Higher Tier

R = Recap (levels 7 & 8); C = Core (bold); E = Extension to include AQA Further Maths (italics) Teacher support material available here: http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm

Y10 & 11 GCSE SOW for Set 1

Date Topic Notes Examples Student

Reference Resources Mid-Jun – Jul (Y10)

1. INDICES: STANDARD FORM

R: Index notation

Prime factors Laws of indices

C: Negative / fractional Indices

Standard form

N1 – N9

N7: Positive integer powers only

N7: With and without calculator

N9: SF

Simplify a5 a3; m4 m2; (p2)5; (2xy2)3;

Prime factors Find HCF of 216 and 240

simplify 812/3

(without calculator);

Evaluate 2.762 10124.97 1021(cal.)

Evaluate 2.8 104 7 106 (no cal.)

Evaluate 2.8 104 7 106 (no cal.)

Starter:

Ex 13, 14 p14-18 (HCF, LCM etc) Ex 13 p14 (roots) Ex1,2 p354-355 (indices) Ex18,19 p68-71 (standard form)

There is teacher support material for

each unit, including teaching notes,

mental tests, practice book answers, lesson plans, revision tests & activities.

The teacher support material is

available HERE

Clip 44 Factors, Multiples and Primes

Clip 95 Product of Prime Factors

Clip 96 HCF & LCM

Clip 99 Four rules of Negatives

Clip 45 Evaluate Powers

Clip 46 Understanding Squares, Cubes

& Roots

Clip 111 Index Notation for

Multiplication. & Division

Clip 135 Standard Form Calculations

Clip 156 Fractional & Negative Indices

Jul – Aug

SUMMER HOLIDAYS

September (Y10)

2. FORMULAE: ALGEBRAIC

FRACTIONS

R: Formation, substitution,

change of subject in formulae

More complex formulae:

– substitution

– powers and roots

– change of subject with subject in more

than 1 term

Common term factorisation

C: Algebraic fractions – addition

and subtraction

A1 – A7

With and without calculator Opportunity for revision of negative

numbers, decimals, simple fractions.

Including denominators with (i) numerical or single term

(ii) linear term

Given q – 2, v 21, find the value of √v2 q2.

Make L the subject of t = 2π√𝐿𝐺

More complex formulae: Given u 2 , v 3, find f when 1 = 1 + 1

f u v

Make v the subject of 1 = 1 + 1

f u v

Factorise x3y4 x4y3 x2y

Simplify 𝑥

𝑥+1+

2𝑥

2𝑥+1

Ex1 p96 (basic of algebra) Ex7 p104 (definitions) Ex24 p75-76 (substitution)

Clip 104 Factorising

Clip 107 Changing the subject of the

Formula

Clip 111 Index Notation for Mult. &

Division

Clip 163 Algebraic Fractions

Clip 164 Rearranging Difficult

Formulae

October (Y10)

3. ANGLE GEOMETRY

R: Angle properties of straight lines,

points, triangles, quadrilaterals, parallel

lines Angle symmetry properties

of polygons

Symmetry properties of 3-D shapes

G1, 3, 4, 6, 13

Include line and rotational symmetry Include plane, axis and point

Symmetry

Calculate interior angle of a regular octagon/decagon

Shade in the diagram so that it has rotational symmetry of

Order 4 but no lines of symmetry.

Ex1 p157-159 (angles) Ex4 p164-166 (angles in polygons)

Clip 67 Alternate angles

Clip 68 Angle sum of a Triangle

Clip 69 Properties of Special Triangles

Clip 70 Angles of Regular Polygons

Clip 150 Circle theorems

Compass bearings

C: Angle in a semi-circle

Radius is perpendicular to the tangent

Radius is perpendicular bisector of

chord

Angles in the same segment are equal

Angle at the centre is twice the angle at

the circumference.

Opposite angles of a cyclic

quadrilateral add up to 180 .

Alternate segment theorem.

Tangents from an external point are

equal.

Intersecting chords

Tangent/secant

8 compass points and 3 figure

bearings

Application of Pythagoras and Trig.

G9: identify and apply circle

definitions and properties, including:

centre, radius, chord, diameter, circumference, tangent, arc, sector and

segment

AX.BX CX.DX

PT2 PA.PB

Describe fully the symmetries

of this shape.

Scale drawings of 2-stage journeys

Calculate angles: BDA, BOD, BAD & DBO

Ex23-25 p337-343 (circle theorems)

(Y10)

4. TRIGONOMETRY

R: Trigonometry (sin, cos, tan)

C: Sine and cosine rules

G20 – G23

Angles of elevation and depression

Bearings 2-D with right-angled triangles only

Including case with two solutions

Angles of any size

G21: know the exact values of sin θ

and cos θ for θ = 0°, 30°, 45°, 60° and

90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°

Ship goes from A to B on a bearing 040

Bearings for 20 km. How far north has it travelled?

Ex6-7 p294 (finding the length) Ex8 p297 (finding angles) Ex9 p299 (trig & bearing) Ex19-20 p328 (sine rule) Ex21 p331 (cosine rule)

Clip 147 Trigonometry

Exact Trig Values resources

Clip 173 (sine & cosine)

E: Graphs of sin, cos, tan.

Solutions of trig equations

find length CB

Solve sin x 1

2or all x in range 0 x 720o.

Ex22 (problem solving with sine & cosine rules) Ex17 p232 (graphs of trig fns) Ex18 p325 (solutions of trig equations)

Clip 168 Graphs of trig fns. (A/A*)

Oct – Nov

OCTOBER HALF TERM

November (Y10)

5. PROBABILITY

R: Relative frequency experimental

probability and expected results

Appropriate methods of determining

probabilities

Probability of 2 events

Multiplication law for independent events

C: Addition law for mutually

exclusive (ME) events

Addition Law for non-

mutually exclusive events

Conditional probability;

dependent events

C: Sets & Venn Diagrams

Enumerate sets and combinations of sets systematically, using tables, grids, Venn

diagrams and tree diagrams."

"Calculate and interpret conditional probabilities through representation using

P1 – 9

Know that a better estimate for a

probability is achieved by increasing

the number of trials Using symmetry, experiment

Simple tree diagrams

By listing, tabulation or tree diagrams ME means both events cannot happen at the same time Non ME mean independent events = both can happen at same time.

Sampling without replacement

Using Venn diagrams (optional)

Using Venn diagrams

Experiment to find probability of drawing pin landing point up.

pace4/52 = 1/13

There are 5 green, 3 red and 2 white balls in a bag. What is the probability of obtaining

(a) a green ball (b) a red ball (c) a non-white ball?

Find the probability of obtaining a head on a coin and a 6 on a dice.

Calculate the probability of obtaining 3 aces when dealt 3 cards from a deck of 52.

Examples of what pupils should know and be able to do for Venn

Diagrams:

Enumerate sets and unions /intersections of sets systematically, using tables, grids and Venn Diagrams. Very simple Venn diagrams previously KS2 content.

Rayner: Ch9 p445 MEP Student book

Unit 5 Teachers Notes

MEP Text Book

Last One Standing Mathsland National Lottery Same Number! Who’s the Winner? Chances Are The Better Bet

Clip 154 Tree Diagrams (Grade B)

Clip 182 Probability – And & Or

questions (Grade A* - A)

Resources for Venn Diagrams Post on Frequency Trees Resources for Frequency Trees Prize Giving (NRich)

expected frequencies with two-way

tables, tree diagrams and Venn diagrams

Investigate – Venn Diagrams:

ξ = {numbers from 1- 15}; A = {odd numbers}; B = {multiples of 3} and C = {square numbers}

(a) Draw a Venn diagram to show sets A, B & C. You’ll need 3 circles

(b) Which elements go in the overlap of

A & B

A & C

B & C

A, B & C (c) Try and come up with three different sets where not all of the

circles overlap. How many different Venn diagrams with three circles that overlap in different ways can you find?

Example:

X is the set of students who enjoy science fiction Y is the set of students who enjoy comedy films The Venn diagrams shows the number of students in each set, work out:

(i) P(X ∩ Y) (ii) P(X U Y)

Example:

One of these 80 students is selected at random. (b) Find the probability that this student speaks German but not Spanish. Given that the student speaks German, (c) Find the probability that this student also speaks French

Frequency Trees

Record describe and analyse the

frequency of outcomes of probability

experiments using tables and frequency trees

(Y10)

6. NUMBER SYSTEM

R: Estimating answers Use of brackets and memory on a

calculator

C: Upper and lower bounds including

use in formulae

Irrational / rational numbers

Surds

Addition, subtraction, multiplication of

surds

N13 – N16

Use of ( ) button

Including area, density, speed

N10: Recurring decimals

N8: Surd form of sin, cos, tan of 30

45 60

N8: Division of surds using

conjugates

Expansion of two brackets

29.4 + 61.2

14.8 ≈

30 + 60

15 ≈ 6

2.5 × 14.3

7.8 + 2.95≈ 3.32558 (𝑡𝑜 5. 𝑑. 𝑝)

9.7 means 9.65 x 9.75

100 metres (to nearest m) is run in 9.8 s (to nearest 0.1 s). Give the range of

values within which the runner's speed must lie.

List some irrational numbers between 5 and 6.

Show that (i) 0.0˙9˙ (ii) 0.16˙ are rational.

Rationalise the denominator; 1

√3;

21

√7

expand 1√2 1√2

If p and q are different irrational numbers, is(i) p q (ii) p q Rational / Irrational / Could be both?

Ex19 p26-31 (estimating) Ex1 p49-50 Q21,22 (decimals to fractions) Ex3 p357 (surds)

Clip 101 Estimating (grade C)

Clip 125 & 160 Upper & lower bounds

Clip 98 & 155 Recurring Decimals to

Fractions

Clip 157 Surds (A)

Clip 158 Rationalising the Denominator

(A)

December (Y10)

7. MENSURATION

R: Difference between discrete

and continuous measures

Areas of parallelograms, trapezia, kites, rhombuses

and composite shapes

Volumes of prisms and composite solids

Surface area of simple solids:

cubes, cuboids, cylinders

Volume/capacity problems

G14: To include estimation of measures

G16: Area of cross-section x length of

prism

G17: Include compound measures

such as density.

Illustrate current postal rates; shoe sizes

G16: Find the area of this kite.

G17: Find the mass of water to fill this swimming pool.

Ex20 p28-29 (estimating measures) Ex13-15 p185-193 (area & perimeter) Ex23-25 p211-217 (Volume & surface area) Ex27-28 p79-82 (compound measures)

Clip 71 & 72 Circles

Clip 73 Area of compound shapes

Clip 120 & 121 surface area

Clip 122 & 177 Volume

Clip 178 Segments & Frustums

Clip 124 metric units

Clip 126 compound measures

Clip 176 Area of a triangle using Sine

rule

2-D representations of 3-D objects

C: Units

Appropriate degree of accuracy

Upper and lower bounds

Volume and surface area pyramid,

cone and sphere and combinations of

these (composite solids)

Length of circular arc, areas of sectors

and segments of a circle

Dimensions

Area of triangle 1

2 a b sinC

E: Area of triangle ss as bs c

where s 1

2a b c

Use of isometric paper

N13: Conversion between m and cm, m2 and cm2, m3 and cm3.

N15: Rounding sensibly for the context and the range of measures

used

N16: apply and interpret limits of

accuracy including UB & LB

G18: arcs & sectors

Notation [L] [T] [M] for basic dimensions

Heron's formula

Given the plan and side elevation, draw a 3D isometric diagram of the object.

l 9.57 m 9.565 l 9.575

Calculate the radius of a sphere which has the same volume as a solid cylinder of base radius 5 cm and height 12 cm.

G18: Calculate the shaded area given a = 5

Which of the following could be volumes?

rl, x3, ab+ cd, (𝑎𝑏)2

7𝑏; where (r, l, x, a, b, c, d, are lengths)

Find the area of these triangles

Ex25-26 p77-78 (metric & imperial)

Dec – Jan

CHRISTMAS HOLIDAYS

January (Y10)

8. DATA HANDLING

R: Two-way tables including timetables

and mileage charts

Frequency graphs

12 hour and 24 hour clock

If a train arrives at a station at 13:26 and the connection leaves at 14:12, how long do you have to wait?

p386-444

Unit 8 Teachers notes

Clip 85 Two-Way Tables (Grade D)

Clip 84 Questionnaires and Data

Collection (Grade D)

Questionnaires and surveys

C: Construct and interpret histograms

with unequal intervals

Frequency polygons

Sampling

Select and justify a sampling method to

investigate a population.

Time series & Moving Averages

For grouped data; equal intervals.

Include frequency polygons and

Histograms

Fairness and bias

Understand and use frequency density Know Area of bar = frequency

Different methods: random, quota,

stratified

Effect of sample size; reliability of conclusions

Identify trends in data over time

Calculate a moving average

Describe the trend in a time series graph

Use a time series graph to predict

futures (extrapolate)

Determine the number of pupils in each school year to represent their views

when the total representation is 20. The numbers of pupils in each year are year

Year 7 8 9 10 11 Number 122 118 100 98 62

choose (5) (5) (4) (4) (2)

Clip 134 Designing Questionnaires

(Grade C)

Clip 181 Histograms (Grade A* - A)

Clip 153 Moving Averages (Grade B)

Clip 183 Stratified Sampling (Grade A*

- A)

Substitution Cipher

(Y10)

9. DATA ANALYSIS

R: Problems involving the mean

Mean, median, modal class for grouped

data

Cumulative frequency graphs; median,

quartiles

Box plots

Including discrete and continuous data

Including percentiles, Inter-quartile

and semi-interquartile range

Use box plots to compare sets of data/distributions

The mean of 6 numbers is 12.3. When an extra number is added, the mean changes to 11.9. What is the extra number?

p386-444

Unit 9 Teachers notes

Clip 133 Averages From a Table

Clip 151 Cumulative Frequency

Clip 152 Boxplots (Grade B)

Olympic Triathlon

February (Y10)

10. EQUATIONS (A17 – A21)

R: Linear equations

Trial and improvement methods

Expansion of brackets

C: Simultaneous linear equations

Factorisation of functions

A17: One fraction and/or one bracket

NB: Trial & Improvement will not be

assessed but we will continue to teach

it – now called: A20: find approximate solutions to equations numerically using iteration

A19: Algebraic solutions

Solve 2x 3 7; 3x 4 x 18

Solve for x to 2 d.p. x3 7x 6 20 using trial & Improvement

Multiply out 2r 3s2r 5s

Solve x 4y 7 and x + 2y = 16; and also 1 linear & 1 quadratic

Ex20-24 p72-76 Ex1-6 p96-103 Ex6-8 p361-363 Ex15 p374

Clip 110 Trial & Improvement

Clip 105 Solving Equations

Clip 106 Forming Equations

Clip 115 Solving Simultaneous Eqs

Graphically

Clip 142 Simultaneous Linear Equations

Clip 140 Solving Quadratic Eqs by

Factorising

Clip 141 Difference of Two Squares

Clip 161 Solving Quadratics using the

Formula

Clip 162 Solve Quadratics by

Completing the Square

Completing the square

Quadratic formula

Multiplying and dividing algebraic

expressions

Equations leading to quadratics;

related problems

C: Iteration

Find approximate solutions to equations

numerically using iteration

(NB: Trial and improvement is not required)

A4: Common terms, difference of two

squares, trinomials, compound

common factor

Including max/min values

A18: solving quadratics

𝑥 =−𝑏 ± √𝑏2 − 4𝑎𝑐

2𝑎

A4: Permissible cancelling

A21: translate simple situations or

procedures into algebraic expressions

or formulae; derive an equation (or two simultaneous equations), solve

the equation(s) and interpret the

solution - Including equations from additions or subtractions of algebraic

fractions

Factorise (i) x4 1 (ii) x3 x2 x 1 (iii) 2x2 x 3

Solve (i) 4x2 – 1= 0 (ii) 4x2 9x 0 (iii) x2 x 6 (iv) x3 x2 x 1 0

By completing the square, find the minimum value of x2 4x 9.

Solve 5x2 x 3 0, giving answers to 2 d.p. use the Formula

Simplify 𝑥2−9

𝑥2−𝑥−6

Solve 𝑥

𝑥+1+

2𝑥

2𝑥−1=

39

20

This iterative process can be used to find approximate solutions to: x3 + 5x – 8 = 0

Post on Iteration by Colleen Young

(a) Use this iterative process to find a solution to 4 decimal places of x 3

+ 5x – 8 = 0. Start with the value x = 1

By substituting your answer to part (a) into x 3 + 5x − 8 and comment on the

accuracy of your solution to x 3 + 5x − 8 = 0

Mid-Feb

FEBRUARY HALF TERM

February (Y10)

11. FRACTIONS and

PERCENTAGES

R: Percentage and fractional changes

C: Compound interest

Appreciation and depreciation

Reverse percentage problems

(N10 – N12)

Discount, VAT, commission

Repeated proportional change

VAT on hotel bill of £200?

Find the compound interest earned by £200 at 5% for 3 years.

A car costs £5,000. It depreciates at a rate of 5% per annum. What is its value

after 3 years?

The price of a television is £79.90 including 17.5% VAT. What would have

been the price with no VAT?

Clip 47 Equivalent Fractions

Clip 48 Simplification of Fractions

Clip 49 Ordering Fractions

Clip 55 Find a Fraction of an Amount

Clip 56 & 57 arithmetic with Fractions

Clip 58 Changing Fractions to Decimals

Clip 139 Four Rules of Fractions

Clip 51 & 52 % of Amount

Clip 53 & 54 Change to a %

Clip 92 Overview of %

Clip 93 & 136 Increase/dec. by a %

Clip 137 Compound Interest

Clip 138 Reverse %

March (Y10)

12. NUMBER PATTERNS and

SEQUENCES

R: Find formula for the n th term of a linear sequence.

C: Recognise and use sequences of

triangular, square and cube numbers,

simple arithmetic progressions,

Fibonacci type sequences, quadratic

sequences, and simple geometric

progressions (rn where n is an integer,

and r is a rational number > 0 or a

surd) and other sequences

Find a quadratic formula for the n th

term of a sequence

C: Express general laws in

symbolic form

A23 – A25

If numbers ascend in 3’s, that’s the 3

x table = 3n.

Then find the number before the 1st term (=5), so, nth term is 3n+5

A24: recognise and use sequences of triangular, square and cube numbers,

simple arithmetic progressions,

Fibonacci type sequences, quadratic sequences, and simple geometric

progressions (rn where n is an integer,

and r is a rational number > 0 or a

surd) and other sequences

A25: nth term of a quadratic sequence

n th term in sequence 8, 11, 14, 17, ..., ..., ... is 3n + 5

Find n th term for

(i) 3, 6, 11, 18, ..., n2 2(ii) 6, 7, 10, 15, ..., n2 2n 7

Ex19 p119-122 (sequences) Ex20 p123-125 (nth term)

Clip 65 Generate a Sequence from Nth

term

Clip 112 Finding the nth term

More resources on Sequences GP sort card GP worksheet

Geometric Series (from Don Steward)

March - April

EASTER HOLIDAYS

April (Y11)

13. GRAPHS

R: Graphs in context, including conversion and travel graphs (s – t and v

– t) and an understanding of speed as a

compound unit

Scatter graphs and lines of best fit

Equation of straight line

Graphical solution of simultaneous equations

Graphs of common functions

C: Solve equations by graphical

methods

Tangent to a Circle

Recognise and use the equation of a circle with centre at the origin; find the

equation of a tangent to a circle at a given

point

A8 – A14

Draw and interpret

Gradient and area under graph a for polygon graphs only

Opportunities for use of ICT (Excel

can find equation for line of best fit)

Quadratic, cubic, reciprocal and

exponential equations

Calculate the speed for each part of the journey

Name the type of correlations illustrated below

Find equation of straight line joining points

(1, 2) and (4, 11).

Use the graph of y x2 5x to solve x2 5x 7.

Draw graphs of y x2 5x and y x3 to solve x2 5x x3.

Solve graphically 2x 5.

Use the graphs of y x2 5x and y 2x 3 to solve

x2 7x 3 0.

Ex21 p126 Ex23 p129 Q1-4 (straight line graphs) Ex 24 p131 (y = mx + c) Ex23 p129 Q5-8 (gradients)

Clip 87 Scatter Graphs (Grade D)

Clip 113 Drawing straight line graphs

Clip 114 Finding the Equation of a

straight line

Clip 116 Drawing Quadratic Graphs

Clip 117 Real-life Graphs

Clip 143 Understanding y=mx+c

Clip 145 Graphs of Cubes & Reciprocal

Functions

Clip 166 Gradients of Parallel and

Perpendicular Lines

Geogebra File for the equation of a Tangent to a Circle

May (Y11)

14. LOCI and TRANSFORMATIONS:

CONGRUENCE and SIMILARITY

R: Constructions of loci

Translation

Enlargements

G2: use the standard ruler and

compass constructions (perpendicular

bisector of a line segment, constructing a perpendicular to a

given line from/at a given point,

bisecting a given angle); use these to construct given figures and solve loci

problems; know that the perpendicular

distance from a point to a line is the shortest distance to the line

G7: About point(s) and line(s)

Using vector notation

Construct the locus of points equidistant from both lines

Draw image after translation (−32

)

Ex2-3 p171-176 (simple construction) Ex13 p310 (Translation & enlargement)

Clip 127 bisecting a line

Clip 128 perpendicular to a line

Clip 129 bisecting an angle

Clip 130 Loci

Clip 74-77 Transformation

Clip 171 Negative scale factor

C: Enlargements

Reflections

Rotations

Combination of two transformations

Congruence – conditions for triangles

Similarity – similar triangles, line, area

and volume ratio

G7: Positive integers and simple

fractions for scale factor

G7: Negative scale factor

Finding the centre of enlargement

Reflection in y = x, y = – x, y = c, x =

c

Finding the axis of symmetry

Rotation about any point 90o , 180o in

a given direction Finding the centre of rotation

G5: SSS SAS AAS RHS

G19: apply the concepts of

congruence and similarity, including

the relationships between lengths, areas and volumes in similar figures

Enlarge diagram by scale factor 1

3 ,

centre A (inside triangle)

Find the Equations of the mirror lines

Prove that ▲ABX & ▲CDX are congruent

Calculate (i) x and y (ii) ratio of

areas ABE and BCDE

Two similar cones have heights 100cm & 50cm.

The volume of the smaller cone is 1000cm3, what is the volume of the larger cone?

E.g. Persil is available in 800 g and 2.7 kg boxes which are similar in shape. The smaller box uses 150 cm3 of card. How much card is needed for the larger

box?

Ex12 p308 (reflection & rotation) Ex14 p313 (combined transformations) Ex6 p169 (congruence) Ex29-30 p227 (lengths & similarity) Ex31 p233(areas of similar shapes) Ex32 p237 (volumes of similar shapes0

Clip 123 Similar Shapes

Clip 124 Dimensions

Clip 149 Similar Shapes

Clip 179 Congruent Triangles

May END OF YEAR 10 EXAMS This will be used to help set for Y11

May – Jun

MAY HALF-TERM

Mid-June (Y11)

15. VARIATION: DIRECT and

INVERSE

R: Direct and inverse variation

C: Functional representation

Graphical representation

R13 – R14

y x , y x2 , y x3 , y 1

𝑥;

y 1

𝑥2 y 1

𝑥3y√𝑥y 1

√𝑥

𝑦 ∝ 1

√𝑥𝑛

For the following data, is y proportional to x?

x 3 4 5 6

y 8 10 12 14

If y is proportional to the square of x and y 9 when x 4, find the positive

value of x for which y 25.

Ex12-13 p263-267 P267-269 (common curves to discuss)

Clip 159 Direct & Inverse Proportion

(Y11)

16. INEQUALITIES

R: Solution of linear inequalities and simple quadratic inequalities

C: Solve linear inequalities in one or

two variable(s), and quadratic

inequalities in one variable; represent

the solution set on a number line, using

set notation and on a graph

C: Graphical applications

E: Linear programming

A22: solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph

Locating and describing regions of graphs

Solve for x: (a) 5x 2 x 16 (b) x2 25

Find the range of values of x for which x2 - 3x - 10 ≤ 0

Sketch lines y x 1, y 3 x and x 2;

hence, shade the region for which: y x 1, y 3 x and x 2.

Ex9-10 p255-258 (solving) Ex11 p259-260 (regions)

See Core 1 LiveText for examples

Clip 108 Inequalities

Clip 109 Solving Inequalities

Clip 144 Regions

Post on Inequalities Collection of Resources

ICT tools for Inequalities: Geogebra 1 / Geogebra 2 / Desmos /

echalk

Jun

START NEW TIMETABLE

Year 11

Mid-June- July (Y11)

17. USING GRAPHS

C: Transformation of functions

C: Find the approximate area between

a curve and the horizontal axis.

C: Construct and use tangents to

estimate rates of change & Interpret

the gradient at a point on a curve as

y f x a, y f xa

y k f x, y f k x

Interpretation of area Drawing trapezia; trapezium rule

Including max/min points

Applications to travel graphs

For given shape of y f x, sketch

y f x2 , y 1

2 f x , y f x 1

Estimate the area between the curve y x2 1, the x-axis and the lines x 1 and

x 3.

A car accelerates so that its velocity is given by the formula

Ex16-17 p378-381 Sections 17.2 (MEP practice book – area under graphs)

See Core 1 LiveText for examples

Clip 167 Transformations of functions

Clip 168 Graphs of trig fns (review)

Clip 169 Transformations of Trig fns Quadratic Graphs Resources Functions resources Heinemann Live Textbook C3_Ch2 Functions Audit

the instantaneous rate of change; apply

the concepts of average and

instantaneous rate of change (gradients

of chords and tangents) in numerical,

algebraic and graphical contexts

C: Finding coefficients

E: Quadratic Graphs

Identify and interpret roots, intercepts,

turning points of quadratic functions

graphically; deduce roots algebraically

and turning points by completing the

square

E: Functions

Interpret simple expressions as functions

with inputs and outputs; interpret the reverse process as the ‘inverse function’;

interpret the succession of two functions

as a ‘composite function

E: Use of logarithms to produce straight line graphs

Speed from a distance/time graph.

Acceleration and distance from a

velocity/time graph.

Find values of a and b in y ax2 b by plotting y against x2.

Find values of p and q from the graph

of y= pqx

v 10 0.3t2 . Sketch the velocity/ time graph for t 0 to t 10, and estimate

the v distance travelled by the car. Also estimate the acceleration when t 5.

The functions f and g are such that: f(x) = 1 – 5x and g(x) = 1 + 5x

(a) Show that gf(1) = – 19

(b) Prove that f–1(x) + g–1(x) = 0 for all values of x.

July – Aug

SUMMER HOLIDAYS

September (Y11)

18. 3-D GEOMETRY

C: Length of slant edge of pyramid

Diagonal of a cuboid Angles between

two lines, a line and a plane, two planes

Producing 2-D diagrams from 3-D

problems

Pythagoras, sine and cosine rules

ABCDE is a regular square-based pyramid of vertical height 10 cm and base,

BCDE, of side 4 cm. Calculate

(i) the slant height of the pyramid

(ii) the angle between the line AB and the base

(iii) the angle between one of the triangular faces and the square base.

October (Y11)

19. VECTORS

C: Vectors and scalars

Sum and difference of vectors

Resultant vectors

Components

Multiplication of a vector by

a scalar

Applications of vector

G24 – G25

G24: Use Vector notation (𝑎𝑏), 𝐴𝐵⃗⃗⃗⃗ ⃗ or

a

Students should think of Vectors as

making a journey from A to B and finding alternative routes.

G25: apply addition and subtraction of

vectors, multiplication of vectors by a

A plane is flying at 80 m/s on a heading of 030However, a wind of 15 m/s is blowing from the west. Determine the actual velocity (speed and bearing) of the

plane.

𝑂𝐴⃗⃗⃗⃗ ⃗ = a and 𝐴𝐵⃗⃗⃗⃗ ⃗ = b

Write down, in terms of a and b,

(i) 𝑂𝐵⃗⃗ ⃗⃗ ⃗, (ii) 𝑂𝐶⃗⃗⃗⃗ ⃗, (iii) 𝐴𝐶⃗⃗⃗⃗ ⃗, (iv) 𝐶𝐵⃗⃗⃗⃗ ⃗

Ex15 p317 (addition & scalar multiplication)

See Mechanics 1 Chapter 1_LiveText for examples

Clip 180 Vecors

methods to 2-dimensional

geometry

E: Know and use commutative

and associative properties of

vector addition

scalar, and diagrammatic and column

representations of vectors and use

vectors to construct geometric

arguments and proofs

Ex16 (vector geometry)

Mid-Oct

OCTOBER HALF TERM

November

20. AQA Level 2 Further Maths

Ch8. Calculus

Hand out the Level 2 Further maths

Workbooks which they work

through. The workbook stays in class

See AQA Level 2 FM specification

Collins Text

(AQA) & the OCR Text for

Add Maths

Collins Text (AQA) & the

OCR Text for Additional Maths Buy each student a CGP Workbook (to

write in)

December Ch1. Number and Algebra I

Ch2, Algebra II

Ch3. Algebra III

December CHRISTMAS HOLIDAYS

January &

February Ch4. Algebra IV

Ch5. Coordinate Geometry

Ch6. Geometry I

Mid-February

FEBRUARY HALF TERM

March Ch7. Geometry II

Ch9. Matrices Start setting Past Papers as

homework

Mar EASTER HOLIDAYS

Intervention Set 4 x Past Papers as homework over Easter & get them to complete their Level 2 Workbooks and their GCSE Maths Workbooks

April Revision & Intervention Past Papers & Intervention

Review all work for both Edexcel GCSE Mathematics & AQA Level 2

Mathematics

Level 2 Past Papers

May Study Leave Intervention & Revision

June

EXAMS, EXAMS, EXAMS Revision Sessions on-going

NOTES FOR THE TEACHER

Resources: Teacher support material for each unit, inc. teaching notes, mental tests, answers, lesson plans, revision tests and additional activities is available online on the

MEP website: http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm

Homework: a variety of tasks can be set ranging from short Q&A to extended pieces of investigation work. When you set

homework – you MUST mark it and record it. You could also ask students to make summary notes of each topic to lay foundations

for independent study. Fronter has been loaded with a wealth of homework practice which students should be directed to by you.

Lesson planning & Expectations: You are expected to have extremely high expectations of all your students at all times – refer to

the diagram. This means stretching the least able as much as the most able. No exceptions.

Closing the Gap: Know your students, Plan effectively, Enthuse & Inspire, Engage & Guide, Feedback appropriately & Evaluate

together

FORMULAE SHEET

Perimeter, area, surface area and volume formulae

Where r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone:

Curved surface area of a cone = rl

Surface area of a sphere = 4 r 2

Volume of a sphere = 3

4 r

3

Volume of a cone = 3

1 r

2h

Kinematics formulae

Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t = 0 and t is time taken:

v = u + at

s = ut + 21 at2

v2 = u2 + 2as