Math F4(2013)

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SMK St. Mark, Butterworth

Scheme of Work

Form 4 Mathematics ( 2013 )

First Term ( 20 weeks )

Weeks Topics Learning Objectives Learning Outcomes Teaching And Learning

Activities

Vocabulary

1 - 2 1. Standard

Form

1.1 Understand and use the

concept of significantfigure.


concept of standard form tosolve problems

i. round off positive numbers to a given

number of significant figures when thenumber are :

a) greater than 1.

b) less than 1ii .perform operations of addition ,

subtraction , multiplication and division

involving a few numbers and state theanswer in specific significant figures .

iii. solve problems involving significant

figures .

i. state positive numbers in standard form

when the numbers are :a) greater than or equal to 10.

b) less than 1.ii. convert numbers in standard form to

single numbers.

iii. perform operations of addition,

subtraction , multiplication anddivision , involving any two numbersand state the answer in standard form

iv. solve problems involving numbers in

standard form.

Discuss the significance

of zero in a number.

- Working out mentally.

- Identifying relations.

Discuss the use of

significant figures ineveryday life and other

areas.

Use everyday life

situations such as inhealth,technology

,industry ,constructionand business involving

numbers in standard

form.

Use the scientificcalculator to explore

numbers in standard

form.

significance

significantfigure

relevant

round offaccuracy

single number

approximate

standard form

single numberscientific

notation

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Week Topics Learning Objectives Learning Outcomes Teaching And Learning

Activities

Vocabulary

34 2. Quadratic

Expressions

And

Equations

2.1 Understand the concept of

quadratic expression.

2.2 Factorise quadratic

expression.


quadratic equation


concept of roots ofquadratic equations to

solve problems.

i. identify quadratic expressions .

angles of a polygons.

ii. form quadratic expressions by

multiplying any two linear expressions.iii. form quadratic expressions based on

specific situations.

polygon given the number of sides.

i. factorise quadratic expressions of the

form ax2 + bx + c , where b = 0 or c = 0.

ii. factorise quadratic expressions of the

form px2q ,p and q are perfect squares.

iii. factorise quadratic expressions of the

form ax2

+ bx + c, where a,b and c arenot equal to zero.

iv. factorise quadratic expressionscontaining coefficients with

common factors.

i. identify quadratic equations with one

unknown.ii. write quadratic equations in general form

i.e ax2 + bx + c = 0

iii. form quadratic equations based on

specific situations.

i. determine whether a given value is a root

of a specific quadratic equation.ii. determine the solution for quadratic

equations by ;a) trial and error method / b) factorizationiii.solve problems involving quadratic

equations

Discuss the

characteristics of

quadratic expressions of

the form ax2 + bx + c =0, where a , b and c are

constants , a 0 and x is

an unknown.

Discuss the various

methods to obtain the

desired product.

Begin with the case a =1

Explore the use ofgraphing calculator to

factorise quadraticexpressions.

Discuss the

characteristics ofquadratic equations.

Discuss the number of

roots of a quadraticequation.

Use everyday lifesituations.

quadratic

expression

constant

constant factorunknown

highest power

coefficient

expandterm

factorise

common factor

perfect squarecross method

inspectioncomplete

factorisation

quadratic

equationsgeneral form

substitute

roottrial and error

methodsolution.

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Week Topics Learning Objectives Learning Outcomes Teaching And Learning

Activities

Vocabulary

5 3. Sets 3.1Understand the concept of

set.


concept o f subset ,universal set and the

complement of a set.

i. sort given objects into groups.

ii. define sets by ;

a) descriptions.

b) using set notation.iii. identify whether a given object is an

element of a set and use the symbol or

iv.represent sets by using Venn diagrams.v. list 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 equal.

i. determine whether a given set is a subset

of a specific set and use the symbol or

ii. represent subset using Venn diagram.

iii.list the subjects for a specific set.

iv. illustrate the relationship between setand universal set using Venn diagram.

v. determine the complement of a given set.

vi. determine the relationship between set ,subset ,universal set and the complement

of a set.

Use everyday life

examples to introduce the

concept of set.

Discuss why { o }and

{ } are not empty

sets.

Comparing and

contrasting

Drawing diagrams

Discuss the relationship

between sets anduniversal sets.

Identifying relations

set

element

description

labelset notation

denote

equal set

subset

universal set

complement of a

set

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Activities

Vocabulary

6 3.3 Perform operations on sets

The intersectionof sets

The union of sets

i. determine the intersection of ;

a) two sets

b) three sets

and use the symbol .ii. represent the intersection of sets using

Venn diagram

iii. state the relationship between

a) A B and Ab) A B and B

iv. Determine the complement of the

intersection of sets.

v. solve problems involving the

intersection of sets.vi. determine the union of

a) two setsb) three sets

and use the symbol

vii. represent the union of sets using

Venn diagram.

viii.state the relationship between

a) A B and A

b) A B and B

ix. determine the complement of the union

of sets.x. solve problems involving the union of

sets.xi. determine the outcome of combined

operations on sets .

xii. solve problems involving combinedoperations on sets.

Discuss cases when;

A B = A B

Include everyday life

situations.

intersection

common

elements

7 Chinese New Year Holidays (11th

February17th

February)

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Activities

Vocabulary

8 4.Mathematical

Reasoning


statement .

4.2 Understand the concept ofquantifiers all and

some

4.3 Perform operations

involving the words not

for no , and and oron statement.

i) determine whether a given sentence is a

statement

ii) determine whether a given statement is

true or false.iii) construct true or false statement using

given numbers and mathematical

symbols.

i) construct statements using the quantifier :a) all

b) someii) determine whether a statement that

contains the quantifier allis true or

falseiii) determine whether a statement can be

generalized to cover all cases by usingthe quantifier all

iv) construct a true statement using the

quantifier all or some given an

object and a property.

i) change the truth value of a given

statement by placing the word not into

the orginal statement.

Introduce this topic

using everyday life

situations.

Focus on mathematical

sentences.

Discuss sentencesconsisting of :1.words only

2. numbers and words

3. numbers and

mathematical symbols.

Quantifiers such asevery and any can be

introduced based oncontext.

Other quantifiers such as several ,one of and

part of can be usedbased on context.

The symbol ~ ( tilde )

denotes negation.

~p denotes negationof p which meansnot p or no p .

statement

true

false

mathematicalsentence

mathematical

statement

mathematicalsymbols

quantifierall

everyany

some

severalone of

part of

negatecontrary

object

negation

not pno ptruth table

truth value

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Activities

Vocabulary

9

4.4 Understand the concept ofimplication

ii) identify two statements from a

compound statement that contains the

word and.

iii) form a compound statement bycombining two givens statements using

the word and

iv) identify two statements from a

compound statement that contains theword or

v) form a compound statements by

combining two given statements using

the word or

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

combination of two statements with theword and

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

combination of two statements with the

word or

i) identify the antecedent and consequentof an implication if p, then q .

ii) write two implication from a compound

statement.

iii) construct mathematical statementin the form of implicationa) if 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.

and

compound

statement

or

implicationantecedent

consequent

converse

10 Assessment 1 (4th

March8th

March)

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Activities

Vocabulary

11 - 12 4.5 Understand the concept of

argument.


concept of deduction andinduction to solve

problems.

i) identify the premise and conclusion of a

given simple argument

ii) make conclusion based on two given

premises for :a) Argument Form I

b) Argument Form II

c) Argument Form III

iii) complete an argument given a premiseand the conclusion.

i) determine whether a conclusion is made

througha) reasoning by deduction

b) reasoning by induction.ii) make a conclusion for a specific case

based on a given general statement ,bydeduction .

iii) make generalization based on

the pattern of a numerical sequence ,byinduction.

iv) use deduction and induction in problemsolving .

Limit to arguments with

true premises.

Encourage students toproduce arguments based

on previous knowledge .

Limit to cases where

formulae can be induced.

Specify that:* making conclusion by

deduction is definite.

* making conclusion by

induction is notnecessarily

definite.

argument

premise

conclusion

reasoning

deductioninduction

pattern

specialconclusion

generalstatement

general

conclusion

specific case

numericalsequence.

Mid-term School Holidays (23rd

March31st

March)

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Activities

Vocabulary

13 5. The Straight

Line


gradient of a straight line.

5.2 Understand the concept ofgradient of a straight line

in Cartesian coordinates.


intercept.

5.4 Understand and useequation of a straight line

i) determine the vertical and horizontal

distances between two given points on a

straight line.

ii) determine the ratio of vertical distanceto horizontal distance.

i) derive the formula for the gradient ofa straight line.

ii) calculate the gradient of a straight linepassing through two points.

iii) determine the relationship between thevalue of the gradient and the

a) steepness

b) direction of inclination of a straightline.

i). determine the xintercept and the y-

intercept of a straight line.

ii) derive the formula for the gradient of a

straight line in terms of the x- interceptand the y- intercept

iii) Perform calculations involving gradient

, xintercept and y- intercept

i) draw the graph given an equation of theform , y = mx +c

ii) determine whether a given point lies on

a specific straight line.

Use technology such as

the Geometers

Sketchpad , graphing ,

calculators , graph boards, magnetic boards , topo

maps as teaching aids

where appropriate.

Discuss :* the relationship

between gradient and

tan .

Discuss the value ofgradient if

* P is chosen as( x1 , y1 ) and Q is

( x2 , y2 )* P is chosen as

( x2 , y2 ) and Q is

( x1 , y1 ).

Discuss the change in theform of the straight lineif the values of m and c

are changed.

straight line

steepness

horizontal

distancevertical distance

gradient

ratio

acute angleobtuse angle

inclined upwards to the

rightinclined

downwards to

the rightundefined

x-intercept

y-intercept

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Weeks Topics Learning Objectives Learning Outcomes Teaching And LearningActivities

Vocabulary

14

5.5 Understand and use

the concept of parallellines.

iii) write the equation of the straight line

given the gradient and yintercept.

iv) determine the gradient and y- intercept

of the straight line which equation isthe form :

a). y = mx + c

b). ax + by = c

v) find the equation of the straight linewhich :a) is parallel to the x- axis

b) is parallel to the y- 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 twostraight lines by :

a) drawing the two straight lines.b) solving simultaneous equations.

i) verify that two parallel lines have thesame gradient and vice versa.

ii) determine from the given equationwhether two straight lines are parallel.

iii) find the quation of the straight line

which passes through a given point and

is parallel to another straight l ine.iv) solve problems involving straight lines

Carry out activities using

the graphing calculator ,

Geometers Sketchpad or

other teaching aids.

Verify that m is the

gradient and c is the y

intercept of a straight linewith equation y = mx + c

Discuss and conclude that

the point of intersection is

the only point thatsatisfies both equation.

Explore properties ofparallel lines .

linear equation

graph

table of valuescoefficient

constant

satisfy

parallel

point of

intersection

simultaneousequation.

parallel lines .

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Weeks Topics Learning Objectives Learning Outcomes Teaching and Learning

Activities

Vocabulary

15 6. Statistics 6.1Understand the concept

of class interval

6.2 Understand and use theconcept of mode and

mean of grouped data

i) complete the class interval for a 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 groupeddata.

iii) calculate the size of a class interval.

iv) determine the class interval given a setof data and the number of classes

v) determine a suitable class interval forgiven set of data.

vi) construct a frequency table for a given

set of data.

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

ii) calculate the midpoint of a classiii) verify the formula for the mean of

grouped data .

iv) calculate the mean from the frequencytable of grouped data .

v) discuss the effect of the size of class

interval on the accuracy of the meanfor a specific set of grouped data.

Use data obtained from

activities and othersources such as research

studies to introduce theconcept of class interval

Size of class interval =

[ upper boundarylowerboundary ]

Discuss criteria for

suitable class intervals

Midpoint of class = ( lower limit + upper

limit )

statistics

class intervaldata

grouped dataupper limit

lower limitupper boundary

lower boundary

size of classinterval

frequency table

modemode class

meanmidpoint of a

class

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Activities

Vocabulary

16

17

6.3Represent and interpret

data in histograms with

class intervala of the samesize to solve problems.

6.4 Represent and interpret

data in frequency

polygons to solveproblems.

6.5 Understand the concept ofcumulative frequency

i) draw a histogram based on the frequency

table of a grouped data.

ii) interpret information from a givenhistogram.

iii) solve problems involving histograms.

i) draw the frequency polygon based on

a) a histogram

b) a frequency table

ii) interpret information from a givenfrequency polygon.

iii) solve problems involving frequencypolygon

i) construct the cumulative frequency tablefor :

a) ungrouped datab) grouped data

ii) draw the ogive for :

a) ungrouped datab) grouped data

Discuss the difference

between histogram and

bar chart .

Use graphing calculator to

explore the effect of

different class interval onhistogram

When drawing a

frequency polygon add a

class with 0 frequencybefore the first class and

after the last class .

Include everyday lifesituations.

When drawing ogive :

use the upperboundaries

add a class withzero frequencybefore the first

class.

uniform class

interval

histogram

vertical axis

horizontal axis

frequency polygon

cumulativefrequency

ungrouped dataogive

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Activities

Vocabulary


concept of measures of

dispersion to solve

problems.

i) determine the range of a set of data

ii) determine :

a) the medium

b) the first quartilec) the third quartile

d) the interquartile range;from the ogive

iii) interpret information from an ogive .

iv) solve problems involving datarepresentations and measures ofdispersion.

For grouped data :

Range = [ midpoint of the

last classmidpoint ofthe first class ]

Emphasise the importance

of honesty and accuracyin managing statisticalresearch

range

measures of

dispersion

medianfirst quartile

third quartile

interquartile range

1819 Mid-year Examination (6th May17

th May)

20 Discussion of the mid-year examination paper

Mid-year School Holidays (25th

May9th

June)

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Second Term (22 weeks)


Activities

Vocabulary

21 7. Probability 1 7.1 Understand the concept ofsample space.

7.2 Understand the concept

of events .

i) determine whether an outcome is apossible outcome of an experiment.

ii) list all the possible outcomes of an

experiment :

a) from activitiesb) by reasoning

iii) determine the sample space of an

experiment

iv) write the sample space by using set

notations.

i) identify the elements of a sample space

which satisfy given conditions .

ii) list all the elements of a sample spacewhich satisfy certain conditions using

set notation .iii) determine whether an event is possible

for a sample space.

Use concrete examplessuch as throwing a die

and tossing a coin .

Classifying Identifying

relations

Drawingdiagrams

An impossible event is an

empty set .

Discuss that an event is a

subset of the samplespace.

Discuss also impossible

events for a sample space.

Discuss that the sample

space itself is an event.

sample spaceoutcome

experiment

possible outcome

event

elementsubset

empty setimpossible event

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Weeks Topics Learning Objectives Learning Outcomes

Teaching And Learning

Activities

Vocabulary

22 - 23 7.3 Understand and use the

concept of probability ofan event to solve

problems

i) find the ratio of the number of times an

event occurs to the number of trials .ii) find the probability of an event from a

big enough number of trials.

iii) calculate the expected number of times

an event will occur ,given theprobability of the event and number oftrials.

iv) solve problems involving probability.

v) predict the occurrence of an outcome

and make a decision based on knowninformation.

Carry out activities to

introduce the concept ofprobability . The graphing

calculator can be used to

simulate such activities.

Probability is obtainedfrom activities and

appropriate data.

Discuss situation whichresults in :

probability ofevent =1

probability ofevent =0

Emphasise that the valueof probability is between0 and 1.

Predict possible events

which might occur indaily situations.

probability

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Activities

Vocabulary

24 - 25 8. Circles II 8.1 Understand and use theconcept of tangents to a

circle .


properties of angle

between tangent andchord to solve problems.

i) identify tangents to a circle .ii) make inference that the tangent to a

circle is a straight line perpendicular tothe radius that passes through the

contact point.iii) construct the tangent to a circle passing

through a point :

a) on the circumference of the circleb) outside the circle .

iv) determine the properties related to twotangents to a circle from a given point

outside the circle.

v) solve problems involving tangents to a

circle .

i) identify the angle in the alternate

segment which is subtended by the chord

through the contact point of the targent.ii) verify the relationship between the angle

formed by the tangent and the chordwith the angle in the alternate segment

which is subtended by the chord.

iii) perform calculations involving theangle in alternate segment .

iv) solve problems involving tangent to a

circle and angle in alternate segment.

Develop concepts andabilities through activities

using technology such asthe Geometers Sketchpad

and graphing calculator .

Relate to Pythagorastheorem.

Explore the property of

angle in alternate segment

using GeometersSketchpad or other

teaching aids

tangent to a circlecircle

perpendicular

radiuscircumference

semicircle

congruent

chords

alternate segment

major sectorsubtended

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Co

Weeks Topics Learning Objectives Learning Outcomes Teaching and LearningActivities

Vocabulary

28 - 30 9. Trigonometry

( II )

9.1Understand and use the

concept of values of sin ,

cos , tan ( 00

3600 ) to solve problems

i) identify the quadrants and angles in the

unit circle .

ii) determine :a) the value of y-coordinate ;

b) the value of x- coordinate ;c) the ratio of ycoordinate to x

coordinate ;of several points on the circumference

of the unit circle ;

iii) verify that , for an angle in quadrant 1of the unit circle;

a) sin = y- coordinateb) cos = x coordinate

c) tan = ycoordinate

xcoordinate

iv) determine the values ofa) sine b) cosine c) tangent

of an angle in quadrant 1 of the unit circle

v) determine the values of:

a) sine b) cosine

c) tangent for 900 3600

vi) determine whether the values of :

a) sine b) cosine c) tangentof an angle in a specific quadrant is

positive or negative;

vii) determine the values of sine ,cosine

and tangent for special anglesviii) determine the values of the angles in

quadrant 1 which correspond to the

values of the angles in other quadrant

Explain the meaning of

unit circle.

The unit circle is the

circle of radius 1 with itscentre at the origin .

Begin with definitions of

sine ,cosine and tangent

of an acute angle.

Explain that the concept

sin = y- coordinatecos = x coordinate

tan = ycoordinate

xcoordinate

can be extended to anglesin quadrant II , III and IV.

quadrant

sine

cosine

tangent

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31

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,

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32

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33

9.

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34

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35

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37

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38

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7/29/2019 Math F4(2013)

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39

t

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40

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41

,

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42

r

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43

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3600

ii)

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44

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45

d

ta

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n

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f

or

ang

le

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46

3

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).

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47

g

r

aph

s

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f

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a

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dt

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ent

3 Assessment

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48

2 2 (2nd

September

6th

September)

Weeks Topics Learning Objectives Learning Outcomes Teaching and LearningActivities Vocabulary

33 10. Angles Of

Elevation

And

Depression

10.1Understand 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 .ii) represent a particular situation involving

a) the angle of elevationb) the angle of depression using

diagrams .

iii) solve problems involving the angle of

elevation and the angleof depression.

Use daily situations to

introduce the concept

Include two observations

on the same horizontalplane.

Involve activities outsidethe classroom

angle of elevation

angle ofdepression

horizontal line

34 11. Lines and

Planes In 3

Dimensions


concept of anglebetween lines and planes

to solve problems .

i) identify planes .

ii) identify horizontal planes ,vertical planesand inclined planes .

iii) sketch a three dimensional shape and

identify the specific planes .iv) identify ;

a) lines that lies on a planeb) lines that intersect with a plane.

v). identify normals to agiven plane .

vi) determine the orthogonal projection ofa line on a plane .

vii) draw and name the orthogonalprojection of a line on a plane.

viii) determine the angle between a line and

a plane.ix) solve problems involving the angle

Carry out activities using

daily situations and 3dimensional models .

Differentiate between 2dimensional and 3

dimensional shapes.Involve planes found in

natural surroundings.

Begin with 3dimensional

models

Include lines in 3

dimensional shapesUse 3dimensional

horizontal

plane

vertical plane

3- dimensionalnormal to a plane

orthogonalprojection

space diagonal

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49

between a line and a plane . models togive clearer

pictures .


Activities

Vocabulary

3536 11. Lines and

Planes In 3

Dimensions

11.2 Understand and use theconcept of angle

between two planes

to solve problems.

i) identify the line of intersection betweentwo planes .

ii) draw a line on each plane which is

perpendicular to the line of intersectionof 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) solve problems involving lines and

planes in 3dimensional shapes .

Angle betweentwo planes

3740 Final Year Examination (7th

October29th

October)

41 - 42 Discussion of the final year examination paper

Revision

Math F4(2013)

Documents

Transcript of Math F4(2013)