rpt maths form 4 2012

7/29/2019 RPT Maths Form 4 2012

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Students will be able to:

TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

1. STANDARD

FORM

1

04/01/12 - 06/01/12

1.1 Understand and use the

concept if significant

figure.

Level 1:

i. Round off positive numbers to a

given number of significant figures

when the numbers are:a) Greater than 1

b) Less than 1

Discuss the significance if zero

in a number.

Rounded numbers are only

approximates.

Limit to positive numbers only.

Teaching aids

Mahjong paper

Pictures

Ccts

Working out mentallyDecision making

Identifying

relationship

Level 2:

ii. Perform operations of addition,

substraction , multiplication and

division, involving a few numbers

and state the answer in specific

significant figures.

Discuss the use of significant

figures in everyday life and other

areas.

Generally, rounding is done on

the final answer.

Moral values

Cooperation rational

Being systematic

Conscientious

Level 3:

iii. Solve problems involving

significant figures.

Vocabulary

Significance

Significant figureRelevant

Round off

Accuracy

2

09/01/12 - 13/01/12

1.2 Understand and use the

concept of standard

form to solve problems

Level 1 :

i. State positive numbers in standard

form when the numbers are:

a) Greater than or equal to 10

b) Less than 1

Use everyday life situations such

as in health, technology,

industry,

Construction and business

involving numbers in standard

form.

Use the scientific calculator to

explore numbers in standard

form.Another term for standard form

is scientific notation.

Teaching aids

Flash card

Scientific calculator

Ccts

Working out mentally

Identifying

relationship

ii. Convert numbers in standard form

to single numbers.

Moral values

Cooperation, rational,

being systematic

Level 2:

iii. Perform operations of addition,

subtraction, multiplication and

division, involving any two

numbers and state the answers in

standard form.

Include two numbers in standard

form.

Vocabulary

Standard form

Single number

Scientific notation

Level 3:MAS AYU ALI/2012

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iv. solve problems involving numbers

in standard form.

2. QUADRATIC

EXPRESSIONS

AND EQUATIONS

3

16/01/12 - 20/01/12

2.1 understand the concept

of quadratic expression;

Level 1:

i. identify quadratic expressions;

Discuss the characteristics of

quadratic expressions of the

form 02 =++ cbxax , wherea, b and c are constants, a 0andx is an unknown.

Include the case when b = 0

and/orc = 0.

Vocabulary

Quadratic expression

ConstantConstant factor

Unknown

Highest power

Expand

Coefficient

Term

ii. form quadratic expressions by

multiplying any two linear

expressions;

Emphasise that for the terms x2

and x, the coefficients are

understood to be 1.

Level 2:

iii. form quadratic expressions based

on specific situations;

Include everyday life situations.

4

23/01/12 - 27/01/12

23/2 & 24/2

Tahun Baru Cina

2.2 factorise quadratic

expression;

Level 1:

i. factorise quadratic expressions of

the form cbxax ++2 , where b =

0 orc = 0;

Discuss the various methods to

obtain the desired product.

Vocabulary

Factorise

Common factor

Perfect square

Cross method

Inspection

Common factor

Complete factorisation

ii. factorise quadratic expressions of

the formpx2q,p and q areperfect squares;

1 is also a perfect square.

5

30/01/12 - 03/02/12

Level 2 :iii. factorise quadratic expressions of

the form cbxax ++2 , where a,

b and c not equal to zero;

factorise quadratic expressions

of the form cbxax ++2 ,

where a, b and c not equal to

zero;

Factorisation methods that can

be used are:

cross method; inspection.

iv. factorise quadratic expressions

containing coefficients with

common factors

6 2.3 understand the concept Level 1 : Discuss the characteristics of VocabularyMAS AYU ALI/2012

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06/02/12 - 10/02/12

5/2

Maulidur Rasul

of quadratic equation; i. identify quadratic equation with

one unknown;

quadratic equations. Quadratic equation

General form

Substitute

Root

Trial and error method

SolutionLevel 2 :

ii. write quadratic equations in

general form i.e.

02

=++ cbxax ;

Moral values

Diligence

Rationality

Justice

Level 3 :

iii. form quadratic equations based on

specific situations;

Include everyday life situations. Ccts

Identifying

relationship

Classifying

Catogerising

Drawing diagrams

Identify patternsProblem solving

7

13/02/12 - 17/02/12

2.4 understand and use the

concept of roots of

quadratic equations to

solve problems.

Level 1 :

.i determine whether a given value is

a root of a specific quadratic

equation;

Level 2 :

.ii determine the solutions for

quadratic equations by:

a) trial and error method;

b) factorisation;

Discuss the number of roots of a

quadratic equation.

There are quadratic equations

that cannot be solved by

factorisation.

Teaching aids

Cd courseware

Level 3 :.iii solve problems involving quadratic

equations.

Use everyday life situations.Check the rationality of the

solution.

3. SET

8

20/02/12 - 24/02/12


of set;

Level 1 :

i. sort given objects into groups;

Use everyday life examples to

introduce the concept of set.

The word set refers to any

collection or group of objects.

Teaching aids

Flash cards

ii. define sets by:

a) descriptions;

b) using set notation;

The notation used for sets is

braces, { }.

The same elements in a set need

not be repeated.

Sets are usually denoted by

Vocabulary

Set

Element

Description

LabelMAS AYU ALI/2012

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capital letters.

The definition of sets has to be

clear and precise so that the

elements can be identified.

Set Notation

Denote

Venn diagram

Empty set

Equal set

iii. identify whether a given object is

an element of a set and use the

symbol or;

The symbol (epsilon) is readis an element of or is a

member of.

The symbol is read is not anelement of or is not a member

of.

Ccts

Classifying

Translating

Identifying

relationships

iv. represent sets by using Venn

diagrams;

Discuss the difference between

the representation of elements

and the number of elements in

Venn diagrams.

Moral values

Paying attention

v. list the elements and state the

number of elements of a set;Discuss why { 0 } and { } arenot empty sets.

The notation n(A) denotes the

number of elements in set A.

vi. determine whether a set is an

empty set;The symbol (phi) or { }denotes an empty set.

Level 2 :

vii. determine whether two sets are

equal;

An empty set is also called a null

set.

9

27/02/12 - 02/03/12


concept of subset,

universal set and the

complement of a set;

Level 1 :

.i determine whether a given set is a

subset of a specific set and use the

symbol or ;

Begin with everyday life

situations.

An empty set is a subset of any

set.

Every set is a subset of itself.

Vocabulary

Subset

Universal set

Complement of a set

.ii represent subset using Venn

diagram;

Teaching aids

Laptop

Diagrams

.iii list the subsets for a specific set;

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TEACHING AND

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STRATEGIES

10

05/03/12 - 09/03/12

TEST 1

10/03/12 - 18/03/12

MID TERM HOLIDAY I

11

19/03/12 - 23/03/12

.iv illustrate the relationship between

set and universal set using Venn

diagram;

Discuss the relationship between

sets and universal sets.

The symbol denotes auniversal set.

Ccts

Translating

Categorizing

.v determine the complement of a

given set;The symbol A denotes thecomplement of set A.

Moral values

Being hard-working

Being honest

Level 2 :

.vi determine the relationship between

set, subset, universal set and the

complement of a set;


3.3 perform operations on

sets:

the intersection of sets; the union of sets.

Level 1 :

i. determine the intersection of:a) two sets;

b) three sets;

and use the symbol ;

Include everyday life situations. Moral values

Paying attention

Cooperation

Concentration

ii. represent the intersection of setsusing Venn diagram;

Discuss cases when:

AB = AB

Teaching aids

Laptop

Diagrams

Text book

Level 2 :

iii. state the relationship betweena) AB and A ;

b) AB and B ;

Vocabulary

Intersection

UnionOperation

iv. determine the complement of theintersection of sets;

Level 3 :

v. solve problems involving theintersection of sets;


12

26/03/12 - 30/03/12

Level 1 :

vi. determine the union of:

c) two sets;

d) three sets;

Teaching aids

Laptop

Diagrams

Text book

MAS AYU ALI/2012

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and use the symbol ;vii. represent the union of sets using

Venn diagram;

Level 2 :

viii. state the relationship between

a) AB and A ;b) AB and B ;

ix. determine the complement of the

union of sets;

Level 3 :

x. solve problems involving the union

of sets;


xi. determine the outcome of

combined operations on sets;

xii. solve problems involving

combined operations on sets.


4. MATHEMATICAL

REASONING

13

01/04/12 - 06/04/12


of statement

Level 1 :

.i determine whether a given

sentence is a statement;

Introduce this topic using

everyday life situations.

Statements consisting of:

Ccts

Making general

statement

.ii determine whether a given

statement is true or false;

Focus on mathematical

sentences.

words only, e.g. Five isgreater than two.;

numbers and words, e.g. 5is greater than 2.;

numbers and symbols, e.g. 5> 2.

Moral values

Cooperation

Teaching aids

Multimedia

Level 2 :

.iii construct true or false statementusing given numbers and

mathematical symbols;

Discuss sentences consisting of:

words only; numbers and words; numbers and mathematical

symbols;

The following are not

statements:

Is the place value of digit 9in 1928 hundreds?;

4n 5m + 2s; Add the two numbers.; x + 2 = 8.

Vocabulary

StatementTrue

False

Mathematical sentence

Mathematical

statement

Mathematical symbol

MAS AYU ALI/2012

7/29/2019 RPT Maths Form 4 2012

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of quantifiers all and

some;

Level 1 :

i. construct statements using the

quantifier:

)a all;

)b some;

Start with everyday life

situations.

Quantifiers such as every and

any can be introduced based

on context.

Ccts

Categorizing

Moral values

Social interaction

ii. determine whether a statement thatcontains the quantifier all is true

or false;

Examples: All squares are four sided

figures.

Every square is a four sidedfigure.

Any square is a four sidedfigure.

VocabularyQuantifier

All

Every

Any

Some

Several

iii. determine whether a statement can

be generalised to cover all cases by

using the quantifier all;

Other quantifiers such as

several, one of and part of

can be used based on context.

One of

Part of

Negate

Contrary

Object

Level 2 :iv. construct a true statement using the

quantifier all or some, given

an object and a property.

Example:Object: Trapezium.

Property: Two sides are parallel

to each other.

Statement: All trapeziums have

two parallel sides.

Object: Even numbers.

Property: Divisible by 4.

Statement: Some even numbers

are divisible by 4.

Teaching aidsMultimedia

14

09/04/12 - 13/04/12

4.3 perform operations

involving the words

not or no, andand or on statements;

Level 1 :

.i change the truth value of a given

statement by placing the wordnot into the original statement;

Begin with everyday life

situations.

The negation no can be usedwhere appropriate.

The symbol ~ (tilde) denotes

negation.

~p denotes negation ofp

which means notp or nop.

The truth table forp and ~p are

as follows:

p ~p

True

False

False

True

Vocabulary

Negation

Not pNo p

Truth table

Truth value

And

Compound statement

Or

Teaching Aids

Multimedia

MAS AYU ALI/2012

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.ii identify two statements from a

compound statement that contains

the word and;

The truth values for p and q

are as follows:

p q p and q

True True True

True False False

False True FalseFalse False False

Ccts

Reasoning

Moral values

Confidence

.iii form a compound statement by

combining two given statements

using the word and;

.iv identify two statement from a

compound statement that contains

the word or ;

The truth values for p orq are

as follows:

.v form a compound statement by

combining two given statements

using the word or;

p q p orq

True True True

True False True

False True TrueFalse False False

Level 2 :

.vi determine the truth value of a

compound statement which is the

combination of two statements

with the word and;

.vii determine the truth value of a

compound statement which is the

combination of two statements

with the word or.

4.4 understand the conceptof implication;

Level 1 :.i identify the antecedent and

consequent of an implication ifp,

then q;

Start with everyday lifesituations.

Implication ifp, then q can be

written aspq, and p if andonly ifq can be written aspq, which meanspq and qp.

CctsIdentifying

information

Moral values

Cooperation

.ii write two implications from a

compound statement containing if

and only if;

Teaching aids

Multimedia

iii. construct mathematical statements

in the form of implication:

Vocabulary

Implication

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a) If p, then q;

b) p if and only ifq;

Antecedent

Consequent

Converse

Level 2 :

iv. determine the converse of a given

implication;

The converse of an implication

is not necessarily true.

v. determine whether the converse of

an implication is true or false.

Example 1:

Ifx < 3, then

x < 5 (true).

Conversely:

Ifx < 5, then

x < 3 (false).

Example 2:

IfPQR is a triangle, then the

sum of the interior angles of

PQR is 180.(true)

Conversely:If the sum of the interior angles

ofPQR is 180, thenPQR is atriangle.

(true)

4.5 understand the conceptof argument;

Level 1 :

.i identify the premise andconclusion of a given simple

argument;

Start with everyday life

situations.

Limit to arguments with true

premises.

Ccts

Making justification

Making conclusion

Level 2 :

ii. make a conclusion based on two

given premises for:

a) Argument Form I;

b) Argument Form II;

c) Argument Form III;

Names for argument forms, i.e.

syllogism (Form I), modus

ponens (Form II) and modus

tollens (Form III), need not be

introduced.

Moral values

Cooperation

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iii. complete an argument given a

premise and the conclusion.

Specify that these three forms of

arguments are deductions based

on two premises only.

Argument Form I

Premise 1: AllA areB.

Premise 2: CisA.Conclusion: CisB.

Argument Form II:

Premise 1: Ifp, then q.

Premise 2:p is true.

Conclusion: q is true.

Argument Form III:

Premise 1: Ifp, then q.

Premise 2: Not q is true.

Conclusion: Notp is true.

Vocabulary

Argument

Premise

Conclusion

Teaching AidsMultimedia


concept of deduction and

induction to solve problems.

Level 1 :

i. determine whether a conclusion is

made through:a) reasoning by deduction;

b) reasoning by induction;

Ccts

Justifying

Making conclusion

Moral values

Cooperation

Level 2 :

ii. make a conclusion for a specific

case based on a given general

statement, by deduction;

iii. make a generalization based on the

pattern of a numerical sequence, by

induction;

Limit to cases where formulae

can be induced.

Teaching aids

Multimedia

5. THE STRAIGHTLINE

15

16/04/12 - 20/04/12

5.1 understand the conceptof gradient of a straight

line;

Level 1 :i. determine the vertical and

horizontal distances between two

given points on a straight line.

Use technology such as theGeometers Sketchpad, graphing

calculators, graph boards,

magnetic boards, topo maps as

teaching aids where appropriate.

ii. determine the ratio of vertical

distance to horizontal distance.

Begin with concrete

examples/daily situations to

introduce the concept of

gradient.

MAS AYU ALI/2012Verticaldistance

Horizontal distance

7/29/2019 RPT Maths Form 4 2012

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Discuss:

the relationship betweengradient and tan .

the steepness of the straightline with different values of

gradient.

Carry out activities to find the

ratio of vertical distance to

horizontal distance for several

pairs of points on a straight line

to conclude that the ratio is

constant.

16

23/04/12 - 27/04/12


of gradient of a straight

line in Cartesian

coordinates;

Level 1 :

i. derive the formula for the gradient

of a straight line;

Discuss the value of gradient if

Pis chosen as (x1,y1) and Qis (x2,y2);

Pis chosen as (x2,y2) and Qis (x1,y1).

The gradient of a straight line

passing throughP(x1,y1) and

Q(x2,y2) is:

12

12

xx

yym

=

ii. calculate the gradient of a straight

line passing through two points;

determine the relationship

between the value of the gradientand the:

c) steepness,

d) direction ofinclination,

of a straight line;

17

30/04/12 - 04/05/12

1/5

Hari Buruh


of intercept;

Level 1 :

i. determine thex-intercept and they-

intercept of a straight line;

Emphasise that thex-intercept

and they-intercept are not

written in the form of

coordinates.

ii. derive the formula for the gradient

of a straight line in terms of the x-

intercept and they-intercept;MAS AYU ALI/2012

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5/5

Hari Wesak

Level 2 :

iii. perform calculations involving

gradient,x-intercept andy-

intercept;

18

07/05/12 - 11/05/12

5.4 understand and use

equation of a straightline;

Level 1 :

i. draw the graph given an equationof the formy = mx + c;

Discuss the change in the form

of the straight line if the valuesofm and c are changed.

Emphasise that the graph

obtained is a straight line.

ii. determine whether a given point

lies on a specific straight line;

Carry out activities using the

graphing calculator, Geometers

Sketchpad or other teaching aids.

If a point lies on a straight line,

then the coordinates of the point

satisfy the equation of the

straight line.

Level 2 :

iii. write the equation of the straightline given the gradient andy-

intercept;

Verify that m is the gradient and

c is they-intercept of a straightline with equationy=mx + c .

iv. determine the gradient andy-

intercept of the straight line which

equation is of the form:

a. y = mx + c;

b. ax + by = c;

The equation

ax + by = c can be written in the

form

y = mx + c.

Level 3 :

v. find the equation of the straight

line which:

a) is parallel to thex-axis;

b) is parallel to they-axis;c) passes through a given point

and has a specific gradient;

d) passes through two given

points;

vi. find the point of intersection of two

straight lines by:

a) drawing the two straight lines;

b) solving simultaneous

equations.

Discuss and conclude that the

point of intersection is the only

point that satisfies both

equations.

Use the graphing calculator and

Geometers Sketchpad or other

teaching aids to find the point of

intersection.MAS AYU ALI/2012

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concept of parallel lines

Level 1 :

i. verify that two parallel lines have

the same gradient and vice versa;

Explore properties of parallel

lines using the graphing

calculator and Geometers

Sketchpad or other teaching aids.

ii. determine from the given equations

whether two straight lines areparallel;

Level 2 :

iii. find the equation of the straight

line which passes through a given

point and is parallel to another

straight line:

19 & 20

14/05/12 - 25/05/12

MID YEAR EXAM

26/05/12 - 10/06/12

MID TERM SCHOOL HOLIDAY

6. STATISTICS

21

11/06/12 - 15/06/12


of class interval;

Level 1 :

i. complete the class interval for a set

of data given one of the class

intervals;

Use data obtained from activities

and other sources such as

research studies to introduce the

concept of class interval.

ii . determine:

a) the upper limit and lower

limit;

b) the upper boundary and lower

boundary of a class in a

grouped data;iii. calculate the size of a class

interval;

Size of class interval

=[upper boundarylower

boundary]

Level 2 :

iv. determine the class interval, given

a set of data and the number of

classes;

v. determine a suitable class interval

for a given set of data;

vi. construct a frequency table for a

given set of data.

Discuss criteria for suitable class

intervals.

6.2 understand and use the Level 1 :MAS AYU ALI/2012

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concept of mode and

mean of grouped data;

i. determine the modal class from the

frequency table of grouped data;

ii. calculate the midpoint of a class; Midpoint of class

=2

1 (lower limit + upper limit)

Level 2 :

iii. verify the formula for the mean of

grouped data;

iv. calculate the mean from the

frequency table of grouped data;

Level 3 :

v. discuss the effect of the size of

class interval on the accuracy of

the mean for a specific set of

grouped data..

22

18/06/12 - 22/06/12

6.3 represent and interpret

data in histograms with

class intervals of thesame size to solve

problems;

Level 1 :

i. draw a histogram based on the

frequency table of a grouped data;

Discuss the difference between

histogram and bar chart.

Level 2 :

ii. interpret information from a given

histogram;

Use graphing calculator to

explore the effect of different

class interval on histogram.

Level 3 :

iii. solve problems involving

histograms.


6.4 represent and interpret

data in frequency

polygons to solve

problems.

Level 1 :

i. draw the frequency polygon based

on:

)a a histogram;

)b a frequency table;

When drawing a frequency

polygon add a class with 0

frequency before the first class

and after the last class.

Level 2 :ii. interpret information from a given

frequency polygon;

Level 3 :

iii. solve problems involving

frequency polygon.


23

25/06/12 - 29/06/12

6.5 understand the conceptof cumulative

frequency;

Level 1 :

i. construct the cumulative frequency

table for:

)a ungrouped data;

)b grouped data;MAS AYU ALI/2012

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Level 2 :

ii. draw the ogive for:

a) ungrouped data;

b) grouped data;

When drawing ogive:

use the upper boundaries; add a class with zero

frequency before the first

class.

6.6 understand and use theconcept of measures of

dispersion to solve

problems.

Level 1 :i. determine the range of a set of

data.

For grouped data:Range = [midpoint of the last

class midpoint of the first

class]

Discuss the meaning of

dispersion by comparing a few

sets of data. Graphing calculator

can be used for this purpose.

CctsInterpreting

Describing

Identifying

information

ii . determine:

a) the median;

b) the first quartile;

c) the third quartile;

d) the interquartile range;from the ogive.

Moral values

Cooperation

Develop social skills

Mental & physical

cleanlinessRationality

Systematic

Level 2 :

iii. interpret information from an

ogive;

7 PROBABILITY

24

02/07/12 - 06/07/12


of sample space;

Level 1 :

i. determine whether an outcome is a

possible outcome of an

experiment;

Use concrete examples such as

throwing a die and tossing a

coin.

ii. list all the possible outcomes of an

experiment:

a) from activities;

b) by reasoning;

iii. determine the sample space of an

experiment;

iv. write the sample space by using set

notations

25

09/07/12 - 13/07/12


of events.

Level 1 :

i. identify the elements of a sample

space which satisfy given

conditions;

An impossible event is an empty

set.

Discuss that an event is a subset

of the sample space.

Discuss also impossible events

for a sample space.

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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

ii. list all the elements of a sample

space which satisfy certain

conditions using set notations;

iii. determine whether an event ispossible for a sample space.

Discuss that the sample spaceitself is an event.

26

16/07/12 - 20/07/12

TEST II

27

23/07/12 - 27/07/12


concept of probability

of an event to solve

problems.

Level 1 :

.i find the ratio of the number of

times an event occurs to the

number of trials;

Probability is obtained from

activities and appropriate data.

Carry out activities to introduce

the concept of probability. The

graphing calculator can be used

to simulate such activities.

.ii find the probability of an eventfrom a big enough number of

trials;

Level 2 :

.iii calculate the expected number of

times an event will occur, given

the probability of the event and

number of trials;

Discuss situation which results

in:

probability of event = 1. probability of event = 0.

.8 CIRCLES III

28

30/07/12 - 03/08/12


concept of tangents to a

circle.

Level 1 :

i. identify tangents to a circle;

Develop concepts and abilities

through activities using

technology such as the

Geometers Sketchpad and

graphing calculator.

Teaching aids

Compass

Geometry set

Gsp

ii. make inference that the tangent to

a circle is a straight line

perpendicular to the radius that

passes through the contact point;

Level 2 :

iii. construct the tangent to a circle

passing through a point:

a) on the circumference of the

circle;

b) outside the circle;

Ccts

Making inference

Drawing diagram

MAS AYU ALI/2012

A

B

O C

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AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iv. determine the properties related to

two tangents to a circle from a

given point outside the circle;

Properties of angle in

semicircles can be used.

Examples of properties of two

tangents to a circle:

AC=BCACO = BCOAOC= BOCAOCand BOCare congruent.

Vocabulary

Tangent to a circle

Circle

Perpendicular

RadiusCircumference

Semi circle

Congruent

Level 3 :

v. solve problems involving tangents

to a circle.

Relate to Pythagoras theorem.

29

06/08/12 - 10/08/12

6/8

Nuzul Quran


properties of angle

between tangent andchord to solve

problems.

Level 1 :

i. identify the angle in the alternate

segment which is subtended by thechord through the contact point of

the tangent;

Explore the property of angle in

alternate segment using

Geometers Sketchpad or other

teaching aids.

Vocabulary

Chords

Alternate segmentMajor sector

Subtended

Moral values

Diligence

Cooperation

Courage

Level 2 :

ii. verify the relationship between theangle formed by the tangent and

the chord with the angle in the

alternate segment which is

subtended by the chord;

ABE= BDE

CBD = BED

Ccts

Identifyinginformation

Justify relationships

Problem solving

iii. perform calculations involving the

angle in alternate segment


properties of common

tangents to solve

problems.

Level 1 :

i. determine the number of common

tangents which can be drawn to

two circles which:

a) intersect at two points;

b) intersect only at one point;

Emphasise that the lengths of

common tangents are equal.

Discuss the maximum number of

common tangents for the three

cases.

Vocabulary

Common tangent

Ccts

Identifying

informationMAS AYU ALI/2012

E

D

A B C

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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

c) do not intersect; Justify

Relationships

Problem solving

Level 2 :

ii. determine the properties related to

the common tangent to two circleswhich:

a) intersect at two points;

b) intersect only at one point;

c) do not intersect;

Include daily situations.

Moral values

DiligenceCooperation

Courage

.9 TRIGONIMETRYII

30

13/08/12 - 17/08/12

9.1 understand and use theconcept of the values of

sin , cos and tan

(0 360) to solveproblems.

Level 1 :

i. identify the quadrants and angles

in the unit circle;

The unit circle is the circle of

radius 1 with its centre at the

origin.

Explain the meaning of unit

circle.

Ccts

Identifying

information

Justify relationships

Making connection

ii . determine:

)a the value ofy-coordinate;

)b the value ofx-coordinate;)c the ratio ofy-coordinate tox-

coordinate;

of several points on the

circumference of the unit circle;

iii. verify that, for an angle in quadrant

I of the unit circle :

a) sin =y-coordinate ;b) cos=x-coordinate.

c)coordinate

coordinatetan

=

x

y ;

Begin with definitions of sine,

cosine and tangent of an acute

angle.

yy

OP

PQ===

1sin

xx

OP

OQ===

1cos

x

y

OQ

PQ==tan

MAS AYU ALI/2012

0

y

x

P (x,y)

y1

x Q

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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iv. determine the values of

a) sine;

b) cosine;

c) tangent;

d) of an angle in quadrant I of the

unit circle;v. determine the values of

a) sin ;

b) cos ;

c) tan ;

for 90 360;

Explain that the concept

sin =y-coordinate ;

cos=x-coordinate;

coordinat

coordinattan

=

x

y

can be extended to angles in

quadrant II, III and IV.

Vocabulary

Quadrant

Sine

Cosine

Tan

vi. determine whether the values of:

a) sine;

b) cosine;

c) tangent,

of an angle in a specific quadrant is

positive or negative;

Consider special angles such as

0, 30, 45, 60, 90, 180,270, 360.

vii. determine the values of sine,

cosine and tangent for special

angles;

Use the above triangles to find

the values of sine, cosine and

tangent for 30, 45, 60.

Level 2 :

viii. determine the values of the angles

in quadrant I which correspond tothe values of the angles in other

quadrants;

Teaching can be expanded

through activities such as

reflection.

ix. state the relationships between the

values of:

a) sine;

b) cosine; and

c) tangent;

of angles in quadrant II, III and IV with

their respective values of the

corresponding angle in quadrant I;

Use the Geometers Sketchpad

to explore the change in the

values of sine, cosine and

tangent relative to the change in

angles.

x. find the values of sine, cosine and Teaching aidsMAS AYU ALI/2012

12

45o

1

60o

30o

1

2

3

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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

tangent of the angles between 90and 360;

Gsp

Graph paper

Graphmatica

Geometry set

18/08/12 - 26/08/12

19/8 & 20/8

Hari Raya Aidilfitri

MID TERM HOLIDAY II

31

27/08/12 - 31/08/12

31/8

Hari Kemerdekaan

9.2 draw and use the graphs

of sine, cosine and

tangent.

Level 1 :

i. draw the graphs of sine, cosine and

tangent for angles between 0 and360;

Use the graphing calculator and

Geometers Sketchpad to

explore the feature of the graphs

of

y = sin ,y = cos ,y = tan .

Ccts

Problem solving

Compare and contrast

Drawing graphs

Level 2 :

ii. compare the graphs of sine, cosine

and tangent for angles between 0and 360;

Discuss the feature of the graphs

of

y = sin,y = cos,y = tan.

Moral values

Cooperation

Honesty

Diligence

Integrity10. ANGLES OF

ELEVATIONS

AND

DEPRESSION

32

03/09/12 - 07/09/12


concept of angle of

elevation and angle of

depression to solve

problems.

Level 1 :

i. identify:

d) the horizontal line;

e) the angle of elevation;

f) the angle of depression,

for a particular situation;

Use daily situations to introduce

the concept.

Ccts

Working out mentally

Compare and contrast

Identifying

relationship

Decision making

Problem solving

Level 2 :

ii. Represent a particular situation

involving:

a) the angle of elevation;

b) the angle of depression, usingdiagrams;

Include two observations on the

same horizontal plane.

Vocabulary

Angle of elevation

Angle of depression

Horizontal line

Moral values

Rationality

Cooperation

33

10/09/12 - 14/09/12

Level 3 :

iii. Solve problems involving the angle

of elevation and the angle of

depression.

Involve activities outside the

classroom.

Teaching aids:

Models

Cd courseware

11. LINES ANDPLANES IN 3-

DIMENSIONS


concept of angle

between lines and

planes to solve

Level 1 :

i. identify planes;

Carry out activities using daily

situations and 3-dimensional

models.

Ccts

Describing

Interpreting

Drawing diagrams

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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

34

17/09/12 - 21/09/12

16/9Hari Malaysia

problems Problem solving

ii. identify horizontal planes, vertical

planes and inclined planes;

Differentiate between 2-

dimensional and 3-dimensional

shapes. Involve planes found in

natural surroundings.

Moral values

Respect

Cooperation

iii. sketch a three dimensional shape

and identify the specific planes;

Approaches

Constructivism

Exploratory

Cooperative learning

iv. identify:

A) lines that lies on a

plane;

B) lines that intersect

with a plane;

Vocabulary

Horizontal plane

Vertical plane

3-dimensional

Normal to a plane

Orthogonal projection

Space diagonal

Angle between twoplanes

Level 2 :

v. identify normals to a given plane;

vi. determine the orthogonal

projection of a line on a plane;

Begin with 3-dimensional

models.

vii. draw and name the orthogonal

projection of a line on a plane;

Include lines in 3-dimensional

shapes.

viii. determine the angle between a line

and a plane;

35

24/09/12 - 28/09/12


concept of anglebetween two planes to

solve problems.

Level 1 :

i. identify the line of intersectionbetween two planes;

ii. draw a line on each plane which is

perpendicular to the line of

intersection of the two planes at a

point on the line of intersection;

Level 2 :

iii. determine the angle between two

planes on a model and a given

diagram;

Use 3-dimensional models to

give clearer pictures.

36

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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

01/10/12 - 05/10/12 REVISION

37 & 38

08/10/12 - 19/10/12

FINAL EXAMINATION

39, 40 & 41

22/10/12 - 09/10/12

REVISION

42

12/11/12 - 16/11/12

DEEPAVALI AND AWAL MUHARAM HOLIDAYS

17/11/12 - 31/12/12 FINAL TERM SCHOOL HOLIDAY

MAS AYU ALI/2012

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SMK SULTAN ABDUL SAMAD

JALAN 12/13, PETALING JAYA, SELANGOR.

YEARLY TEACHING PLAN

MATHEMATICS

FORM 4

2012

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MAS AYU ALI/2012

rpt maths form 4 2012

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