yearly plan maths f4 repaired)

8/8/2019 Yearly Plan Maths F4 Repaired)

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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOMEStudents will be able to:

TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

1. STANDARD FORM 1.1 Understand and use theconcept if significant

figure.

i. Round off positive numbers to agiven 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 onlyapproximates.

Limit to positive numbers only.

Teaching aids

Mahjong paper

Pictures

Ccts

Working out mentallyDecision making

Identifying relationship

ii. Perform operations of addition,substraction , multiplication and

division, involving a few numbersand 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 systematicConscientious

iii. Solve problems involvingsignificant figures.

Vocabulary

Significance

Significant figureRelevant

Round off

Accuracy

1.2 Understand and use theconcept of standard

form to solve problems

i. State positive numbers in standardform when the numbers are:

a) Greater than or equal to 10b) 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 formis scientific notation.

Teaching aids

Flash card

Scientific calculator

Ccts

Working out mentally

Identifying relationship

ii. Convert numbers in standard formto single numbers.

Moral values

Cooperation, rational,

being systematic


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iii. Perform operations of addition,subtraction, multiplication and

division, involving any twonumbers and state the answers in

standard form.

Include two numbers in standard

form.

Vocabulary

Standard form

Single numberScientific notation

iv. solve problems involving numbersin standard form.

2. QUADRATICEXPRESSIONS

AND EQUATIONS

2.1 understand the conceptof quadratic expression;

i. identify quadratic expressions; Discuss the characteristics ofquadratic expressions of the

form 02 ! cbxax , where a,b and c are constants, a{ 0 andxis 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 bymultiplying any two linearexpressions;

Emphasise that for the terms x2

and x, the coefficients areunderstood to be 1.

iii. form quadratic expressions basedon specific situations;

Include everyday life situations.

2.2 factorise quadraticexpression;

i. factorise quadratic expressions ofthe form cbxax

2, where b =

0 orc = 0;

Discuss the various methods to

obtain the desired product.

Vocabulary

Factorise

Common factor

Perfect square

Cross methodInspection

Common factor

Complete factorisation

ii. factorise quadratic expressions ofthe form px2q, p and q are

perfect squares;

1 is also a perfect square.


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iii. factorise quadratic expressions ofthe form cbxax

2

, where a, band c not equal to zero;

factorise quadratic expressions

of the form cbxax

2

,where a, b and c not equal tozero;

Factorisation methods that can

be used are:

y cross method;y inspection.

iv. factorise quadratic expressionscontaining coefficients with

common factors

2.3 understand the conceptof quadratic equation;

i. identify quadratic equation withone unknown;

Discuss the characteristics of

quadratic equations.

Vocabulary

Quadratic equationGeneral form

Substitute

Root

Trial and error methodSolution

ii. write quadratic equations ingeneral form i.e. 0

2! cbxax

;

Moral values

Diligence

Rationality

Justice

iii. form quadratic equations based onspecific situations;

Include everyday life situations. CctsIdentifying relationship

Classifying

CatogerisingDrawing diagramsIdentify patterns

Problem solving

2.4 understand and use theconcept of roots of

quadratic equations to

solve problems.

i. determine whether a given value isa root of a specific quadratic

equation;


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

ii. determine the solutions forquadratic equations by:

a) trial and error method;b) factorisation;

Discuss the number of roots of a

quadratic equation.

There are quadratic equationsthat cannot be solved by

factorisation.

Teaching aids

Cd courseware

iii. solve problems involving quadraticequations.

Use everyday life situations.

Check the rationality of the

solution.

3. SETS 3.1 understand the conceptof set;

i. sort given objects into groups; Use everyday life examples tointroduce 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

capital letters.The definition of sets has to be

clear and precise so that the

elements can be identified.

Vocabulary

Set

Element

DescriptionLabel

Set NotationDenote

Venn diagram

Empty set

Equal set

iii. identify whether a given object isan 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 Venndiagrams;

Discuss the difference between

the representation of elements

and the number of elements in

Venn diagrams.

Moral values

Paying attention


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

v. list the elements and state thenumber of elements of a set;

Discuss why { 0 } and { } arenot empty sets.

The notation n(A) denotes thenumber of elements in set A.

vi. determine whether a set is anempty set;

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

vii. determine whether two sets areequal;

An empty set is also called a nullset.

3.2 understand and use theconcept of subset,

universal set and thecomplement of a set;

i. determine whether a given set is asubset of a specific set and use the

symbol or ;

Begin with everyday life

situations.

An empty set is a subset of anyset.

Every set is a subset of itself.

Vocabulary

Subset

Universal setComplement of a set

ii. represent subset using Venndiagram;

Teaching aids

Laptop

Diagramsiii. list the subsets for a specific set;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 agiven set;

The symbol Ad denotes thecomplement of set A.

Moral values

Being hard-workingBeing honest

vi. determine the relationship betweenset, subset, universal set and the

complement of a set;


3.3perform operations onsets:

y the intersection of sets;y the union of sets.

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

b) three sets;and use the symbol ;

Include everyday life situations. Moral values

Paying attentionCooperation

Concentration


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

ii. represent the intersection of setsusing Venn diagram;

Discuss cases when:

y AB =y AB

Teaching aids

Laptop

DiagramsText book

iii. state the relationship betweena) AB and A ;

b) AB and B ;VocabularyIntersection

Union

Operation

iv. determine the complement of theintersection of sets;

v. solve problems involving theintersection of sets;


vi. determine the union of:c) two sets;d) three sets;and use the symbol ;

Teaching aidsLaptop

Diagrams

Text book

vii. represent the union of sets usingVenn diagram;

viii.state the relationship betweena) AB and A ;

b) AB and B ;ix. determine the complement of the

union of sets;

x. solve problems involving the unionof sets;


xi. determine the outcome ofcombined operations on sets;

xii. solve problems involvingcombined operations on sets.



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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

4. MATHEMATICALREASONING

4.1 understand the conceptof statement

i. determine whether a givensentence is a statement;

Introduce this topic using

everyday life situations.

Statements consisting of:

Ccts

Making general

statement

ii. determine whether a givenstatement is true or false;

Focus on mathematical

sentences.

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

y numbers and words, e.g. 5 isgreater than 2.;

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

Moral values

Cooperation

Teaching aids

Multimedia

iii. construct true or false statementusing given numbers andmathematical symbols;

Discuss sentences consisting of:

y words only;y numbers and words;y numbers and mathematical

symbols;The following are not

statements:

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

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

Vocabulary

StatementTrue

False

Mathematical sentence

Mathematical statement

Mathematical symbol

4.2 understand the conceptof quantifiers all and

some;

i. construct statements using thequantifier:

a) all;b) some;

Start with everyday life

situations.

Quantifiers such as every and

any can be introduced basedon context.

Ccts

Categorizing

Moral valuesSocial interaction

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

or false;

Examples:

y All squares are four sidedfigures.

y Every square is a four sidedfigure.

y Any square is a four sidedfigure.

Vocabulary

Quantifier

AllEvery

Any

Some

Several


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iii. determine whether a statement canbe 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

NegateContrary

Object

iv. construct a true statement using thequantifier 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 aids

Multimedia

4.4perform operationsinvolving the words

not or no, andand or on statements;

i. change the truth value of a givenstatement by placing the word

not into the original statement;

Begin with everyday lifesituations.

The negation no can be usedwhere appropriate.

The symbol ~ (tilde) denotes

negation.

~p denotes negation ofp

which means not p or no p.

The truth table forp and ~p are

as follows:

p ~p

True

False

False

True

VocabularyNegation

Not pNo p

Truth table

Truth value

And

Compound statement

Or

Teaching Aids

Multimedia

ii. identify two statements from acompound statement that contains

the word and;

The truth values for p and qare as follows:

p q p and q

True True True

True False False

False True False

False False False

CctsReasoning

Moral values

Confidence


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iii. form a compound statement bycombining two given statements

using the word and;

iv. identify two statement from acompound statement that containsthe word or ;

The truth values for p orq are

as follows:

v. form a compound statement bycombining two given statements

using the word or;

p q p orq

True True True

True False True

False True TrueFalse False False

vi. determine the truth value of acompound statement which is the

combination of two statements

with the word and;

vii. determine the truth value of acompound statement which is the

combination of two statements

with the word or.

4.4 understand the conceptof implication;

i. identify the antecedent andconsequent of an implication ifp,

then q;

Start with everyday life

situations.

Implication ifp, then q can be

written aspq, and p if andonly ifq can be written as pq, which means pq and qp.

Ccts

Identifying information

Moral values

Cooperation

ii. write two implications from acompound statement containing if

and only if;

Teaching aids

Multimedia

iii. construct mathematical statementsin the form of implication:

a) Ifp, then q;b) p if and only ifq;

Vocabulary

Implication

Antecedent

Consequent

Converse


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iv. determine the converse of a givenimplication;

The converse of an implication

is not necessarily true.

v. determine whether the converse ofan 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 ofPQR is 180r.(true)

Conversely:

If the sum of the interior angles

ofPQR is 180r, thenPQR is atriangle.

(true)

4.5understand the conceptof argument; i.

identify the premise andconclusion of a given simple

argument;

Start with everyday lifesituations.Limit to arguments with true

premises.

CctsMaking justificationMaking conclusion

ii. make a conclusion based on twogiven 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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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

iii. complete an argument given apremise and the conclusion.

Specify that these three forms of

arguments are deductions based

on two premises only.Argument Form I

Premise 1: All A areB.

Premise 2: C isA.Conclusion: C is B.

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: Not p is true.

Vocabulary

Argument

PremiseConclusion

Teaching AidsMultimedia

understand and use the

concept of deduction and

induction to solve problems.

i. determine whether a conclusion ismade through:

a) reasoning by deduction;b) reasoning by induction;

Ccts

Justifying

Making conclusion

Moral valuesCooperation

ii. make a conclusion for a specificcase based on a given general

statement, by deduction;

iii. make a generalization based on thepattern of a numerical sequence, by

induction;

Limit to cases where formulae

can be induced.

Teaching aids

Multimedia

iv. use deduction and induction inproblem solving.

Specify that:y making conclusion by

deduction is definite;

y making conclusion byinduction is not necessarily

definite.

VocabularyReasoning

DeductionInduction

Pattern

Special conclusion

General statement

General conclusion

Specific case

Numerical sequence


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

5. THE STRAIGHTLINE

5.1 understand the conceptof gradient of a straight

line;

i. determine the vertical andhorizontal distances between two

given points on a straight line.

Use technology such as the

Geometers Sketchpad, graphing

calculators, graph boards,magnetic boards, topo maps as

teaching aids where appropriate.

ii. determine the ratio of verticaldistance to horizontal distance.

Begin with concrete

examples/daily situations to

introduce the concept of

gradient.

Discuss:

y the relationship betweengradient and tan

U.

y the steepness of the straightline with different values ofgradient.

Carry out activities to find the

ratio of vertical distance tohorizontal distance for several

pairs of points on a straight line

to conclude that the ratio is

constant.

Vertical

distance

Horizontal distance

U


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

5.2 understand the conceptof gradient of a straight

line in Cartesiancoordinates;

i. derive the formula for the gradientof a straight line;

Discuss the value of gradient if

yPis chosen as (x1,y1) and Q is(x2,y2);

yPis chosen as (x2,y2) and Q is(x1,y1).

The gradient of a straight line

passing through P(x1,y1) and

Q(x2,y2) is:

12

12

xx

yym

!

ii. calculate the gradient of a straightline passing through two points;

determine the relationship

between the value of the gradient

and the:

a) steepness,b) direction of

inclination,

of a straight line;

5.3 understand the conceptof intercept;

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 gradientof a straight line in terms of thex-

intercept and they-intercept;

iii. perform calculations involvinggradient,x-intercept andy-intercept;

5.4 understand and useequation of a straightline;

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.


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

ii. determine whether a given pointlies 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 thestraight line.

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 straight

line with equationy=mx + c .

iv. determine the gradient andy-intercept of the straight line whichequation is of the form:

a. y = mx + c;b. ax + by = c;

The equation

ax + by = c can be written in theform

y = mx + c.

v. find the equation of the straightline 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 givenpoints;

vi. find the point of intersection of twostraight lines by:a) drawing the two straight lines;

b) solving simultaneousequations.

Discuss and conclude that the

point of intersection is the onlypoint that satisfies both

equations.Use the graphing calculator and

Geometers Sketchpad or other

teaching aids to find the point of

intersection.

5.5 understand and use theconcept of parallel lines

i. verify that two parallel lines havethe same gradient and vice versa;

Explore properties of parallel

lines using the graphing

calculator and Geometers

Sketchpad or other teaching aids.


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

ii. determine from the given equationswhether two straight lines are

parallel;

iii. find the equation of the straightline which passes through a given

point and is parallel to another

straight line;

iv. solve problems involvingequations of straight lines.

6. STATISTICS 6.1 understand the conceptof class interval;

i. complete the class interval for a setof 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 lowerboundary of a class in agrouped data;

iii. calculate the size of a classinterval;

Size of class interval

=[upper boundarylower

boundary]

iv. determine the class interval, givena set of data and the number of

classes;

v. determine a suitable class intervalfor a given set of data;

vi. construct a frequency table for agiven set of data.

Discuss criteria for suitable class

intervals.


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

6.2 understand and use theconcept of mode and

mean of grouped data;

i. determine the modal class from thefrequency table of grouped data;

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

21 (lower limit + upper limit)

iii. verify the formula for the mean ofgrouped data;

iv. calculate the mean from thefrequency table of grouped data;

v. discuss the effect of the size ofclass interval on the accuracy of

the mean for a specific set of

grouped data..

6.3 represent and interpretdata in histograms with

class intervals of thesame size to solve

problems;

i. draw a histogram based on thefrequency table of a grouped data;

Discuss the difference between

histogram and bar chart.

ii. interpret information from a givenhistogram;

Use graphing calculator to

explore the effect of different

class interval on histogram.

iii. solve problems involvinghistograms.


6.4 represent and interpretdata in frequency

polygons to solveproblems.

i. draw the frequency polygon basedon:

a) a histogram;b) a frequency table;

When drawing a frequencypolygon add a class with 0

frequency before the first class andafter the last class.


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

6.5 ii.

interpret information from a given frequency polygon;

solve problems involving frequency polygon.Include everyday life situations.

understand the concept of cumulative frequency;construct the cumulative frequency table for:

ungrouped data;grouped data;

draw the ogive for:ungrouped data;

grouped data;When drawing ogive:use the upper boundaries;

add a class with zero frequency before the first class.understand and use the concept of measures of dispersion to solve problems.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

DescribingIdentifying information


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determine:the median;

the first quartile;

the third quartile;the interquartile range;from the ogive.Moral values

CooperationDevelop social skills

Mental & physical cleanlinessRationality

Systematicinterpret information from an ogive;

solve problems involving data representations and measures of dispersion.Carry out a project/research and analyse as well as interpret the data. Present the findings of the project/research.Emphasise the importance of honesty and accuracy in managing statistical researchTeaching aids Courseware

Graphing calculatorStatistical data

PROBABILITY

understand the concept of sample space;determine whether an outcome is a possible outcome of an experiment;Use concrete examples

such as throwing a die and tossing a coin.list all the possible outcomes of an experiment:from activities;

by reasoning;determine the sample space of an experiment;

write the sample space by using set notationsunderstand the concept of events.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.list all the elements of a sample space which satisfy certain conditions using set notations;

determine whether an event is possible for a sample space.Discuss that the sample space itself is an event.understand and use the concept of probability of an event to solve problems.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.

find the probability of an event from a big enough number of trials;calculate the expected number of times an event will occur, given the probability of the event and number of trials;Discuss situation


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which results in:probability of event = 1.

probability of event = 0.

solve problems involving probabilityEmphasise that the value of probability is between 0 and 1.predict the occurrence of an outcome and make a decision based on known information.Predict possible events which might occur indaily situations.

CIRCLES III

understand and use the concept of tangents to a circle.identify tangents to a circle;Develop concepts and abilities through activitiesusing technology such as the Geometers Sketchpad and graphing calculator.

Teaching aids

CompassGeometry setGspmake inference that the tangent to a circle is a straight line perpendicular to the radius that passes through the contact point;

construct the tangent to a circle passing through a point:on the circumference of the circle;

outside the circle;Ccts

Making inference

Drawing diagramdetermine the properties related to two tangents to a circle from a given point outside the circle;Properties of angle insemicircles can be used. Examples of properties of two tangents to a circle:AC = BC

(ACO = (BCO(AOC = (BOC

(AOC and (BOC are congruent.VocabularyTangent to a circle

Circle

PerpendicularRadiusCircumference

Semi circleCongruent

solve problems involving tangents to a circle.Relate to Pythagoras theorem.

O


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understand and use the properties of angle between tangent and chord to solve problems.identify the angle in the alternate segmentwhich is subtended by the chord through the contact point of the tangent;

Explore the property of angle in alternate segment using Geometers Sketchpad or other teaching aids.

VocabularyChordsAlternate segment

Major sectorSubtended

Moral values

Diligence

CooperationCourageverify the relationship between the angle formed by the tangent and the chord with the angle in the alternate segment which is

subtended by the chord;( ABE = ( BDE

( CBD = ( BEDCctsIdentifying information

Justify relationships

Problem solvingperform calculations involving the angle in alternate segmentsolve problems involving tangent to a circle and angle in alternate segment.understand and use the properties of common tangents to solve problems.determine the number of common tangents which can be

drawn to two circles which:intersect at two points;

intersect only at one point;do not intersect;Emphasise that the lengths of common tangents are equal.

Discuss the maximum number of common tangents for the three cases.VocabularyCommon tangent

E

D

A B


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verify that, for an angle in quadrant I of the unit circle :

sin ( = y-coordinate ;cos( = x-coordinate.

EMBED Equation.3 ;Begin with definitions of sine, cosine and tangent of an acute angle.

EMBED Equation.3EMBED Equation.3

EMBED Equation.3

determine the values ofsine;

cosine;tangent;

of an angle in quadrant I of the unit circle;determine the values of

sin (;cos (;tan (;

for 90( ( ( ( 360(;Explain that the conceptsin ( = y-coordinate ;

cos( = x-coordinate;EMBED Equation.3

can be extended to angles inquadrant II, III and IV.


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VocabularyQuadrant

Sine (Cosine (

Tan (determine whether the values of:

sine;cosine;

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(.

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(.determine the values of the angles in quadrant I which correspond to the values of the angles in otherquadrants;Teaching can be expanded through activities such as reflection.

state the relationships between the values of:sine;

cosine; andtangent;

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.

find the values of sine, cosine and tangent of the angles between 90( and 360(;

Teaching aids

Gsp

12

45o

1

60o

30o

1

2

3


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Graph paperGraphmatica

Geometry set

find the angles between 0( and 360(, given the values of sine, cosine or tangent;

solve problems involving sine, cosine and tangent.

Relate to daily situations.

i. 9.2 draw and usethe graphs of sine,cosine and

tangent.draw the

graphs of sine,cosine and tangentfor angles between

0( and 360(;Use

the graphingcalculator andGeometers

Sketchpad toexplore the feature

of the graphs of

y = sin (, y = cos(, y = tan

(.CctsProblem

solve problems involving

graphs of sine, cosine and

tangent.


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solvingCompare

andcontrastDrawing

graphscompare

the graphs of sine,cosine and tangentfor angles between

0( and

360(;Discuss thefeature of the

graphs of y =sin(, y = cos(, y =

tan(.MoralvaluesCooperati

onHonestyDiligenceIntegritysolve problems

involving graphs

of sine, cosine andtangent.

10. ANGLES OFELEVATIONSAND

DEPRESSION

10.1 understand and use the

concept of angle ofelevation and angle of

depression to solve

problems.

i. identify:a) the horizontal line;b) the angle of elevation;c) the angle of depression,

for a particular situation;

Use daily situations to introduce

the concept.

Ccts

Working out mentallyCompare and contrast

Identifying

relationship

Decision making

Problem solving

ii. Represent a particular situationinvolving:

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 depressionHorizontal line

Moral values

Rationality

Cooperation

iii. Solve problems involving theangle of elevation and the angle of

depression.

Involve activities outside the

classroom.

Teaching aids:

Models

Cd courseware


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11.LINES ANDPLANES IN 3-

DIMENSIONS


concept of angle

between lines and

planes to solveproblems

i. identify planes; Carry out activities using dailysituations and 3-dimensional

models.

Ccts

Describing

Interpreting

Drawing diagramsProblem solving

ii. identify horizontal planes, verticalplanes and inclined planes;

Differentiate between 2-

dimensional and 3-dimensional

shapes. Involve planes found innatural surroundings.

Moral values

Respect

Cooperation

iii. sketch a three dimensional shapeand identify the specific planes;

Approaches

Constructivism

Exploratory

Cooperative learning

iv. identify:A) lines that lies on a

plane;

B) lines that intersectwith a plane;

Vocabulary

Horizontal plane

Vertical plane

3-dimensional

Normal to a planeOrthogonal projectionSpace diagonal

Angle between twoplanes

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 orthogonalprojection of a line on a plane;

Include lines in 3-dimensional

shapes.

viii.determine the angle between a lineand a plane;

ix. solve problems involving the anglebetween a line and a plane.

Use 3-dimensional models to

give clearer pictures.


concept of angle

i. identify the line of intersectionbetween two planes;


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between two planes to

solve problems.

ii. draw a line on each plane which isperpendicular to the line ofintersection of the two planes at a

point on the line of intersection;

iii. determine the angle between twoplanes on a model and a given

diagram;

Use 3-dimensional models to

give clearer pictures.

iv. solve problems involving lines andplanes in 3-dimensional shapes.

yearly plan maths f4 repaired)

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