Add Maths T5

8/6/2019 Add Maths T5

http://slidepdf.com/reader/full/add-maths-t5 1/21

YEARLY TEACHING PLAN FOR ADDITIONAL MATHEMATICS FORM 5

WEEK/S LEARNING OBJECTIVES

Students will be taught to…LEARNING OUTCOMES

Students will be able to…SUGGESTED TEACHING

AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

ALGEBRAIC COMPONENT

A6: PROGRESSION

1. Understand and use theconcept of arithmetic

progression.

Level 1

1.1 Identify characteristics

of arithmetic progressions.

1.2 Determine whether

given sequence is anarithmetic progression.

Level 2

1.3 Determine by usingformula:

a) specific terms in arithmetic progressions;

b) the number of terms inarithmetic progressions.

Use example from real-lifesituations, scientific or graphingcalculator software to explorearithmetic progressions.

Begin withsequences tointroducearithmetical andgeometrical

progressions.

Include examples inalgebraic form.

Patience anddiligence.

Include the use of the formula

1−−= nnn S S T

Careful, systematicand rational.

Coloured blocks, blackboard,text book,chards,scientificcalculator,work sheet,list of formulae.

Identifying patterns,conceptualizing andcharacterizing

Evaluating,analyzing andworking

backwards

1






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

2. Understand and use theconcept of geometric

progression.

1.4 Find:a) the sum of the first n terms of

arithmetic progressions. b) the sum of a specific number

of consecutive terms of arithmetic progressions.

c) the value of n, given the sumof the first n terms of arithmetic progressions.

Level 3

1.5 Solve problems involvingarithmetic progressions.

Level 1

2.1 Identify characteristics of geometric progressions.

2.2 Determine whether a givensequence is a geometric

progression.

Use example from real-lifesituations, scientific or graphingcalculator software to exploregeometric progressions.

Include problemsinvolving real-lifesituations.

Rational, careful,independent and co-operation

Include examples inalgebraic form.

Independent andco-operation

Problemsolving andinterpreting

OHP/CD/Worksheet

Difference or similaritiesandidentifying

patterns

2






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

Level 2

2.3 Determine by using formula:a) specific terms in geometric

progressions,

b) the number of terms ingeometric progressions.

2.4 Find:

a) the sum of the first n terms of geometric progressions;

b) the sum of a specific number of consecutive terms of

geometric progressions.c) the value of n, given the sum

of the first n terms of geometric progressions.

Level 3

2.5 Find:a) the sum to infinity of

geometric progressions.

b) the first term or common

ratio, given the sum toinfinity of geometric

progressions.

Careful and

systematic

Discuss:

As ,∞→n

0→n

r then

r

aS

−

=∞

1

nS read as “sum

to infinity”.

Include recurringdecimals. Limit to 2recurring digitssuch as 0.3, 0.15, .…

Evaluating and

analyzing

Estimating,finding all

possiblesolution and

predicting

3






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

2.6 Solve problems involvinggeometric progressions.

Exclude:

a) combination of arithmetic

progressions

and geometric progressions.

b) Cumulativesequences such

as, (1), (2, 3),(4, 5, 6), (7, 8,9, 10), …

Rational andsystematic

ALGEBRAIC COMPONENT

A7: LINEAR LAW

1. Understand and use theconcept of lines of best fit.

2. Apply linear law to non-

Level 1

1.4 Draw lines of best fit byinspection of given data.

Level 2

1.5 Write equations for lines of best fit.

1.6 Determine values of variables form:

a) lines of best fit b) equations of lines of

best fit.

Level 3

Use example from real-lifesituations to introduce theconcept of linear law.

Use graphing calculators or computer software such asGeometer’s Sketchpad toexplore lines of best fit.

Respect, Fairness,careful

Limit data to linear relations betweentwo variables.

Aids:

TeachingCourseware

Geometer’sSketchpad

GraphingCalculator

CCTS:

IdentifyingRelationship

DrawingGraph

4






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

linear relations. 2.1 Reduce non-linear relations to

linear form.

2.2 Determine value of constants of

non-linear relations given:a) lines of best fit

b) data

2.3 Obtain information from:c) lines of best fitb) equations of lines of best fit.

Problem

Solving

CALCULUS COMPONENT

C2: INTEGRATION

1. Understand and use theconcept of indefiniteintegral.

Level 1

1.1 Determine integrals by reversingdifferentiation.

1.2 Determine integrals of axn ,where a is a constant and n is aninteger, n ≠ - 1.

1.3 Determine integrals of algebraicexpressions.

1.4 Find constants of integration, c,in indefinite integrals.

Level 2

Use computer software such asGeometer’s Sketchpad toexplore the concept of integration.

Systematic

Confidence

Patience

Careful

AID :

ColourfulWhite BoardMaker,

Text Book,

Chart,

OHP

5






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

1.5 Determine equations of curves

from functions of gradients.

1.6 Determine by substitution the

integrals of expressions of theform (ax + b)n , where a and b

are constants, n is an integer andn ≠ -1.

2. Understand and use theconcept of definite integral.

Level 2

2.1 Find definite integrals of

algebraicexpressions.

Level 3

2.2 Find areas under curves as thelimit of a sum of areas.

2.3 Determine areas under curvesusing formula.

2.4 Find volumes of revolutions when

region bounded by a curve isrotated completely about the

a) x- axis

b) y- axis

as the limit of a sum of volumes.2.5 Determine volumes of revolutions

using formula.

Use scientific or graphing

calculators to explore theconcept of definite integrals.

Use computer software andgraphing calculators to exploreareas under curves and thesignificance of positive andnegative values of areas.

Use dynamic computer softwareto explore volumes of

revolutions.

Systematic

Confidence

Patience

Careful

CCTS :

Identifyingrelationship,

Interpreting,

MakingConclusion,

GeneratingIdea,

6






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

GEOMETRIC

COMPONENT

G2: VECTORS

1. Understand and use theconcept of vectors.

Level 1

1.1 Differentiate between vector andscalar quantities .

1.2 Draw and label directed linesegments to represent vectors.

Level 2

1.3 Determine the magnitude and

direction of vectors represented by directed line segments.

1.4 Determine whether two vectorsare equal.

1.5 Multiply vectors by scalars.1.6 Determine whether two vectors

are parallel.

Use example from real-life

situations and dynamiccomputer software such as

Geometer’s Sketchpad toexplore vectors.

Systematic and

cooperative.

Use notations:

Vector:~

a , a, AB.

Magnitude:

~

a , AB , |a|, |

AB|

Zero vector:~

0

Emphasise that azero vector has a

magnitude of zero.Emphasise negative

vector:

- AB = BA

Includea) collinear points

b) non-parallel

non-zero vectors.

Teaching

courseware,GSP , text

books andworkbooks.

7






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

2. Understand and use theconcept of addition andsubtraction of vectors .

3. Understand and use vectorsin the Cartesian plane

Level 12.1 Determine the resultant vector of

two parallel vectors.

Level 2

2.2 Determine the resultant vector of two non-parallel vectors using :

a) triangle law b) parallelogram law

2.3 Determine the resultant vector of three or more vectors using the

polygon law .

Level 3

2.4 Subtract two vectors which are :a) parallel

b) non-parallel.2.5 Represent vectors as a

combination of other vectors.2.6 Solve problems involving

addition and subtraction of vectors.

Level 1

3.1 Express vectors in the form

a) j yi x +

Use real-life situations andmanipulative material to exploreaddition and subtraction of

vectors..

Use computer software toexplore vectors in the Cartesian

plane.

Patience, rational,careful, systematicand diligence.

Emphasise:

)(~~~~baba −+=−

Relate unit vector i and j to Cartesian

coordinates.Emphasis:

GSP

Teaching

courseware

ScientificCalculator

Textbook WorksheetDifference andSimilarities

ProblemSolvingClassifying

GSP

Teachingcourseware

Scientific

Calculator

8






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

b)

y

x

3.2 Determine magnitudes of vectors

Level 2

3.3 Determine unit vectors in givendirections.

3.4 Add two or more vectors.3.5 Subtract two vectors.3.6 Multiply vectors by scalars.

Level 33.7 Perform combined operations on

vectors.3.8 Solve problem involving vectors.

For learning outcomes 3.2 to 3.7

all vectors are given in the form

j yi x + or

y

x

Limit combined operations toaddition, subtraction andmultiplication of vectors byscalars.

Vectors i =

0

1

and

Vectors j =

1

0

Rational

Systematic

Co-operation

Textbook

Worksheet

Difference and

Similarities

ProblemSolving

Classifying

9






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

TRIGONOMETRIC

COMPONENT

T2: TRIGONOMETRIC

FUNCTIONS

1. Understand and use theconcept of positive and

negative anglesmeasured in degreesand radians.

2. Understand and use thesix trigonometricfunctions and of anyangles.

Level 1

1.1 Represent in a Cartesian planeangles greater than 360° or 2π

radians for:a) Positive angles

b) Negative angles

Level 1

2.1 Define sine , cosine and tangentof any angle in a Cartesian

plane.

2.2 Define cotangent, secant andcosecant of any angle in aCartesian plane.

Level 2

2.3 Find values of six trigonometricfunctions of any angle.

2.4 Solve trigonometric equations.

Introduce the four quadrants inthe Cartesian plane.

Teacher explain clockwise andanticlockwise direction to drawnegative angles and positiveangles.

Use dynamic computer software such as a Geometer Sketchpad to explore angles inCartesian plane.

Use dynamic computer softwareto explore trigonometricfunctions in degrees and radians

Use scientific or graphing

calculators to exploretrigonometric functions of anyangle.

Careful, rationaland hardworking.

Use unit circle todetermine the sign

of trigonometricratios.

Emphasise:Sin θ = cos (90- θ )cos θ = sin (90- θ )tan θ = cot (90- θ )cosec θ = sec(90-θ )sec θ = cosec(90-θ )cot θ = tan (90- θ )

Emphasise the useof triangles to findtrigonometric ratiosfor special angles30°,45° and 60°.

Use angles in

a) degrees b)radians, in term

Identifyingrelationship,

Drawingdiagram,

Using of ICT,

TeachingCourseware,Projector AndGeometer’sSketchpad.MakingInference,Finding all

possiblesolution.

10






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

3. Understand and usegraphs of sine, cosineand tangent functions.

Level 2

3.1 Draw and sketch graphs of trigonometric functions.

a. y = c + a sin bx,b. y = c + a cos bx

c. y = c + a tan bxwhere a, b, and c are constants and

b> 0.

3.2 Determine the number of solutions to a trigonometricequation using sketchedgraphs.

3.3 Solve trigonometric equationusing drawn graphs.

Use examples from real-lifesituations to introduce graphsof trigonometric functions.

Use graphing calculators anddynamic computer softwaresuch as geometer’s sketchpadto explore graphs of trigonometric functions.

Discuss minimum andmaximum value of sin and cosfunctions.

Discuss properties of graphs of

trigonometric functions:a. y = c + a sin bx,b. y = c + a cos bxc. y = c + a tan bx

where a, b, and c are constantsand b> 0.

of π.

Emphasise thecharacteristics of

sine, cosine andtangent graphs.

Include

trigonometricfunctions involvingmodulus.

Excludecombinations of trigonometricfunctions.

STATISTICS COMPONENT

S2: PERMUTATIONS AND

11






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

COMBINATIONS

1. Understand and use theconcept of permutations.

2. Understand and use theconcept of Combinations.

Level 11.1 Determine the total number of

ways to perform successive

events using multiplication rule.1.2 Determine the number of

permutations of n differentobjects.

Level 2

1.3 Determine the number of permutations of n different

objects taken r at a time

Level 3

1.4 Determine the number of permutations of n differentobjects for given conditions.

1.5 Determine the number of permutations of n differentobjects taken r at a time for given conditions.

Level 22.1 To determine the number of

combination of r objects chosenfrom n different objects.

Level 3

2.2 To determine the number of

combinations of r objects for given condition.

Use manipulative materials toexplore multiplication rule. If

A event occurs in r ways, and B event occurs in s ways.

The total number of ways for event A and B to occur

successively is r x s ways

To expand the concept of permutations by listing down

all the possible arrangementsnotation.n! = n(n-1)(n-2)(3)(2)(1)0! = 1

Use real-life situations andcomputer software such asspreadsheet to explore

permutations

To expand the concept of combination of r objects from nobjects by listing down all the

possible selections.

Use examples to illustrate

nCr =

!r

P r

n

Rational andcareful

Systematic

Careful

Scientificcalculator

CCTS

Arranging in

order Identifying patternsAnalyzing

Problemsolving

Difference or similarities

Scientific

calculator

12






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

STATISTICS COMPONENT

S3 : PROBABILITY

1. Understand and use theconcept of probability.

Level 1

1.1 Describe the sample space of anexperiment.

1.2 Determine the number of outcomes of an event.

1.3 Determine the probability of anevent.

Use real-life situations tointroduce probability.

Use manipulative materials,

computer software and scientificor graphing calculator to exposethe concept of probability.

Use set notations.

Discuss:a) classical probability(theoretical

probability)

b) subjective probability

c) relative

frequency probability(experimental

probability).

Emphasise:

Only classical probability is usedto solve problems.

Computer Software

Reference books

CCTS:- Relate- Applyingconcept-Problemsolving

13






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

2. Understand and use theconcept of probability of mutually exclusive events.

3. Understand and use theconcept of probability of

Level 21.4 Determine the probability of two

events:

d) A or B occurring;

e) A and B occurring.

Level 2

2.1 Determine whether two eventsare mutually exclusive.

Level 3

2.2 Determine the probability of twoor more events that are mutuallyexclusive.

Level 3

3.1 Determine whether two eventsare independent

Use manipulative materials andgraphing calculator to explorethe concept of probability of mutually exclusive events.

Use computer software tostimulate experiment involving

probability of mutually

exclusive events.

Use manipulative materials andgraphing calculators to explore

Emphasise:P(A U B) = P(A) +P(B) – P (A ∩ B)

using Venndiagrams.

-Cooperation- Patient- Accuracy

Include events thatare mutuallyexclusive andexhaustive.

Limit to threemutually exclusiveevents.

-Cooperation- Patient- Accuracy

Include treediagrams.

Reference books

Courseware

CCTS:- Relate

- Find value- Identify

pattern- Predicting- Classifying

Computer software

14






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

independent events. 3.2 Determine the probability of two

independent events3.3 Determine the probability of

three independent events

the concept of probability of

independent events.

Use computer software to

stimulate experiments involving probability of independent

events.

-Cooperation- Patient

- Accuracy

Reference books

CCTS:- Relate

- Applyingconcept

- Problemsolving

STATISTICS

COMPONENT

S4 : PROBABILITY

DISTRIBUTIONS

Understand and use the

concept of binomialdistribution .

Level 1

1.1 List all possible values of adiscrete random variable

1.2 Determine the probability of an

event in a binomial distribution.

Level 2

1.3 Plot binomial distribution graphs

1.4 Determine mean , variance andstandard deviation of a binomialdistribution.

Use real-life situations tointroduce the concept of

binomial distribution

Use graphing calculators and

computer software to explore binomial distribution.

Find out the difference or similarities of

P( x ≥ a ) = 1 – P ( x < a )

Identifying relationship between

FairnessRationalHonestyIndependent

For learning

outcomes 1.2 and1.4 , derivation of formulae notrequired.

Include thecharacteristicsof Bernoullitrials

Coin

Dice

Marble

15






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

2. Understand and use theconcept of normal

distributions

Level 31.5 Solve problems involving

binomial distributions.

Level 1

2.1 Describe continuous randomvariables using set notations.

2.2 Find probability of z-values for Standard normal distributions.

Level 2

2.3 Convert random variable of normal distributions, X, tostandardised variable, Z.

2.4 Represent probability of an eventusing set notation.

2.5 Determine probability of an event

2.6 Solve problem involving normaldistributions.

p and q

p = 1 – q

Use real-life situations andcomputer software such as

statistical packages to explorethe concept of normaldistributions.

Co-operation,Fairness,

Careful,Hardworking,Rational.

Discusscharacteristics of :

a) normaldistribution graphs.

b) standard normaldistribution graphs.

Z is calledstandardised

variable.

Integration of normal distributionfunction todetermine

probability is not

required.

Blackboard,text book,

scientificcalculator,work sheet,list of

formulae.Teachingcourseware,Interpreting,Identifyingrelations,MakingInference,Using of ICT,Problemsolving,

Mathematicalcommunication, Statisticaltable,Evaluating.

16






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

SCIENCE AND

TECHNOLOGY PACKAGE

AST2: MOTION ALONG A

STRAIGHT LINE

1 Understand and use theconcept of displacement.

Level 1

1.1 Identify direction of displacement of a particle from a

fixed point.

Level 2

1.2 Determine displacement of a

particle from a fixed point.

Level 3

1.3 Determine the total distancetraveled by a particle over atime interval using graphicalmethod.

Use real-life examples,

graphing calculators andcomputer software such asGeometer’s Sketchpad toexplore displacement.

Emphasize the use

of the followingsymbols:s = displacement,v = velocity,

a = accelerationt = timewhere s, v and a arefunctions of time.

Emphasise thedifferences betweendisplacement anddistance.

Discuss positive,

negative and zerodisplacements.

Include the use of number line.

Careful, systematic,

rational,confidence.

Coloured

pens, blackboard,text book,charts,

scientificcalculator,worksheet, listof formulae.

Interpreting,Identifyingrelations,MakingInference,translating,

Identifying patterns,comparing andcontrasting,drawingdiagram,working

backwards.

17






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

2 Understand and use theconcept of velocity

3 Understand and use theconcept of acceleration

Level 2

2.1 Determine velocity function of a particle by differentiation .

2.2 Determine instantaneous velocityof a particle.

Level 3

2.3 Determine displacement of a particle from velocity function by

integration.

Level 2

3.1 Determine acceleration functionof a particle by differentiation.

Level 3

3.2 Determine instantaneousacceleration of a particle.

3.3 Determine instantaneous velocity

of a particle from accelerationfunction by integration.

Use real-life examples, graphingcalculators and computer

software such as Geometer’sSketchpad to explore the

concept of velocity.

Use real-life examples, graphingcalculators and computer software such as Geometer’sSketchpad to exploreacceleration.

Emphasise velocityas the rate of

change of displacement.

Include graphs of velocity functions.Discussa)uniform velocity.

b)Zeroinstantaneousvelocity.c)positive velocityd)negative velocity.

Careful,systematic, rational,confidence.

Emphasiseacceleration as therate of change of velocity.Discuss: a)uniformacceleration

b)zero acceleration

c)positiveacceleration

Using of ICT,

Problemsolving,Mathematical

communication

18






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

3.4 Determine displacement of a

particle from accelerationfunction by integration.

3.5 Solve problems involving motion

along a straight line.

.

d)negative .

acceleration.

Careful,

systematic, rational,confidence

SOCIAL SCIENCE

PACKAGE

ASS2 : LINEAR PROGRAMMING

1. Understand and use theconcept of graphs of linear inequalities

Level 1

1.1 Identify and shade the region onthe graph that satisfies a linear inequality.

1.2 Find the linear inequality thatdefines a shaded region.

Level 2

1.3 Shade region on the graph thatsatisfies several linear inequalities.

1.4 Find linear inequalities thatdefine a shaded region.

Use example from real-lifesituations, scientific or graphingcalculator software.

Emphasize the useof solid lines anddashed lines

limit to regionsdefined by amaximum of 3linear inequalities

(not including the x -axis and

y -axis)

Co-operation,Rational,

Systematic,Hardworking

Whiteboard,text book,coloredmarker pens,color pencil,graph paper,graph chart,scientific

calculator,dynamiccomputer software,GSP,worksheet.

Identifyingrelationships

19






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

2. Understand and use the

concept of linear programming.

Level 3

2.1 Solve problems related to linear

programming by :

a) Writing linear inequalitiesand equation describing asituation.

b) Shading the region of

feasible solution.c) Determining and drawing the

objective functionk byax =+ where ba,

and k are constants.

d) Determining graphically theoptimum value of the

objective function.

Use real-life examples, graphing

calculators and dynamiccomputer software such as

Geometer’s Sketchpad to programming.

Constructivism

Cooperative learning.

Optimum valuesrefer to maximumor minimum values

Include the use of vertices to find the

optimum valueCo-operation,diligence, courage,cleanliness,systematic,confidence,

patience, carefuland hardworking

and patterns.

Characterizingandtranslating.

Whiteboard,

text book,colored

marker pens,color pencil,set square ,rulers, graph

paper, graphchart,scientificcalculator,graphiccalculator,dynamiccomputer software,GSP,worksheet.

Identifyingrelationshipand patterns.Analyzing,drawingdiagram and

interpreting.Problem

20






AND LEARNING

ACTIVITIES

VALUES AND

POINTS TO

NOTE

TEACHING

Aids / CCTS

solving and

makingconclusions.

21

Add Maths T5

Documents

Transcript of Add Maths T5