Yearly Plan Mathematiccs F4

8/9/2019 Yearly Plan Mathematiccs F4

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1

LEARNING AREA:

Form 4

LEARNING OBJECTIVES

Pupils will be taught to…

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOMES

Pupils will be able to…POINTS TO NOTE WEEK

1 Understand and use the

concept of significant figure.


concept of standard form to

solve problems.

Discuss the significance of zero in a

number.

Discuss the use of significant figures

in everyday life and other areas.

Use everyday life situations such as in

health, technology, industry,

construction and business involving

numbers in standard form.

Use scientific calculator to explore


(i) Round off positive numbers to

a given number of significant

figures when the numbers are

a) greater than !,

b) less than !.

(ii) "erform operations of addition,

subtraction, multiplication and

division, involving a fewnumbers and state the answer

in specific significant figures.

(iii) #olve problems involving

significant figures.

(i) #tate positive numbers in

standard form when the

numbers are

a) greater than or e$ual to !%,

b) less than !.

(ii) &onvert numbers in standardform to single numbers.

(iii) "erform operations of addition,

subtraction, multiplication and

division, involving any two

numbers and state the answers

in standard form.

(iv) #olve problems involving


Rounded numbers are

only approximates.

'imit to positive

numbers only.

enerally, rounding

is done on the final

answer.

nother term for

standard form is

scientific notation.

*nclude two numbers

in standard form.

1



2 Form 4LEARNING OBJECTIVES



LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand the concept

of $uadratic expression.

Discuss the characteristics of $uadratic

expressions of the

form ax ++ bx + c = % , where a, b

and c are constants, a ≠ % and x is anunnown.

Discuss the various methods to obtain

the desired product.

-egin with the case a !.

/xplore the use of graphing calculator

to factorise $uadratic expressions.

(i) *dentify $uadratic expressions.

(ii) 0orm $uadratic expressions by

multiplying any two linear

expressions.

(iii) 0orm $uadratic expressions

based on specific situations.(i) 0actorise $uadratic expressions

of the form ax ++ bx + c , b

% or c %.

(ii) 0actorise $uadratic expressions

of the form px+− q, p and q are

perfect s$uares.

(iii) 0actorise $uadratic expressions

of the form ax+

1 bx 1 c, a, band c not e$ual to zero.

(iv) 0actorise $uadratic expressions

containing coefficients with

common factors.

*nclude the case

when b % and2or

c %.

/mphasise that for

the terms x+

and x, the

coefficients are

understood to be !.

*nclude everyday life

situations.

! is also a perfect

s$uare.

0actorisation

methods that can be

used are

• cross method3

• inspection.

2 0actorise $uadratic

expression.

2






LEARNING ACTIVITIES

LEARNING OUTCOMES



of $uadratic e$uation.

Discuss the characteristics of $uadratic

e$uations.

Discuss the number of roots of a

$uadratic e$uation.

Use everyday life situations.

(i) *dentify $uadratic e$uations

with one unnown.

(ii) 4rite $uadratic e$uations in

general form i.e.

ax ++ bx + c = % .

(iii) 0orm $uadratic e$uations

based on specific situations.

(i) Determine whether a given

value is a root of a specific

$uadratic e$uation.

(ii) Determine the solutions for

$uadratic e$uations by

a) trial and error method,

b) factorisation.


$uadratic e$uations.


situations.

5here are $uadratic

e$uations that cannot

be solved by

factorisation.

&hec the rationality

of the solution.


concept of roots of $uadratic

e$uations to solve problems.

3



3LEARNING AREA:

Form 4LEARNING OBJECTIVES



LEARNING ACTIVITIES

LEARNING OUTCOMES



of set.

Use everyday life examples to

introduce the concept of set.

Discuss the difference between the

representation of elements and the

number of elements in 7enn diagrams.

(i) #ort given ob8ects into groups.

(ii) Define sets by

a) descriptions,

b) using set notation.

(iii) *dentify whether a given ob8ectis an element of a set and usethe symbol ∈ or ∉.

(iv) Represent sets by using 7enn

diagrams.

5he word set refers to

any collection or

group of ob8ects.

5he notation used for

sets is braces, 9 :.

5he same elements in

a set need not be

repeated.

#ets are usually

denoted by capital

letters.5he definition of sets

has to be clear and

precise so that the

elements can be

identified.

5he symbol ∈

(epsilon) is read ;is

an element of< or ;is

a member of<.

5he symbol ∉ is read

;is not an element of<

or ;is not a member

of<.

4



3LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


Discuss why 9 % : and 9∅ : are

not empty sets.

-egin with everyday life situations.

Discuss the relationship between sets

and universal sets.

(v) 'ist the elements and state the

number of elements of a set.

(vi) Determine whether a set is an

empty set.

(vii) Determine whether two sets are

e$ual.

(i) Determine whether a given setis a subset of a specific set anduse the symbol ⊂ or ⊄ .

(ii) Represent subset using 7enn

diagram.

(iii) 'ist the subsets for a specific

set.

(iv) *llustrate the relationship

between set and universal set

using 7enn diagram.

(v) Determine the complement of a

given set.

(vi) Determine the relationship

between set, subset, universal

set and the complement of a

set.

5he notation n(A)

denotes the number

of elements in set A.

5he symbol∅

(phi) or 9 : denotes

an

empty set.

n empty set is also

called a null set.

n empty set is a

subset of any set.

/very set is a subset

of itself.

5he symbol ξdenotes a universal

set.

5he symbol A′denotes

the complement of setA.


situations.


concept of subset, universal

set and the complement of a

set.

5



3LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


3 "erform operations on

sets

• the intersection of sets,

• the union of sets.

Discuss cases when

• A ∩B ∅,

• A ⊂ B.

(i) Determine the intersection of

a) two sets,

b) three sets,

and use the symbol ∩.

(ii) Represent the intersection of

sets using 7enn diagram.

(iii) #tate the relationship between

a) A ∩B and A,

b) A ∩B and B.(iv) Determine the complement of

the intersection of sets3

(v) #olve problems involving the

intersection of sets.

(vi) Determine the union of

a) two sets,

b) three sets,

and use the symbol ∪.

(vii) Represent the union of sets

using 7enn diagram.(viii) #tate the relationship between

a) A ∪B and A,

b) A ∪B and B.

(ix) Determine the complement of

the union of sets.


situations.


situations.

6



3LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES

Pupils will be able to…POINTS TO NOTE

WEEK

(x) #olve problems involving the

union of sets.

(xi) Determine the outcome of

combined operations on sets.

(xii) #olve problems involving

combined operations on sets.


situations.


situations.

7






LEARNING ACTIVITIES

LEARNING OUTCOMES



of statement.

*ntroduce this topic using everyday

life situations.

0ocus on mathematical sentences.

Discuss sentences consisting of

• words only,

• numbers and words,

• numbers and mathematical symbols.

#tart with everyday life situations.

(i) Determine whether a given

sentence is a statement.

(ii) Determine whether a given

statement is true or false.

(iii) &onstruct true or false

statements using given

numbers and mathematical

symbols.

(i) &onstruct statements using the

$uantifiera) all,

b) some.

#tatements consisting

of

• words only,

e.g. ;0ive is

greater than

two<3

• numbers and

words, e.g. ;= is

greater than +<3

• numbers and

symbols, e.g. = > +

5he following are not

statements

• ;*s the place

value of digit ? in

!?+@ hundredsA<

• 6n − =m 1 + s

• ;dd the

two

numbers.<

• x 1 + @

Buantifiers such as

;every< and ;any<

can be introduced

based on context.


of $uantifiers ;all< and;some<.

8






LEARNING ACTIVITIES

LEARNING OUTCOMES


(ii) Determine whether a statement

that contains the $uantifier

;all< is true or false.

(iii) Determine whether a statement

can be generalised to cover all

cases by using the $uantifier

;all<.

(iv) &onstruct a true statement

using the $uantifier ;all< or

;some<, given an ob8ect and a

property.

Examples

• ll s$uares are

four sided figures.

• /very s$uare is

a four sided

figure.

• ny s$uare is a

four sided figure.

Cther $uantifiers

such as ;several<,

;one of< and ;part

of< can be used basedon context.

Example

Object 5rapezium.

Property 5wo sides

are parallel to each

other.

Statement ll

trapeziums have two

parallel sides.

Object /vennumbers.

Property Divisible

by 6.

Statement #ome

even numbers are

divisible by 6.

9



p p5rue

0alse

0alse

5rue

p q p and q

5rue 5rue 5rue

5rue 0alse 0alse

0alse 5rue 0alse

0alse 0alse 0alse




LEARNING ACTIVITIES

LEARNING OUTCOMES


3 "erform operations

involving the words ;not< or

;no<, ;and< and ;or< on

statements.

-egin with everyday life situations. (i) &hange the truth value of a

given statement by placing the

word ;not< into the original

statement.

(ii) *dentify two statements from a

compound statement that

contains the word ;and<.

5he negation ;no< can

be used where

appropriate.

5he symbol ;< (tilde)

denotes negation.

; p< denotes negation of

p which means ;not p<

or ;no p<.

5he truth table for p and

p are as follows

5he truth values for ; p

and q< are as follows

10



p q p or q

5rue 5rue 5rue

5rue 0alse 5rue

0alse 5rue 5rue0alse 0alse 0alse




LEARNING ACTIVITIES

LEARNING OUTCOMES


(iii) 0orm a compound statement by

combining two given

statements using the word

;and<.

(iv) *dentify two statement from a

compound statement that

contains the word ;or<.

(v) 0orm a compound statement by

combining two given

statements using the word ;or<.

(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<.

5he truth values for ; p

or q< are as follows

11






LEARNING ACTIVITIES

LEARNING OUTCOMES



of implication.

#tart with everyday life situations. (i) *dentify the antecedent and

conse$uent of an implication

;if p, then q<.

(ii) 4rite two implications from a

compound statement

containing ;if and only if<.

(iii) &onstruct mathematical

statements in the form of

implication

a) *f p, then q,

b) p if and only if q.

(iv) Determine the converse of a

given implication.

(v) Determine whether the

converse of an implication is

true or false.

*mplication ;if p, then

q< can be written as

p ⇒ q, and ; p if andonly if q< can be writtenas p ⇔ q, which means

p ⇒ q and q ⇒ p.

5he converse of an

implication is not

necessarily true.

Example 1

*f x E F, then

x E = (true)

&onversely

*f x E =, then

x E F (false)

12






LEARNING ACTIVITIES

LEARNING OUTCOMES


#tart with everyday life situations. (i) *dentify the premise andconclusion of a given simple

argument.

(ii) Gae a conclusion based on

two given premises for

a) rgument 0orm *,

b) rgument 0orm **,

c) rgument 0orm ***.

Example 2

*f PQR is a triangle, thenthe sum of the interiorangles of PQR is !@%°.

(true)

&onversely

*f the sum of the interiorangles of PQR is !@%°,then PQR is a triangle.

(true)

'imit to arguments withtrue premises.

Hames for argument

forms, i.e. syllogism

(0orm *), modus ponens

(0orm **) and modus

tollens (0orm ***), need

not be introduced.

5 Understand the conceptof argument.

13






LEARNING ACTIVITIES

LEARNING OUTCOMES



concept of deduction and

induction to solve problems.

/ncourage students to producearguments based on previous

nowledge.

Use specific examples2activities to

introduce the concept.

(iii) &omplete an argument given a premise and the conclusion.

(i) Determine whether a

conclusion is made through

a) reasoning by deduction,

b) reasoning by induction.

#pecify that these threeforms of arguments are

deductions based on two

premises only.

Argument Form I

Premise 1 ll A are B.

Premise 2 is A.

onclusion is B.

Argument Form II

Premise 1 *f p, then q.

Premise 2 p is true.

onclusion q is true.

Argument Form III

Premise 1 *f p, then q.

Premise 2 Hot q is true.

onclusion Hot p is

true.

14






LEARNING ACTIVITIES

LEARNING OUTCOMES


WEEK

(ii) Gae a conclusion for aspecific case based on a given

general statement, by

deduction.

(iii) Gae a generalization based on

the pattern of a numerical

se$uence, by induction.

'imit to cases where

formulae can be

induced.

(iv) Use deduction and induction in

problem solving.#pecify that

maing conclusion by

deduction is definite3

maing conclusion by

induction is not

necessarily definite.

15



5LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand the conceptof gradient of a straight line.

Use technology such as theeometerIs #etchpad, graphing

calculators, graph boards, magnetic

boards or topo maps as teaching aids

where appropriate.

-egin with concrete examples2daily

situations to introduce the concept of

gradient.

7ertical

distanceθ

Jorizontal distance

Discuss

• the relationship between

gradient and tan θ,

• the steepness of the straight line

with different values of gradient.

&arry out activities to find the ratio of

vertical distance to horizontal distance

for several pairs of points on a straightline to conclude that the ratio is

constant.

(i) Determine the vertical andhorizontal distances between

two given points on a straight

line.

(ii) Determine the ratio of vertical

distance to horizontal distance.

16



5LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


2 Understand the conceptof gradient of a straight line

in &artesian coordinates.

Discuss the value of gradient if• P is chosen as ( x!, !!) and Q is

( x+, !+),

• P is chosen as ( x+, !+) and Q is

( x!, !!).

(i) Derive the formula for thegradient of a straight line.

(ii) &alculate the gradient of a

straight line passing through

two points.

(iii) Determine the relationship between the value of the

gradient and the

a) steepness,

b) direction of inclination

of a straight line.

(i) Determine the xKintercept and

the !Kintercept of a straight

line.

(ii) Derive the formula for thegradient of a straight line in

terms of the xKintercept and the

!Kintercept.

(iii) "erform calculations involving

gradient, xKintercept and

!Kintercept.

5he gradient of astraight line passing

through P ( x!, !!) and

Q( x+, !+) is

m =

! + − !!

x+− x!

/mphasise that

xKintercept and

!Kintercept are not

written in the form

of coordinates.


of intercept.

17



5LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


4 Understand and usee$uation of a straight line.

Discuss the change in the form of thestraight line if the values of m and c

are changed.

&arry out activities using the graphing

calculator, eometerIs #etchpad or

other teaching aids.

7erify that m is the gradient and c is

the !Kintercept of a straight line with

e$uation ! mx 1 c .

(i) Draw the graph given ane$uation of the form

! mx 1 c.

(ii) Determine whether a given

point lies on a specific straight

line.

(iii) 4rite the e$uation of the

straight line given the gradient

and !Kintercept.

(iv) Determine the gradient and

!Kintercept of the straight line

which e$uation is of the form

a) ! mx 1 c,

b) ax 1 b! c.

(v) 0ind the e$uation of the

straight line which

a) is parallel to the xKaxis,

b) is parallel to the !Kaxis,

c) passes through a given

point and has a specific

gradient,

d) passes through two given

points.

/mphasise that thegraph obtained is a

straight line.

*f a point lies on a

straight line, then the

coordinates of the

point satisfy the

e$uation of the

straight line.

5he e$uation

ax 1 b! c can be

written in the form

! mx 1 c.

18



5LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


Discuss and conclude that the point of intersection is the only point that

satisfies both e$uations.

Use the graphing calculator and

eometerIs #etchpad or other

teaching aids to find the point of

intersection.

/xplore properties of parallel lines

using the graphing calculator and

eometerIs #etchpad or other

teaching aids.

(vi) 0ind the point of intersectionof two straight lines by

a) drawing the two straight

lines,

b) solving simultaneous

e$uations.

(i) 7erify that two parallel lines

have the same gradient and

vice versa.

(ii) Determine from the givene$uations whether two straight

lines are parallel.

(iii) 0ind the e$uation of the straight

line which passes through a

given point and is parallel to

another straight line.


e$uations of straight lines.


concept of parallel lines.

19






LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand the conceptof class interval.

Use data obtained from activities andother sources such as research studies

to introduce the concept of class

interval.

Discuss criteria for suitable class

intervals.

(i) &omplete the class interval fora set of data given one of the

class intervals.

(ii) Determine

a) the upper limit and lower

limit,

b) the upper boundary and

lower boundary

of a class in a grouped data.

(iii) &alculate the size of a class

interval.

(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) &onstruct a fre$uency table for

a given set of data.

(i) Determine the modal class

from the fre$uency table of

grouped data.

(ii) &alculate the midpoint of a

class.

#ize of class interval

Lupper boundary M

lower boundaryN

Gidpoint of class

!

(lower limit 1+

upper limit)


concept of mode and mean of

grouped data.

20



WEEK6 Form 4LEARNING OBJECTIVES



LEARNING ACTIVITIES

LEARNING OUTCOMES


(iii) 7erify the formula for themean of grouped data.

(iv) &alculate the mean from the

fre$uency table of grouped

data.

(v) Discuss the effect of the size of

class interval on the accuracy

of the mean for a specific set of

grouped data.

3 Represent and interpret

data in histograms with class

intervals of the same size tosolve problems.

4 Represent and interpret

data in fre$uency polygons to

solve problems.

Discuss the difference between

histogram and bar chart.

Use graphing calculator to explore the

effect of different class interval on

histogram.

(i) Draw a histogram based on the

fre$uency table of a grouped

data.

(ii) *nterpret information from a

given histogram.


histograms.

(i) Draw the fre$uency polygon

based on

a) a histogram,

b) a fre$uency table.

(ii) *nterpret information from a

given fre$uency polygon.


fre$uency polygon.


situations.

4hen drawing a

fre$uency polygon

add a class with %

fre$uency before the

first class and after

the last class.


situations.

21






LEARNING ACTIVITIES

LEARNING OUTCOMES


5 Understand the conceptof cumulative fre$uency.

Discuss the meaning of dispersion by

comparing a few sets of data.

raphing calculator can be used for

this purpose.

(i) &onstruct the cumulativefre$uency table for

a) ungrouped data,

b) grouped data.

(ii) Draw the ogive for

a) ungrouped data,

b) grouped data.

(i) Determine the range of a set of

data.

(ii) Determine

a) the median,

b) the first $uartile,

c) the third $uartile,

d) the inter$uartile range,

from the ogive.

(iii) *nterpret information from an

ogive.

4hen drawing ogive

• use the

upper

boundaries3

• add a class

with zero

fre$uency

before the firstclass.

0or grouped data

Range Lmidpoint of

the last class M

midpoint of the first

classN


concept of measures of

dispersion to solve problems.

22



WEEK




LEARNING ACTIVITIES

&arry out a pro8ect2research andanalyse as well as interpret the data.

"resent the findings of the

pro8ect2research.

/mphasise the importance of honesty

and accuracy in managing statistical

research.

LEARNING OUTCOMES


(iv) #olve problems involving datarepresentations and measures

of dispersion.

23






LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand the conceptof sample space.

Use concrete examples such asthrowing a die and tossing a coin.

Discuss that an event is a subset of the

sample space.

Discuss also impossible events for a

sample space.

Discuss that the sample space itself is

an event.

&arry out activities to introduce the

concept of probability. 5he graphing

calculator can be used to simulate such

activities.

(i) Determine whether an outcomeis a possible outcome of an

experiment.

(ii) 'ist all the possible outcomes

of an experiment

a) from activities,

b) by reasoning.

(iii) Determine the sample space of

an experiment.

(iv) 4rite the sample space by

using set notations.

(i) *dentify the elements of a

sample space which satisfy

given conditions.

(ii) 'ist all the elements of a

sample space which satisfy

certain conditions using set

notations.

(iii) Determine whether an event is

possible for a sample space.

(i) 0ind the ratio of the number oftimes an event occurs to the

number of trials.

(ii) 0ind the probability of an event

from a big enough number of

trials.

n impossible event

is an empty set.

"robability is

obtained from

activities and

appropriate data.


of events.


concept of probability of an

event to solve problems.

24



7 Form 4

LEARNING OBJECTIVES



LEARNING ACTIVITIES

LEARNING OUTCOMES

Pupils will be able to…

POINTS TO NOTE WEEK

Discuss situation which results in

• probability of event !.

• probability of event %.

/mphasise that the value of

probability is between % and !.

"redict possible events which might

occur in daily situations.

(iii) &alculate the expected number

of times an event will occur,

given the probability of the

event and number of trials.


probability.

(v) "redict the occurrence of an

outcome and mae a decision

based on nown information.

25



8LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand and use theconcept of tangents to a

circle.

Develop concepts and abilities throughactivities using technology such as the

eometerIs #etchpad and graphing

calculator.

(i) *dentify tangents to a circle.

"roperties of angle in

semicircles can be

used. /xamples of

properties of two

tangents to a circle A

"

B A B

∠ A" ∠ B"

∠ A" ∠ B"

Δ A" and Δ B" are

congruent.

(ii) Gae inference that the tangent

to a circle is a straight line

perpendicular to the radius that

passes through the contact

point.

(iii) &onstruct the tangent to a

circle passing through a point

a) on the circumference of the

circle,

b) outside the circle.

(iv) Determine the properties

related to two tangents to a

circle from a given point

outside the circle.

26



8LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


/xplore the property of angle in

alternate segment using eometerIs

#etchpad or other teaching aids.

Discuss the maximum number ofcommon tangents for the three cases.

(v) #olve problems involvingtangents to a circle.

(i) *dentify the angle in the

alternate segment which is

subtended by the chord through

the contact point of the tangent.

(ii) 7erify the relationship betweenthe angle formed by the

tangent and the chord with the

angle in the alternate segment

which is subtended by the

chord.

(iii) "erform calculations involving

the angle in alternate segment.


tangent to a circle and angle in

alternate segment.

(i) Determine the number ofcommon tangents which can be

drawn to two circles which

a) intersect at two points,

b) intersect only at one point,

c) do not intersect.

Relate to "ythagorasI5heorem

E

#

A B

∠ ABE ∠ B#E ∠B# ∠ BE#

/mphasise that thelengths of common

tangents are e$ual.


properties of angle between

tangent and chord to solve

problems.


properties of common

tangents to solve problems.

27



WEEK

8LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


*nclude daily situations. (ii) Determine the propertiesrelated to the common tangent

to two circles which

a) intersect at two points,

b) intersect only at one point,

c) do not intersect.


common tangents to two

circles.


tangents and common tangents.*nclude problems

involving

"ythagorasI

5heorem.

28



9LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand and use theconcept of the values of

sin θ, cos θ and tan θ (%° ≤ θ

≤ FO%°) to solve problems.

/xplain the meaning of unit circle.

!

P$x%!&

! !

x% x Q

-egin with definitions of sine, cosine

and tangent of an acute angle.

PQ !sin θ

= = = !"P !

cosθ ="Q

= x= x

"P !

tan θ =

PQ=

!

"Q x

(i) *dentify the $uadrants andangles in the unit circle.

(ii) Determine

a) the value of !Kcoordinate,

b) the value of xKcoordinate,

c) the ratio of !Kcoordinate to

xKcoordinate

of several points on the

circumference of the unit

circle.

(iii) 7erify that, for an angle in

$uadrant * of the unit circle

a) sin θ !Kcoordinate,

b) cosθ xKcoordinate,

!Kcoordinatec) tan θ

xKcoordinate.

(iv) Determine the values ofa) sine,

b) cosine,

c) tangent

of an angle in $uadrant * of the

unit circle.

5he unit circle is thecircle of radius ! with

its centre at the

origin.

29



9LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


/xplain that the conceptsin θ !Kcoordinate ,

cosθ xKcoordinate,

tan θ !Kcoordinate

xKcoordinate

can be extended to angles in

$uadrant **, *** and *7.

+ o

!√+ F%

√F

6=o

O%o

! !

Use the above triangles to find the

values of sine, cosine and tangent for

F%°, 6=°, O%°.

5eaching can be expanded through

activities such as reflection.

(v) Determine the values ofa) sin θ,

b) cos θ ,

c) tan θ ,

for ?%° ≤ θ ≤ FO%°.

(vi) Determine whether the values

of

a) sine,

b) cosine,

c) tangent,of an angle in a specific

$uadrant is positive or

negative.

(vii) Determine the values of sine,

cosine and tangent for special

angles.

(viii) Determine the values of the

angles in $uadrant * which

correspond to the values of the

angles in other $uadrants.

&onsider special

angles such as %°,

F%°, 6=°, O%°, ?%°,

!@%°, +P%

°, FO%

°.

30



WEEK

9LEARNING AREA:




LEARNING ACTIVITIES

Use the eometerIs #etchpad toexplore the change in the values of

sine, cosine and tangent relative to the

change in angles.

LEARNING OUTCOMES


(ix) #tate the relationships betweenthe values of

a) sine,

b) cosine, and

c) tangent

of angles in $uadrant **, *** and

*7 with their respective values

of the corresponding angle in

$uadrant *.

(x) 0ind the values of sine, cosineand tangent of the angles

between ?%° and FO%°.

(xi) 0ind the angles between %° and

FO%°, given the values of sine,

cosine or tangent.

Relate to daily situations. (xii) #olve problems involving sine,

cosine and tangent.

31



9LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


2 Draw and use the graphsof sine, cosine and tangent.

Use the graphing calculator andeometerIs #etchpad to explore the

feature of the graphs of

! sin θ, ! cos θ, ! tan θ.

Discuss the feature of the graphs of

! sin θ, ! cos θ, ! tan θ.

Discuss the examples of these graphs

in other areas.

(i) Draw the graphs of sine, cosineand tangent for angles between

%° and FO%°.

(ii) &ompare the graphs of sine,cosine and tangent for angles between %° and FO%°.


graphs of sine, cosine and

tangent.

32






LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand and use theconcept of angle of elevation

and angle of depression to

solve problems.

Use daily situations to introduce theconcept.

(i) *dentifya) the horizontal line,

b) the angle of elevation,

c) the angle of depression

for a particular situation.

(ii) Represent a particular situation

involving

a) the angle of elevation,

b) the angle of depression

using diagrams.

(iii) #olve problems involving theangle of elevation and the

angle of depression.

*nclude two

observations on the

same horizontal

plane.

*nvolve activitiesoutside the

classroom.

33



11LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


1 Understand and use theconcept of angle between

lines and planes to solve

problems.

&arry out activities using dailysituations and FKdimensional models.

Differentiate between +Kdimensional

and FKdimensional shapes. *nvolve

planes found in natural surroundings.

-egin with FKdimensional models.

Use FKdimensional models to give

clearer pictures.

(i) *dentify planes.

(ii) *dentify horizontal planes,

vertical planes and inclined

planes.

(iii) #etch a three dimensional

shape and identify the specific

planes.

(iv) *dentifya) lines that lie on a plane,

b) lines that intersect with a

plane.

(v) *dentify normals to a given

plane.

(vi) Determine the orthogonal

pro8ection of a line on a plane.

(vii) Draw and name the orthogonal

pro8ection of a line on a plane.

(viii) Determine the angle between a

line and a plane.

(ix) #olve problems involving the

angle between a line and a

plane.

*nclude lines in

FKdimensional

shapes.

34



11LEARNING AREA:




LEARNING ACTIVITIES

LEARNING OUTCOMES


2 Understand and use theconcept of angle between

two planes to solve

problems.

Use FKdimensional models to give

clearer pictures.

(i) *dentify the line of intersection between 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.

(iii) Determine the angle between

two planes on a model and a

given diagram.

(iv) #olve problems involving lines

and planes in FKdimensionalshapes.

35

Documents

Yearly Plan Mathematiccs F4