( )12

m +

where m is an integer and is the wavelength.

• Use a geometrical construction to identify the locations of maximum and minimum amplitude due to the

interference of light from two wave sources of the same frequency.

• Use constructive and destructive interference to explain the maximum and minimum amplitudes.

Young’s double-slit experiment can be used to demonstrate the wave behaviour of light.

The formulae sind m = and L

yd

= can be used to analyse the interference pattern, where d is the distance between

the slits, is the angular position of the maximum, y is the distance between adjacent minima or maxima on the

screen, and L is the slit-to-screen distance.

• Describe how two-slit interference is produced in the laboratory using a coherent light source or using a single slit between a light source and the double slit.

• Describe how diffraction of the light by the slits in a two-slit interference apparatus allows the light to overlap and

hence interfere.

• Sketch a graph of the intensity distribution for two-slit interference of monochromatic light. (Consider only cases

where the slit separation is much greater than the width of the slits.)

• Explain the bright fringes of a two-slit interference pattern using constructive interference, and the dark fringes

using destructive interference.

• Solve problems involving the use of sind m = and L

yd

= .

• Determine the wavelength of monochromatic light from measurements of the two-slit interference pattern.

The interference pattern produced by light passing through a transmission diffraction grating demonstrates the wave

behaviour of light.

Transmission diffraction gratings can be used to analyse the spectra of various light sources.

The formula sind m = can be used to analyse the interference pattern.

63 | P a g e

• Describe how diffraction by the very thin slits in a grating allows the light from the slits to overlap and hence

interfere to produce significant intensity maxima at large angles.

• Derive sind m = for the intensity maxima in the pattern produced by a transmission diffraction grating, where

d is the distance between the slits in the grating and is the angular position of the thm maximum (m specifies

the order of the maximum).

• Solve problems involving the use of sind m = .

• Sketch a graph of the intensity distribution of the maxima produced by a grating, for monochromatic light.

• Determine, from the distance between the slits in the grating, the maximum number of orders possible for a given

grating and wavelength.

• Describe how a grating can be used to experimentally determine the wavelength of light from a monochromatic

source.

• Describe and explain the white-light pattern produced by a grating.

• Identify the properties of a grating that make it useful in spectroscopy.


Learn the names and of the four key concepts of science as a human endeavor (SHE):


o Science is a global enterprise that relies on clear communication, international conventions, and review and verification of results.

o Collaboration between scientists, governments, and other agencies is often required in scientific research and enterprise.

● Development

o Development of complex scientific models and/or theories often requires a wide range of evidence from many sources and across disciplines.

o New technologies improve the efficiency of scientific procedures and data collection and analysis. This can reveal new evidence that may modify or replace models, theories, and processes.

● Influence

o Advances in scientific understanding in one field can influence and be influenced by other areas of science, technology, engineering, and mathematics.

o The acceptance and use of scientific knowledge can be influenced by social, economic, cultural, and ethical considerations.


o Scientific knowledge, understanding, and inquiry can enable scientists to develop solutions, make discoveries, design action for sustainability, evaluate economic, social, cultural, and environmental impacts, offer valid explanations, and make reliable predictions.

o The use of scientific knowledge may have beneficial or unexpected consequences; this requires monitoring, assessment, and evaluation of risk, and provides opportunities for innovation.

o Science informs public debate and is in turn influenced by public debate; at times, there may be complex, unanticipated variables or insufficient data that may limit possible conclusions.

Develop and apply an understanding of the complex ways in which science interacts with society, and investigate the

dynamic nature of physics, according to the four key concepts of SHE.

64 | P a g e


Scientific methods enable systematic investigation to obtain measurable evidence.

● Deconstruct a problem to determine the most appropriate method for investigation.

● Design investigations, including:

o a hypothesis or inquiry question

o types of variables

– dependent

– independent

– factors held constant (how and why they are controlled)

– factors that may not be able to be controlled (and why not)

o materials required

o the method/procedure to be followed

o the type and amount of data to be collected

o identification of ethical and safety considerations.

Obtaining meaningful data depends on conducting investigations using appropriate procedures and safe, ethical working

practices.

● Conduct investigations, including:

o selection and safe use of appropriate materials, apparatus, and equipment

o collection of appropriate primary and/or secondary data (numerical, visual, descriptive)

o individual and collaborative work.


● Represent results of investigations in appropriate ways, including:

o use of appropriate SI units, symbols





● Select, use, and interpret appropriate representations, including:

o mathematical relationships, including direct and inverse proportion and exponential relationships

o diagrams and multi-image representations

o dformulae

65 | P a g e


● Analysis of the results of investigations allows them to be interpreted in a meaningful way.

Analyse data, including:

▪ Multi- image representations ▪ identification and discussion of trends, patterns, and relationships

▪ interpolation/extrapolation where appropriate.


● Identify sources of uncertainty, including:

o random and systematic errors

o uncontrolled factors.

● Evaluate reliability, accuracy, and validity of results, by discussing factors including:

o sample size

o precision

o resolution of equipment

o random error

o systematic error

o factors that cannot be controlled.


● Select and use evidence and scientific understanding to make and justify conclusions.

● Recognise the limitations of conclusions.

● Recognise that the results of some investigations may not lead to definitive conclusions.


● Communicate to specific audiences and for specific purposes using:

o appropriate language

o terminology

o conventions.

66 | P a g e

Content guide: Stage 2 Physics - Semester 2

Subtopic 3.2: Wave–particle duality

Students compare the wave model of light to the particle model needed to explain the interaction of light with matter. The properties of photons are introduced and the phenomena of the photoelectric effect and X-rays are then examined and explained in terms of photons. In addition, the wave behaviour of particles, such as electrons, is also introduced. Students explore applications of photons, X-rays, and the wave behaviour of particles.

In interacting with matter, light behaves like particles (called ‘photons’), with energy given by E hf= and momentum given

by h

p

= , where h is Planck’s constant, f is the frequency of the light, and is its wavelength.

• Calculate the energy and momentum of the photons in various regions of the electromagnetic spectrum.

The intensity of X-rays is decreased (i.e. attenuated) as they pass through matter by scattering and absorption.

• Describe the purpose of the following features of a simple X-ray tube: filament, target, high-voltage supply, evacuated tube, and a means of cooling the target.

• Sketch a graph of the spectrum from an X-ray tube, showing the three main features of the spectrum.

• Explain the continuous range of frequencies and the maximum frequency in the spectrum of the X-rays.

• Derive the formula for the maximum frequency, max

e Vf

h

= .

• Solve problems involving the use of max

e Vf

h

= .

• Relate the attenuation of X-rays to the types of tissue through which they pass (e.g. soft tissue or bone).

• Relate the penetrating power (hardness) of X-rays required to pass through a particular type of tissue to the energy and frequency of the X-rays, and hence to the potential difference across the X-ray tube.

• Relate the minimum exposure time for X-ray photographs of a given hardness to the intensity of the X-rays, and hence to the tube current, which is determined by the filament current.

Particles exhibit wave behaviour with a wavelength that depends on the momentum of the particle. This de Broglie

wavelength can be determined using the formula h

p = , where h is Planck’s constant and p is the momentum of the

particles.

• The wave behaviour of particles can be demonstrated using a double-slit experiment and the Davisson–Germer experiment.

• Solve problems involving the use of the formula h

p = , for electrons and other particles.

• Describe two-slit interference pattern produced by electrons in double-slit experiments.

• Describe the Davisson–Germer experiment, in which the diffraction of electrons by the surface layers of a crystal lattice was observed.

• Compare the de Broglie wavelength of electrons with the wavelength required to produce the observations of the Davisson–Germer experiment and in two-slit interference experiments.

Subtopic 3.3: Structure of the atom

Students investigate the production and features of line emission spectra from atomic gases to infer the structure of the atom, consisting of excited states with discrete energies.

Students describe and explain the visible continuous spectra emitted by hot objects and atomic absorption spectra.

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Students are introduced to the phenomena of a population inversion and stimulated emission to provide a simple explanation of the operation of a laser.

A continuous spectrum contains a continuous range of frequencies.

Solid, liquid, or dense gaseous objects radiate a continuous spectrum, which may extend into or beyond the visible region. The process is known as incandescence. The frequency distribution, and hence the dominant colour, depends on the temperature of the object.

• Describe the changes in the spectrum of a filament globe as the temperature of the filament increases.

The presence of discrete frequencies in the spectra of atoms is evidence for the existence of different states in atoms. The states have their own specific energies.

The different energies can be represented on an energy-level diagram.

When an electron makes a transition from a higher-energy state to a lower-energy state in an atom, the energy of the atom decreases and can be released as a photon.

The energy of the emitted photon is given by the difference in the energy levels of the atom. An atom is in its ground state when its electrons have their lowest energy.

If an electron is in any of the higher-energy states, the atom is said to be in an excited state.

• Explain how the presence of discrete frequencies in line emission spectra provides evidence for the existence of states with discrete energies in atoms.

• Solve problems involving emitted photons and energy levels of atoms.

• Draw energy-level diagrams to represent the energies of different states in an atom.

• Given an energy-level diagram, calculate the frequencies and wavelengths of lines corresponding to specified transitions.

The line emission spectrum of atomic hydrogen consists of several series of lines.

• Draw, on an energy-level diagram of hydrogen, transitions corresponding to each of the series terminating at the three lowest-energy levels.

• Relate the magnitude of the transitions on an energy-level diagram to the region in the electromagnetic spectrum of the emitted photons (ultraviolet, visible, or infrared).

The ionisation energy of hydrogen is the minimum energy required to remove the electron from hydrogen in its ground state.

• Using an energy-level diagram, determine the ionisation energy (in either joules or electronvolts) of hydrogen.

When light with a continuous spectrum is incident on a gas of an element, discrete frequencies of light are absorbed, resulting in a line absorption spectrum.

The frequencies of the absorption lines are a subset of those in the line emission spectrum of the same element.

• Describe the line absorption spectrum of atomic hydrogen.

• On an energy-level diagram, draw transitions corresponding to the line absorption spectrum of hydrogen.

• Explain why there are no absorption lines in the visible region for hydrogen at room temperature.

• Account for the presence of absorption lines (Fraunhofer lines) in the Sun’s spectrum.

The photon emitted in stimulated emission is identical (in energy, direction, and phase) to the incident photon.

• Explain how stimulated emission can produce coherent light in a laser.

A population inversion is produced in a set of atoms whenever there are more atoms in a higher-energy state than in a lower-energy state. For practical systems, the higher-energy state must be metastable if a population inversion is to be produced.

• Explain the conditions required for stimulated emission to predominate over absorption when light is incident on a set of atoms.

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The energy carried by a laser beam is concentrated in a small area and can travel efficiently over large distances, giving laser radiation a far greater potential to cause injury than light from other sources.

• Describe the useful properties of laser light (i.e. it is coherent and monochromatic and may be of high intensity).

• Discuss the requirements for the safe handling of lasers.

Subtopic 3.4: Standard Model

In this subtopic students explore theories that describe the composition of subatomic particles and how interactions between those particles can then be used to describe phenomena such as electrostatic repulsion, beta decay, and positron–electron annihilation.

The Standard Model suggests that there are three fundamental types of particles: gauge bosons, leptons, and quarks.

The Standard Model identifies four fundamental forces: electromagnetic, weak nuclear, strong nuclear, and gravitational.

Gauge bosons are particles which mediate the four fundamental forces. They are often called ‘exchange particles’.

Force Gauge Boson

Electromagnetic photon

Weak nuclear W, Z

Strong nuclear gluon

Gravitational graviton

The gauge boson for gravitational forces, the graviton, is still to be discovered.

• Describe the electromagnetic, weak nuclear, and strong nuclear forces in terms of gauge bosons.

Leptons, such as electrons, are particles that are not affected by the strong nuclear force.

Quarks are fractionally charged particles that are affected by all of the fundamental forces.

Quarks combine to form composite particles and are never directly observed or found in isolation.

• Distinguish between the three types of fundamental particles.

There are six types of quark, with different properties, such as mass and charge. Each quark has a charge of either +2/3 or -1/3.

Quark Symbol Charge (e)

Up u 2/3

Down d 1/3

Strange s 1/3

Charm c 2/3

Top t 2/3

Bottom b 1/3

All other composite matter particles, such as atoms, are thought to be combinations of quarks and leptons.

Baryons are composite particles that consist of a combination of three quarks.

• Describe how protons, neutrons, and other baryons can be formed from different combinations of quarks. Antiquarks have the opposite charge to their quark equivalent. Quarks and antiquarks can form particles called mesons.

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Content guide: Stage 2 Psychology

Topic: Introduction to Psychology

Key Ideas

• Empirical investigations in psychology may be experimental, quantitative observational, or qualitative.

• All investigation designs and methods for assessing psychological responses have advantages and disadvantages.

• All research involving humans has ethical dimensions.

• Different types of representation are appropriate for different types of data. Areas of Learning

• The range of investigation designs that can be used to answer a particular research question and their advantages and disadvantages; the three investigation designs used in psychology — experimental, quantitative observational, and qualitative; focus groups and the Delphi technique as examples of qualitative investigations; advantages and disadvantages of quantitative and qualitative investigations; and the difference in design between experimental investigations and quantitative observational investigations

• The three methods of assessing psychological responses — objective quantitative measures (e.g. physiological measures such as heart rate, behavioural counts, and scores on standardised intelligence tests), subjective quantitative measures (e.g. responses on checklists and rating scales, and scores on personality tests), and qualitative assessment of data; content analysis of responses in focus groups; awareness of the limitations of drawing conclusions using small or unrepresentative samples; and consideration of the validity and reliability of the methods

• Descriptive statistics (that is, the ways in which quantitative data may be represented and described); the generalisation of research findings (instruction in statistics should be limited to determining medians and means; generating graphical representations of data; interpreting medians, means, standard deviations; and graphical representations of data. A brief description of the function of inferential statistics and criteria for significance, however, will enable students to read original research with some understanding)

• Ethical issues associated with investigations; and the ethical safeguards that have been incorporated in particular investigations

Topic: Social Cognition

Key Ideas

Knowledge and understanding should be relevant to the following key ideas:

• The relationship between social cognition and behaviour is bidirectional. In particular, attitudes influence behaviour, but behaviour also influences attitudes.

• Our perceptions of others and of ourselves are vulnerable to a number of biases. Areas of Learning

• The structure of attitudes and the functions they serve; the factors that influence attitude formation and attitude change (including source, message, and audience, and peripheral and central processing routes); the bidirectional relationship between attitudes and behaviour; the factors that influence impression formation; self-knowledge from social comparisons; and impression management

• Psychological principles concerning social cognition in everyday experiences and events (e.g. meeting a new person, or advertising) and in psychological interventions, including public safety campaigns that target attitude change

• The application of these psychological principles to social issues (e.g. reducing prejudice, or increasing the effectiveness of health-promotion campaigns) and personal growth (e.g. more effective persuasive communication and impression management)

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• Investigation designs and methods of assessing psychological responses used to study social cognition

• Ethical issues associated with research and applications in the area of social cognition

Topic: Learning

Key Ideas


• Our future behaviour is influenced by the events that followed our past behaviour.

• Our future behaviour is also influenced by past and present observations of the behaviour of others.

• Some associations are easier to learn and maintain than others. Areas of Learning

• Components in classical conditioning (unconditioned and conditioned stimuli and unconditioned and conditioned responses); components in operant conditioning (positive reinforcement, negative reinforcement, punishment, schedules of reinforcement, and preparedness); the importance of timing in classical and operant conditioning (contiguity and contingency); stimulus generalisation, stimulus discrimination, and extinction; the factors that influence learning through observation; and the distinction between the acquisition and performance of a learned response

• Psychological principles concerning learning in everyday experiences and events (e.g. coin deposit incentives to return shopping trolleys, customer loyalty programs, classical conditioning in advertising, and explicit and implicit observational learning from television programs) and in psychological interventions, including behaviour modification and the systematic desensitisation of phobias

• The application of these psychological principles to social issues (e.g. reducing criminal behaviour, and increasing recycling) and personal growth (e.g. overcoming one’s own annoying habits)

• Investigation designs and methods for assessing psychological responses used to study learning

• Ethical issues associated with research and applications in the area of learning

Topic: Personality

Key Ideas


• Personality is a socially and culturally constructed concept.

• Many different descriptions of the structure of personality have been proposed.

• Ways of measuring personality are linked to particular beliefs about its structure. Areas of Learning

• Psychodynamic, humanistic, and trait theories of personality; and the main forms of personality assessment used today, including standardised self-report inventories, clinical interviews, and behavioural observations

• Psychological principles concerning personality in everyday experiences and events (e.g. character depictions in the popular media) and in psychological interventions, including assertiveness training

• Application of these psychological principles to social issues (e.g. personality disorders, the relationship between personality and learning styles, and the relationship between culture and personality) and personal growth (e.g. gaining greater insight into one’s own personality and the factors that have shaped it)

• Investigation designs and methods for assessing psychological responses used to study personality, including validity and reliability

• Ethical issues associated with research and applications in the area of personality

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Topic: Psychobiology of Altered States of Awareness

Key Ideas

• Knowledge and understanding should be relevant to the following key ideas:

• Our level of awareness is constantly changing.

• Arousal can have both beneficial and deleterious effects.

• There are many effective ways to improve coping with stress. Areas of Learning

• Circadian rhythms; sleep deprivation and sleep needs; stages of sleep; common sleep disorders; psychological and physiological arousal; the relationship between arousal and task performance; and stress and its effect on health

• Psychological principles concerning altered states of awareness in everyday experiences and events, including shift work, and in psychological interventions, including psychological therapies for insomnia and stress

• The application of these psychological principles to social issues (e.g. the road toll, workplace accidents, the influence of shift work on health, and the influence of jet lag on sporting performance) and personal growth (e.g. improving one’s own stress management, and ‘sleep hygiene’)

• Investigation designs and methods for assessing psychological responses used to study altered states of awareness

• Ethical issues associated with research and applications in the area of altered states of awareness

Topic: Healthy Minds

Key Ideas


• There are effective ways to promote healthy minds.

• Definitions of mental disorders are culturally constructed.

• Many different interventions for mental health problems are effective. Areas of Learning

• Effective coping strategies; the factors that influence resilience; protective factors for mental health; symptoms of, and effective treatment for, anxiety disorders and depression; and the relationships between factors at the biological, basic processes, person, and sociocultural levels of explanation of behaviour in the psychology of healthy minds and mental health issues

• Psychological principles concerning healthy minds in everyday experiences and events (e.g. cultural and historical differences in concepts of mental health and mental illness) and in psychological interventions, including cognitive-behavioural therapy; behaviour modification; systematic desensitisation of phobias; assertiveness training; therapy for insomnia; and stress management therapy

• The application of principles from the psychology of healthy minds to social issues (e.g. preventing the development of mental disorders, and reducing prejudice against people with a mental illness) and personal growth, including the advantages and disadvantages of different psychological interventions

• Investigation designs and methods for assessing psychological responses used to study healthy minds and mental disorders; and investigation designs and methods used to evaluate psychological interventions

• Ethical issues associated with research and applications in the area of healthy minds and mental health issues

* Please note that a much more cohesive revision guide is available on Canvas.

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Content Guide: Stage 2 Physical Education

Topic 1 – Energy Sources for Physical Performance Concepts

• Sources of macronutrients: fats, carbohydrates, protein

• Food breakdown into nutrients: glucose, glycogen, triglycerides, free fatty acids

• Aerobic and anaerobic energy: ATP–CP system, lactic acid system, oxygen system

• Contribution of energy systems in specific activities

• Acute responses to exercise: responses in the circulatory, respiratory, and muscular systems.

Knowledge and Understanding

• Sources of Nutrients: Fats, Carbohydrates and Protein. LIVE IT UP 2 Chapter 2 Pg60-63

• Sources of fuel, storage and location of energy in the body.

• Chemical breakdown of Nutrients: Glucose, Glycogen, Free Fatty Acids. LIVE IT UP 2 Chapter 2 Pg60-63

• Glucose, glycogen (where is it stored?), Fatty acids, triglyceride, adipose tissue and amino acids.

• Aerobic and Anaerobic Energy: ATP-CP System, Lactic Acid System, Aerobic System. LIVE IT UP 1 Chapter 7 Pg214-225

• Characteristics of each energy system (Anaerobic vs Aerobic), why?

• Associated terminology: phosphate, alactacid, glycolysis, pyruvic acid, lactacid, ‘hitting the wall’.

• Recovery times for each energy system, by products.

• CP and glycogen replenishment, lactic acid removal, EPOC/O2 Dept. and O2 Deficit.

• Contribution of energy system for specific activities.

• Application to specific sports.

• Interplay of energy systems (eg. 100m sprint vs netball game).

• Comparison of energy demands across a spectrum of activities with differing intensities and duration.

• Acute responses to exercise: Responses in Circulatory, Respiratory and Muscular Systems to provide energy LIVE IT UP 2 Chapter 2 Pg74-79 and LIVE IT UP 1 Chapter 6 Pg184-204

• Cardiovascular responses: Heart rate, Stroke volume, Blood pressure, a-v O2 difference, Blood volume, Redirection of blood flow, OBLA, Steady state, EPOC, VO2 max, Lactate threshold, Oxygen deficit.

• Respiratory responses: Ventilation, Breathing rate, Lung diffusion, VO2 Uptake.

Muscular – Motor unit activation, Fuel stores depletion, Muscle temperature changes.

Application

• Record and analyse Heart rate changes

• Read graphs to obtain information related to energy systems eg HR, lactate levels, oxygen uptake

• Write a practical report investigating aspects of physical education

• Apply knowledge about fitness factors and energy systems to analyse sports and their contributions.

Topic 2 – Training and Evaluation of Physical Performance Key Concepts

• Chronic adaptations to aerobic and anaerobic training in the circulatory, respiratory, and muscular systems


• Chronic responses to aerobic and anaerobic training. LIVE IT

UP 2 Chapter 8 Pg248-264

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at different levels of intensity and duration (e.g. rest, submaximal effort, and maximal intensity)

• Activity analysis of the demands of sport and physical activity

• Measurement and monitoring of fitness and energy components relevant to performance

• Training principles and methods specific to fitness factors and to physical activities

• Understand, explain and analyse the chronic responses to

exercise including: long term responses to anaerobic and

aerobic exercise.

• Other physiological changes that are long term responses to

exercise.

• Analysis of Energy Demands of Sport and Training. Self-

Reflection on Key points from Topics 1 and 2

• Analyse sports/games in terms of energy demands/fitness

components/major muscle groups.

• Measurement and Monitoring of Fitness Relevant to

Performance. LIVE IT UP 2 Chapter 6 Pg181-206

• Understanding the benefits and purpose of fitness testing.

• Recognise the relevance and appropriateness of an array of

tests.

• Identify testing standards in the following: Power, Aerobic

endurance, agility, flexibility, strength and speed.

• Training Principles and Methods Specific to Fitness levels and

the demands of a sport/activity. LIVE IT UP 2 Chapter 7

Pg212-244

• Understand the program design based on game analysis.

• Knowledge of training methods, principles and the phases of

a season.

• The importance of evaluation, monitoring and adapting a

program accordingly.

Application

• Discuss how training makes changes to the body and activities suited to those changes.

• Develop a training program with appropriate methods and principles

• Identify and set up tests suited to particular fitness factors

• Analyse fitness programs and their suitability to different sports


Topic 3 – Specific Physiological Factors that Affect Performance

Key Concepts

• Body stature and composition

• Environmental considerations and performance


• Body Structure, composition and sex differences.

• Body composition – Muscle fibre types.

• Body structure – Somatotype.

• Sex difference and performance.

• Population groups, race and ethnic background.

• Environmental consideration and performance (heat/altitude). Heat vs cold.

• Altitude and acclimatisation.

• Sex differences.

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• Nutrition and performance

• Fatigue, recovery, and physical performance

• Nutrition and Physical Performance: pre-event, during, post-event and hydration. LIVE IT UP 2 Chapter 11 Pg340-353

• Essential nutrients pre, during and post event (glycaemic index - GI).

• Hydration and what happens when dehydrated to performance.

• Fatigue and Physical Performance. LIVE IT UP 2 Chapter 4 Pg102-120

• Causes of muscular fatigue as a result of varied exercise intensities and durations.

• Fuel depletion, metabolic by-products and thermoregulation.

Application

• Be able to structure a program for sporting teams of varying abilities.

• Apply knowledge of training to set up training sessions

• Identify somatotypes and stereotypical/suitable activities

• Plan a pre-game meal

Topic 4 – Skill Acquisition Key Concepts

• The classification of skills

• The characteristics of a skilled performer

• The stages of skill learning

• The learning process in acquiring physical skills


• Knowledge of the characteristics of skills and their classification (e.g. open/closed, externally paced)

• Identification and application of skills in physical activities

• Knowledge of the characteristics of a skilled performer (e.g. acting as if there is all the time in the world)

• Identification of these characteristics and application to a performance

• Understanding of the different stages of learning and their characteristics (e.g. cognitive, associative, and autonomous)

• Understanding of how a learner progresses from one stage to the next

• Understanding of the information processing model (e.g. skill learning model)

• Understanding of specific factors that influence different parts of the model (e.g. information processing and decision-making)

• Investigation of differences in processing at different stages of learning (e.g. selective attention)

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Application

• Discuss how training makes changes to the body and activities suited to those changes.

• Develop a training program with appropriate methods and principles

• Identify and set up tests suited to particular fitness factors

• Analyse fitness programs and their suitability to different sports


Topic 5 – Specific Factors Affecting Skill Learning Concepts

• The nature of the task

• Practice and feedback

• Physical environmental factors

• Characteristics of a skill learner

• Retention of learning

• Timing and anticipation


• Understanding of how tasks vary in complexity of understanding and execution (e.g. complex versus simple tasks)

• Understanding of how the type of task affects the skill learner and his or her performance

• Differentiation between types of practice (e.g. massed, distributed, fixed, and variable)

• Understanding of the relationship between practice, competency of the learner, and performance

• Understanding and application of the different types of feedback and their characteristics

• Understanding of the function of feedback and its psychological and physiological effects

• Identification and understanding of the effect of environmental factors on skill learning and performance (e.g. weather, settings/equipment, and facilities)

• Identification of different characteristics of learners (e.g. gender, age,

previous experience)

• Understanding of effect of physiological characteristics on learning capacity (e.g. stage of physical development)

• Understanding of effect of psychological characteristics on learning capacity (e.g. ability to remain on task)

• Understanding of the process involving learning retention in short-term and long-term memory

• Understanding and application of techniques to enhance learning (e.g. ‘chunking’ and visual association)

• Understanding of the relationship between learning and practice

• Understanding of the factors that affect skill execution (e.g. timing, subroutines)

• Understanding of anticipation and the factors that affect it (e.g. previous experience, signal detection)

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Application





Topic 6 – The Effects of Psychology of Learning on the Performance of physical Skills Concepts

• Goal Setting

• Anxiety, arousal and performance

• Visualisation

• Self esteem

• Skill learning and Coaching Methods


• Understanding of the function of goal-setting

• Understanding and application of different types of goals and their characteristics (e.g. SMART (specific, measurable, achievable, relevant, and time-framed) goals)

• Understanding of the nature of anxiety and arousal

• Knowledge of different theories of arousal (e.g. inverted U hypothesis)

• Understanding of how the complexity of the task affects levels of anxiety and arousal

• Understanding of how levels of anxiety and arousal affect performance in different activities (e.g. information overload, responding to incorrect cues)

• Understanding of how levels of anxiety and arousal affect performance during competition (e.g. opposition pressure, scoreboard pressure)

• Understanding of the effect of coaching technique on the learner and performance

• Identification and understanding of the effect of environmental factors on skill learning and performance (e.g. weather, settings/equipment, and facilities)

• Understanding of the function of visualisation

• Identification and application of the different types of visualisation used in sport (e.g. technical and motivational visualisation)

• Understanding of the role of self-esteem in skill performance

• Understanding of the factors that affect self-esteem (e.g. coach, feedback, level of competition)

• Knowledge of the different types of skill learning (e.g. audible, visual, kinaesthetic) and their effectiveness

• Understanding and application of the methods of coaching skills (e.g. whole practice and part practice)

• The effect of these types of skill learning on skill development (e.g. learning curves)

• Understanding of the function of communication and its effect on skill learning (e.g. level of technical feedback)

Application



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Topic 7 – The Ways in which Biomechanics Improve Skilled Performance Concepts

• Force and Momentum

• Motion

• Levers

• Equilibrium (static and dynamic)

• Technology and Performance


• Understanding of internal and external forces that influence skill

• Understanding of the relationship of force to motion and momentum

• Understanding of the application of force summation to performance

• Understanding of the different types of motion (e.g. linear and non-linear, curvilinear, angular, general) and the biomechanical principles that affect them (e.g. moment of inertia)

• Understanding of how speed, velocity, and acceleration affect performance

• Understanding of the factors that affect projectile motion and its application in sport (e.g. speed, angle, and height of release)

• Application of Newton’s three laws of motion to sports performance

• Understanding of the application and effect of levers in sporting performance (e.g. length and mass of lever)

• Understanding and application of static and dynamic equilibrium in sporting performance

• Understanding and application of balance and stability in sporting performance (e.g. centre of gravity inside stable base)

• Investigation of contemporary technology advances in sporting performance (e.g. clothing, innovation, coaching)

Application





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Basketball

Individual Performance Ability Individual Offence

• Complete the skills of passing, receiving, dribbling, shooting, one on one moves and rebound with control and effective technique in games

• Cut and lead effectively

• Square up into triple threat

• Fake and drive

• Accomplish low post moves

• Shoot consistently under pressure Individual Defence

• Use a variety of strategies in defence in game situations • Block out effectively • Rebound and outlet pass • Position effectively to deny the player the ball or against the player with the ball • Defend the low post

Team Strategies and Tactics

Team Offence

• Play a variety of team offensive strategies effectively

• Recognise appropriate spacing

• Maintain court balance

• Screen and cut

• Recognise appropriate shot selection

• Run a fast break and/or fill the lanes

Demonstrate an understanding of one-on-one and zone defence

Team Defence

• Recognise, and use effectively a variety of defensive strategies

• Recognise opponents weaknesses and strengths

• Play a one to one defence and zone defence

• Can use a help and recover defence

• Recognise switching

Respond effectively to transition

Interpersonal Skills • Act independently to demonstrate initiative and improvement where appropriate (e.g. practice drills,

games, equipment handling etc.)

• Use tactics effectively in game situations to demonstrate leadership and understanding of game strategy

• Demonstrate leadership in a variety of situations

• Perform specialist roles contributing to the morale and etiquette of the sport through appropriate communication

• Demonstrate determination and perseverance in all practical tasks

• Work collaboratively in various scenarios to improve individual and/or team performance.

Badminton

Individual Performance Ability

Serving (High / Short / Flick)

• Serve with control and variation in height, speed, direction and placement

Overhead Shots (Clear / Smash / Drop Shot)

Ability to consistently:

• Use identical technique to place shuttle away from opponent applying the appropriate disguise, force and trajectory

Net Shots (Lift / Kill / Drop)

Strategies and Tactics

• Use identical technique to place shuttle away from opponent applying the appropriate disguise, force and trajectory of shots such as the drop, smash and clear.

• Employ a variety of appropriate shots in attack and defence in response to opponent’s strengths and weaknesses

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• Use identical technique to place shuttle away from opponent applying the appropriate disguise, force and trajectory

Singles Play



• Cover the court effectively to get to the shuttle early and recover quickly to base

Doubles Play



• Apply when appropriate effective attacking and defensive formations utilizing effective communication and teamwork.

• Apply when appropriate effective attacking and defensive formations in doubles play utilizing effective communication and teamwork.

• Consistently move into a central position ready for the next shot from opponent.

• Placement of shuttle to move opponent around the court- up, back, left, right.

Interpersonal Skills • Act independently to demonstrate initiative and improvement where appropriate (e.g. practice drills,

games, equipment handling etc.)

• Use tactics effectively in game situations to demonstrate leadership and understanding of game strategy

• Demonstrate leadership in a variety of situations

• Perform specialist roles contributing to the morale and etiquette of the sport through appropriate communication

• Demonstrate determination and perseverance in all practical tasks

• Work collaboratively in various scenarios to improve individual and/or team performance.

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Content Guide: 12 English Literary Studies – Critical Reading


• Know the conventions of a range of text types including reviews, narratives, poems, advertisements, blogs, film posters, obituaries, letters, plays etc • Structure and intention of different question types • Stylistic features such as narrative viewpoint, juxtaposition, nominalisation, alliteration, lexical choices, metaphor • Language features such as figurative language, sentence structures, vocabulary, punctuation • Metalanguage, such as sentence, clause, conjunction, mise-en-scene, symbolism

Language Features

• Third person • Present tense • Ability to analyse authors’ use of stylistic, language and text conventions

Writing and Speaking

• Varied and sophisticated vocabulary • Concise responses • Accurate spelling, grammar and punctuation – few errors

Conventions

• TEEEL structure for answers • Authors referred to by surnames • Quotations embedded where possible (Longer quotations used sparingly) • Balance between techniques and ideas • Links to the reader and what the reader understands • Ability to decipher texts, plan out responses and write to a time limit • Responses build on previous replies without repetition • Reference to text type conventions and how they influence text type/reader

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Content/Revision guide: Stage 2 Geography

Migration Understanding

• global distribution of the human population

• types of migration within countries and between countries

• causes of migration, including push and pull factors

• the impacts of migration at origin and destination

• the impacts of forced migration at origin and destination Application and Evaluation • Ensure examples and case studies are place specific

• Use definitions and correct terminology

Revision

• Complete revision activities on R2BC – Migration 1, 2 and 3

• Review example exam questions for each activity in this topic

Population Understanding

• changing birth and death rates

• increased life expectancy and ageing

• changing population structures

• the consequences of changing population structures

• economic and sociocultural factors influencing population trends

• contemporary case studies of population trends in LEDC’s and MEDC’s

Application and Evaluation

• Ensure examples and case studies are place specific

• Use definitions and correct terminology Revision

• Complete revision activities on R2BC – Population 1 and 2


Ecosystems Understanding

• characteristics of ecosystems and ecosystem functions, including the interconnections between water, soil, atmosphere, vegetation, and other living things

• resources provided by ecosystems, including food, water, wood, and medicines

• services provided by ecosystems, including the regulation of climate, natural hazard mitigation, water purification, nutrient cycling, and erosion control

• the impacts of people on ecosystems, including land-cover changes, land degradation, and biodiversity loss

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• explain the ecological footprint and how it is measured

• the relationship between population change, resource use, biocapacity, biodiversity, sustainability, and ecological footprints using case studies and country comparisons.

• strategies to reduce the ecological footprint of people and improve sustainability of ecosystems.


• Ensure examples and case studies are place specific


• Describe trends using evidence in graphs, maps and tables Revision

• Complete revision activities on R2BC – Ecosystems 1 & 2 and Footprints 1 & 2


Mapping and Fieldwork Understanding

• evaluate the usefulness and accuracy of fieldwork techniques

• evaluate the limitations of data collected

• choose and interpret secondary sources of data and information

• use maps and spatial technologies (latitudes, longitudes, grid references, legends or keys, directions, and contours)

• interpret images, including aerial, oblique, and ground photographs, and satellite images


• Analyse maps, tables, fieldwork representations make recommendations, form conclusions, and solve problems


• Describe trends using evidence in graphs, maps and tables Revision

Complete revision activities on R2BC – Data Analysis, Mapping, Fieldwork and Diagrams

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Content/Revision guide: Stage 2, Modern History, The Struggle for Peace in the

Middle East 1945-

Understanding and Exploration • understanding and exploration of the historical concepts: • A contested region: Palestine; the establishment of the state of Israel; and the significance of the 1952 Egyptian revolution, the 1953 Iranian coup d’état, and the 1958 Suez Crisis. • National and regional conflicts Arab–Israeli conflicts (1967, 1973); the Lebanese Civil War (1975–1990); the Iranian Revolution (1979); the Iran–Iraq War (1980–88); the Intifada (1987, 2000); the First Gulf War (1990); the Second Gulf War (2003); the Arab Spring (2011); • Peace processes: The course and short-term and long-term impacts of peace processes and settlements. • Unresolved issues: including refugees and migration; persecuted minorities; pan-national militant groups; the recognition of and threats to national sovereignty; civil war; military incursions; border protection; and access to resources such as oil, water, and land.

Application and Evaluation Source Analysis is a key historical skill. At the conclusion of this unit/Stage 2 Modern History students should be able to implement the following skills of sources analysis:

• locate relevant sources • design source analysis investigative questions • undertake insightful analysis of sources • draw conclusions from source evidence • interpret different perspectives • effectively communicate historical arguments • draw conclusions from source evidence • clearly and coherently articulate the uses and limitations of a wide range of primary and secondary sources • evaluate and respond to propositions using a selected range of primary and secondary sources as evidence. • Use the Oxford referencing system (footnotes) to properly acknowledge sources • Writing in past tense and third person

Analysis Through an investigation of the features of Understanding and Exploration students will be expected to know and understand that the conflict in the Middle East has been shaped by internal and external factors. These include the United Nations, the US, the USSR/Putin’s Russia, Israeli domestic and foreign policy, The Arab League, the PLO, Hezbollah, Hamas, terrorism and the fallout from the war in Iraq/Afghanistan and the Syrian Civil War. They will be expected to critically analyse and rationalise the impact this conflict has had on the region since 1945 and on the modern world today.

Communication At the conclusion of this unit/Stage 2 Modern History students will be able to:

• Provide reasoned historical arguments using a range of source material in written, oral and multi-modal forms across a range of forums • Design a research question(s) and undertake research to respond accordingly in a variety of situations • Communicate ideas and arguments appropriate to purpose and audience • Practise ethical scholarship, including the use of appropriate referencing techniques.

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Content/Revision guide: Stage 2, Modern History, Germany 1919-1948

Understanding and Exploration

The liberal experiment. The changing economic conditions, including reparations, hyperinflation, and the Great Depression. The nature and response to political threats from the left and right, which questioned stability and legitimacy. The changing nature and expression of social class, including movements in architecture, art, music, and/or cinema. The road to dictatorship. The failure of democrats to stem moves toward radical politics. The aims, methods, and appeal of the Nazi movement, which resulted in the move from political fringe to government. The role of key individuals and groups working for and against the Nazi victory. The consolidation of power in the hands of an elite within one party. The Nazi State in peace and war. The creation and consolidation of the totalitarian state. The experience of Nazism for people and groups, including women, and those who resisted the Nazi state from within Germany. The institutionalisation of anti-Semitism leading to the genocide of the ‘Final Solution’. The impact of the Second World War on Germany as a nation, and the German people. The defeat of the Nazi State/Third Reich in the face of external and internal opposition. The initial post-war division of Germany. The Nuremberg trials. The Berlin crisis in 1948.

Application and Evaluation Source Analysis is a key historical skill. At the conclusion of this unit/Stage 2 Modern History students should be able to implement the following skills of sources analysis:

• locate relevant sources • design source analysis investigative questions • undertake insightful analysis of sources • draw conclusions from source evidence • interpret different perspectives • effectively communicate historical arguments • draw conclusions from source evidence • clearly and coherently articulate the uses and limitations of a wide range of primary and secondary sources • evaluate and respond to propositions using a selected range of primary and secondary sources as evidence. • Use the Oxford referencing system (footnotes) to properly acknowledge sources • Writing in past tense and third person

Analysis Through an investigation of the features of Understanding and Exploration students will be expected to know and understand that the modern nation of Germany has been shaped by internal and external factors. These include the impact of the First and Second World Wars, the failure of democracy: 1919-1933, the impact and characteristics of the Nazi Dictatorship and the post Second World War Cold War tensions.

Communication At the conclusion of this topic/Stage 2 Modern History students will be able to:

• Provide reasoned historical arguments using a range of source material in written, oral and multi-modal forms across a range of forums • Design a research question(s) and undertake research to respond accordingly in a variety of situations • communicate ideas and arguments appropriate to purpose and audience • practise ethical scholarship, including the use of appropriate referencing techniques.

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Revision guide: Stage 2 Chinese Background Speakers

Each topic will have its own description on https://stjohnsgs.instructure.com/courses/1821

https://stjohnsgs.instructure.com/courses/1821

https://stjohnsgs.instructure.com/courses/1821

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Year 12 Revision Guide - St John's Grammar School€¦ · • Simple Interest • Compound Interest...

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Transcript of Year 12 Revision Guide - St John's Grammar School€¦ · • Simple Interest • Compound Interest...