2008 form 5 am teaching scheme

8/3/2019 2008 Form 5 Am Teaching Scheme

1/11

FORM 5 ADDITIONAL MATHEMATICS TEACHING SCHEME 2012

SMK TUNKU PUTRA

BY RABIHAH BINTI RAMLI

FIRST SEMESTER

WEEKS/

DATES

LEARNING

AREA

LEARNING

OBJECTIVES

LEARNING OUTCOMES CCTS NOTES

Wk 1 3

5/1 24/1

Chapter 1.

Progressions

1. Understand anduse the concept of

arithmetic

progression.


geometric

progression

1.1 Identify characteristics of arithmetic

progressions.

1.2 Determine whether a given sequence is an

arithmetic progression.

1.3 Determine by using formula:

a) specific terms in arithmeticprogressions;

b) the number of terms in arithmetic

progressions.

1.4 Find:

a) sum of the first n terms of arithmetic

progressions.

b) sum of a specific number of consecutive

terms of arithmetic progressions.

c) value of n, given the sum of the first n

terms of arithmetic progressions.1.5 Solve problems involving arithmetic

progressions.

2.1 Identify characteristics of geometric

progressions.

2.2 Determine whether a given sequence is a

geometric progression.

Comparing &

contrasting

Identifying relations

Classifying

Interpreting

Use examples from

real-life situations &computer software to

explore arithmetic

progressions

1


2/11

2.3 Determine by using formula:

a) specific terms in geometric progressions;

b) number of terms in geo progressions.

2.4 Find:

a) sum of the first n terms of

geometric progressions;

b) sum of a specific number of consecutiveterms of geometric progressions.

c) value ofn, given the sum of the first nterms of geometric progressions.

2.5 Find:a) sum to infinity of geometric

progressions.

b) first term or common ratio, given the

sum to infinity of geometric

progressions.2.6 Solve problems involving geometric

progressions.

Use examples from

real-life situations &

computer software toexplore geometric

progressions

Wk 4- 52/2 14/2

Chapter 2.

Linear law1. Understand anduse the concept of

lines of best fit.

2. Apply linear lawto non-linear relations

1.1 Draw lines of best fit by inspection of

given data.

1.2 Write equations for lines of best fit.

1.3 Determine values of variables from:a) lines of best fit

b) equations of lines of best fit.

2.1 Reduce non-linear relations to linear form.

2.2 Determine values of constants of non-linearrelations given:

a) lines of best fit ,

b) data.

2.3 Obtain information from:a) lines of best fit

b) equations of lines of best fit

Interpreting

Drawing graphs


Use examples from

real-life situations

to introduce the

concept of linearlaw.

Use GeometersSketchpad to

explore lines of

best fit.

2


3/11

Wk 6 821/2 7/3

Chapter 3.

Integration1. Understand anduse the concept of

indefinite integral.


definite integral

1.1 Determine integrals by reversing

differentiation.

1.2 Determine integrals of nax , where a is a

constant and n is an integer, n 1.1.3 Determine integrals of algebraic expressions.

1.4 Find constants of integration, c, in indefinite

integrals.1.5 Determine equations of curves from functions

of gradients.

1.6 Determine by substitution the integrals of

expressions of the form (ax+b)n, where a

and b are constants, n is an integer and n

1.

2.1 Find definite integrals of algebraicexpressions.

2.2 Find areas under curves as the limit of a

sum of areas.

2.3 Determine areas under curves using

formula.

2.4 Find volumes of revolutions when region

bounded by a curve is rotated 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.

Interpreting

Drawing graphs


Drawing diagrams

Working out mentally Comparing and

contrasting

Wk 9

9/3 14/3

UJIAN SETARA 1

First Examination : All Form 4 topics, Progressions, Linear law

3


4/11

Discussion of First Examination questions

15/3 22/3 Mid-Semester 1 break

Wk 10-1223/3 3/4

Chapter 5.

Vectors


vector.

2. Understand anduse the concept ofaddition and

subtraction of vectors

3. Understand anduse vectors in the

Cartesian plane.

1.1 Differentiate between vector and scalar

quantities.

1.2 Draw and label directed line segments torepresent vectors.

1.3 Determine the magnitude and direction of

vectors represented by directed line

segments.1.4 Determine whether two vectors are equal.

1.5 Multiply vectors by scalars.1.6 Determine whether two vectors are parallel.

2.1 Determine the resultant vector of two parallelvectors.

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.

2.4 Subtract two vectors which are:

a) parallelb) non-parallel.

2.5 Represent vectors as a combination of othervectors.

2.6 Solve problems involving addition andsubtraction of vectors.

3.1 Express vectors in the form:

a)~

~

jyix +


Drawing diagrams

Comparing and

contrasting

Classifying

Translating

Discuss first exam

Use examples from

real-life situations

and Geometers

Sketchpad to explore

vectors.

4


5/11

b)

y

x.

3.2 Determine magnitudes of vectors.

3.3 Determine unit vectors in given directions.

3.4 Add two or more vectors.

3.5 Subtract two vectors.

3.6 Multiply vectors by scalars.

3.7 Perform combined operations on vectors.

3.8 Solve problems involving vectors.

Wk 13 14

6/4 17/4

17w

Chapter 6.

Permutations

andcombinations

1. Understand and

use the concept of

permutation.

2. Understand and

use the concept of

combination.

1.1 Determine the total number of ways to

perform successive events using

multiplication rule.1.2 Determine the number of permutations ofn

different objects.

1.3 Determine the number of permutations ofn

different objects taken rat a time.


different objects for given conditions.


different objects taken rat a time for given

conditions.

2.1 Determine the number of combinations

ofrobjects chosen from n different

objects.

2.2 Determine the number of combinations r

objects chosen from n different objects

for given conditions.


Translating

Interpreting

Working out mentally

Comparing and

contrasting

5


6/11

Wk 15 16

20/4 30/4

Chapter 7.

Probability

1. Understand and

use the concept of

probability.


probability of

mutually exclusive

events.


probability ofindependent events.

1.1 Describe the sample space of an experiment.

1.2 Determine the number of outcomes of an

event.

1.3 Determine the probability of an event.

1.4 Determine the probability of two events:

a) A orB occurring

b) A andB occurring.

2.1 Determine whether two events are mutually

exclusive.

2.2 Determine the probability of two or more

events that are mutually exclusive.

3.1 Determine whether two events are

independent.

3.2 Determine the probability of twoindependent events.

3.3 Determine the probability of three

independent events.

Comparing &contrasting


Interpreting

Drawing diagrams

Working out mentally Classifying

Translating

*Students have learnt

probabilty in CoreMath

*Use real-life

situations tointroduce

probability

Wk 17 -18

4/4 15/5

Revision

Wk 19 20

18/5 29/5

Second examination

All Form 4 topics; progression, linear law, integration, vectors, permutation & combination

(23/5 Teachers Day celebration.)

30/5 13/6 First Semester holiday

Project work assignment to be given to pupils to do during holiday

6


7/11

SECOND SEMESTER

WEEKS/

DATES

LEARNING

AREA

LEARNING

OBJECTIVES

LEARNING OUTCOMES CCTS NOTES

Wk 1-3

15/6 3/7

Chapter 8.

Probability

distribution


binomial distribution.

2. Understand and

use the concept ofnormal distribution.

1.1 List all possible values of a discrete randomvariable.

1.2 Determine the probability of an event in a

binomial distribution.

1.3 Plot binomial distribution graphs.

1.4 Determine mean, variance and standard

deviation of a binomial distribution.

1.5 Solve problems involving binomial

distributions.

2.1 Describe continuous random variables using

set notations.2.2 Find probability ofz-values for standard

normal distribution.

2.3 Convert random variable of normal

distributions,X, to standardised variable,Z.

2.4 Represent probability of an event using set

notation.

2.5 Determine probability of an event.

2.6 Solve problems involving normal

distributions.

Comparing &

contrasting


Interpreting

Drawing diagrams

Classifying

Translating

*Discussion of

second exam

questions beforestarting this chapter

Wk 4-6

6/6 24/7Chapter 5.

Trigonometric

functions

1. Understand theconcept of positiveand negative angles

measured in degrees

and radians.

1.1 Represent in a Cartesian plane, angles

greater than 360o or 2 radians for:

a) positive anglesb) negative angles.


Interpreting

Making inferences

Drawing diagrams


7


8/11

2. Understand and

use the six

trigonometric

functions of any

angle.

3. Understand and

use graphs of sine,

cosine and tangent

functions

4. Understand anduse basic identities.

5. Understand anduse addition formulae

and double angle

formulae.

2.1 Define sine, cosine and tangent of any angle

in a Cartesian plane.

2.2 Define cotangent, secant and cosecant of anyangle in a Cartesian plane.

2.3 Find values of the six trigonometricfunctions of any angle.

2.4 Solve trigonometric equations.

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 bx

where a, b and c are constants and b > 03.2 Determine the number of solutions to a

trigonometric equation using sketched

graphs.3.3 Solve trigonometric equations using drawn

graphs.

4.1 Prove basic identities:a) sin2A + cos2A = 1

b) 1 + tan2A = sec2A

c) 1 + cot2A = cosec2A

4.2 Prove trigonometric identities using basicidentities.

4.3 Solve trigonometric equations using basic

identities.

5.1 Prove trigonometric identities using addition

formulae for sin(A B), cos (A B) and

tan (A B).

5.2 Derive double angle formulae for sin 2A, cos

2A and tan 2A.

Comparing andcontrasting

Classifying

Finding all possible

solutions

8


9/11

5.3 Prove trigonometric identities using addition

formulae and/or double angle formulae.

5.4 Solve trigonometric equations.

Wk 7 8

27/7 7/8

Chapter 9.

Motion along

a straight line

1. Understand and

use the concept of

displacement.

2. Understand and

use the concept ofvelocity.

3. Understand and

use the concept of

acceleration.

1.1 Identify direction of displacement of aparticle from a fixed point.

1.2 Determine displacement of a particle from afixed point.

1.3Determine the total distance travelled by aparticle over a time interval using graphical

method

2.1 Determine velocity function of a particle by

differentiation.2.2 Determine instantaneous velocity of a

particle.

2.3 Determine displacement of a particle fromvelocity function by integration.

3.1 Determine acceleration function of a particle

by differentiation.

3.2 Determine instantaneous acceleration of a

particle.

3.3 Determine instantaneous velocity of aparticle from acceleration function by

integration.3.4 Determine displacement of a particle from

acceleration function by integration.3.5 Solve problems involving motion along a

straight line.

Comparing &

contrasting


Interpreting

Drawing diagrams


Classifying

Translating

This topic is only

taught to the science

class the same time aslinear programming

is taught to the non

science class

9


10/11

Wk 7 8

27/7 7/8

Chapter 10

Linear

programming

1. Understand anduse the concept ofgraphs of linear

inequalities.


linear programming.

1.1 Identify and shade the region on the graph

that satisfies a linear inequality

1.2 Find the linear inequality that defines a

shaded region.

1.3 Shade region on the graph that satisfiesseveral linear inequalities.

1.4 Find linear inequalities that define a shaded

region.

2.1 Solve problems related to linear programming

by:

a) writing linear inequalities and equations

describing a situation.

b) shading the region of feasible solutions.

c) determining and drawing the objective

function ax + by = kwhere a,

b and kare constants.

d) determining graphically the optimum

value of the objective function

This topic is only

taught to non scienceclass

Wk 9 10

10/8 21/8

UJIAN SETARA 2

First Trial Examination

All topics

24/8 31/8 Mid Semester 2 break

Wk 11

1/9 4/9 Revision

Wk 12 13

1/9 19/9 Excel 2 SPM

10


11/11

Wk 14

21/9 26/9 (Wk 14 Hari Raya Puasa)

Wk 15-1628/9 9/10 Discussion of Second SPM Trial Exam questions

Wk 17 2212/10 14/11

Revision

11

2008 form 5 am teaching scheme

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