topics opsme t4

8/14/2019 Topics Opsme t4

1/20

WEEK TOPICS LEARNING

OBJECTIVES

LEARNING OUTCOMES VALUES TEACHING

AIDS/ CCTS

2-3 OPSME T4

4, 5, 6

Standard Form 1.1 Understand and

use the concept of

significant figure.

1.2 Understand and

use the concept of

standard form to

solve problems.

i. round off positive numbers to a

given number of significant figures

when the numbers are :a) greater then 1b) less then 1

ii. 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 then 1

ii. convert numbers in standard form

to single numbers;iii. perform operation of addition, subtraction,

multiplication and division, involving any

two numbers and state the answer instandard form;

iv. solve problems involving numbers in

standard form.

CorporationWorking outmentally

Identifyingrelations

Textbook,worksheets

Refer to the OPSME f4 Modul

Kementerian Pelajaran Malaysia/hns Page 1 11/7/2008


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OBJECTIVES


AIDS/ CCT

7, 8, 9

CHAPTER 2 :

QUADRATIC

EXPRESSIONS

AND

EQUATIONS

2.1 Understand the

concept Of

quadratic

expressions;

2.2 Factorisequadratic

expression;

2.3 understand theconcept of

quadratic

equations.

2.4 understand and

use the concept ofroots of quadratic

equations to solve

problems.

Student will be able to:i. identify quadratic expressions;

ii. form quadratic expressions by

multiplying any two linear expressions;

iii. form quadratic expressions base onspecific situations.

i. factorise quadratic expressions of theform ax2 + bx + c , whereb=0 or c=0

ii. factorise quadratic expressions of the form

px2

q , p and q are perfect squares;iii. factorise quadratic expressions of the form

ax2

+ bx + c where a, b, and c not equal to zero ;

iv. factorise quadratic expressions containing

coefficients with common factors.

i. identify quadratic equations with one unknown;

ii. write quadratic equations in general formi.e;

ax2

+ bx + c = 0iii. form quadratic equations base on specific

situations;

i. determine whether a given value is a root ofa specific quadratic equations;ii. determine the solutions for quadratic equations by

a) trial and error method;b) factorisations;

iii. solve problems involving quadratic equations.

CorporationWorking out

mentally

Comparing

and

contrasting

Translating,

Interpreting

Find allpossible

solutions

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Kementerian Pelajaran Malaysia Page 2 11/7/2008


3/20


OBJECTIVES


AIDS/ CCT

10, 11,

12

CHAPTER 3 :

SETS

3.1 Understand theconcept Of

set

3.2 Understand the

concept Of

subset and the

compliment of a set

3.3 Perform operationof set;

the intersectionset

the union of set

Student will be able to:i. sort given objects into groups;ii. define sets by :

a) descriptions ;b) using set notation;

iii. identify whether the given object is an element of

a set and use the symbol or

iv. represents sets by using Venn diagrams;

v. list the elements and state the number of elementsof a set;

vi. determine whether a set is an empty set;.vii. determine whether two sets are equal

Student will be able to:i. determine whether a given set is a subsets of a

specific set and use the symbol

or

;ii. represents subsets by using Venn diagrams

iii. List the subsets for a specific set;

iv. ilustrate the relationship between set and

universal set using Venn diagram;v. determine the complement of a given set;

vi. determine the relationship between the set,

subset, universal set and the complement of a set;

Student will be able to:i. determine the intersection of :

a) two sets;b) three sets ;

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

diagrams;


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4/20


OBJECTIVES


AIDS/ CCT

13 CHAPTER 3 :SETS

3.3 Perform operationof set;

the intersectionset

the union of set

Student will be able to:iii. state the relationship between

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

iv. determine the complement of the intersection of

set ;

v solve problems involving the intersection ofset ;

vi. determine the union of ;

a) two sets ;b) three sets ;

vii. represent the union of sets using Venn diagram;

viii.state the relationship between

c) A B and A ;d) 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 combined operations

on sets;

Corporation

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5/20


OBJECTIVES


AIDS/ CCT

14CHAPTER 4 :

MATHEMATICAL

REASONING

4.1 Understand theconcept of

statement;


quantifier

all or some ;

4.3 Perform

operations involving

the words not or

no,and and or

on statements ;

Student will be able to:i. determine whether the given sentence is a

statement ;

ii. determine whether the given statement is true or

false;

iii. Contruct true or false statement using givennumbers and mathematical symbols ;

i. contruct statement using the quantifier :a) all ;

b) some ;

ii. determine whether a statement that contains thequantifier all true or false;

iii. determine whether a statement can be

generalized to cover all cases by using the

quantifier all ;iv. contruct 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 words not into the original

statement ;ii. identify two statements from a compound

statement that contains the word and ;iii. form a compound statement by combining twogiven statements using the words and ;

Corporation

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6/20


OBJECTIVES


AIDS/ CCT

15MATHEMATICALREASONING 4.3 Perform

operations involving

the words not or

no,and and or

on statements ;

4.4 Understand the

concept of

implication ;

Student will be able to:iv. identify two statements from a compound that

contains the word or ;

v. form a compound statement by combining two

given statements using the words or ;

vi. determine the truth value of a compoundstatement which is the combination of two

statements using the words and ;

vii. determine the truth value of a compoundstatement which is the combination of two

statements using the words or ;

i. identify the antecedent and consequent of an

implication if p, then q

ii. write two implications from a compound

statement that containing if and only if ;iii. contruct mathematical statement in the form of

implication :

a) 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 animplication is true or false.


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7/20


OBJECTIVES


AIDS/ CCT

16

CHAPTER 4 :

MATHEMATICAL

REASONING

4.5 Understand the

concept of

argument ;

4.6 Understand and

use the concept of

deduction and

induction to solve

problems ;

Student will be able to:i. identify thepremise andconclusion of a given

simple argument ;

ii. make a conclusion based on two given premises

for;

a) Argument Form Ib) Argument Form II

c) Argument Form III

iii. Complete an argument given apremise andconclusion ;

i. determine whether the conclusion is madethrough :

a) reasoning by deduction ;

b) reasoning by induction ;

ii. make a cloncusion for a specific case based on agiven general statement by deduction ;

iii. make a generalization based on the pattern of

numerical sequence, by induction ;iv. use deduction and induction in problem solving

Corporation

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8/20


OBJECTIVES


AIDS/ CCT

17

18

CHAPTER 5 :

THE STRAIGHT

LINE

5.1 understand the

concept of gradient

of a straight line ;

5.2 understand the

concept of gradient

of a straight line inCartesian

coordinates;

5.3 Understand the

Concept of

Intercept ;

Student will be able to:i. determine the vertical and horizontal distances

between two given points on a straight line ;

ii. determine the ratio of vertical distance and

horizontal distance.

i. derive the formula for the gradient of a straight

line ;

ii. calculate the gradient of a straight line passingthrough two points ;

iii. determine the relationship between the value of

gradient and the :a) steepness,b) direction of inclination,of a straight line ;

i. determine the x-intersept and the y-intercept of a

straight line ;

ii. derive the formula for the gradient of a straightline in terms of the x-intersept and the

y-intercept;

iii. perform calculations involving gradient,x-intersept and the y-intercept


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9/20


OBJECTIVES


AIDS/ CCT

19CHAPTER 5 :

THE STRAIGHT

LINE

5.4 understand and

use equation

of a straight line ;

5.5 Understand and

use the Concept of

Parallel lines

Student will be able to:i. draw the graph given an equation of the form

y = mx + c ;

ii. determine whether the given points lies on a

specific straight line ;

iii. write the equation of the straight line given thegradient and y-intercept ;

iv. determine the gradient and y-intercept of the

straight line which equation is of the form :a) y = mx + cb) ax + by = c

v. find the equation of the straight line which :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 two given points.vi. find the point of intersection of two straight lines

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

i. verify that two parallel lines have the samegradient and vice versa ;

ii. determine from the given equations whether two

straight lines are parallel ;iii. find the equations of the straight line which

passes through a given point and is parallel to

another straight line ;

iv. solve problems involving equation of straight line

Corporation

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10/20


OBJECTIVES


AIDS/ CCT

20, 21CHAPTER 6 :STATISTICS 6.1 understand the

Concept of class

Interval ;

6.2 Understand and

use the Concept of

Mode and mean ofgrouped data ;

6.3represent and

interpret data in

histograms with class

intervals of the same

size to solve problems;

Student will be able to:i. complete the class interval for a set of data given

one of the class interval ;

ii. determine

a) the upper limit and the lower limit ;b) the upper boundary and lower boundary ;of a class in a grouped data ;

iii. calculate the size of a class interval ;

iv. determine the class interval, given a set of dataand the number of classes ;

v. determine the suitable class interval for a given

set of data ;vi. Contruct a frequency table for a given a set of

data.

i. determine the modal class from the frequency

table of groped data ;

ii. calculate a midpoint of a class ;iii. verify the formula for the mean of grouped data ;

iv. calculate the mean from the frequency table ofgrouped data ;

v. discuss the effect of the size of class interval on

the accuracy of the mean for a specific sets ofgrouped data.

i. draw a histogram based on the frequency table ofgrouped data ;

ii. interpret information from a given histogram ;

iii. solve problems involving histogram.

Corporation

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11/20


OBJECTIVES


AIDS/ CCT

22, 23 CHAPTER 6 :STATISTICS

6.4 represent and

interpret data in

frequency polygons

to solve problems;


cumulative

frequency

6.6 Understand and

use the Concept ofmeasures of

dispersion to solve

problems;

Student will be able to:i. draw the frequency polygon based on :

a) a histogramb) a frequency table ;

ii. interpret information from a given frequency

polygons ;

iii. solve problems involving frequency polygons ;

i. construc the cumulative frequency table for :a) ungrouped data

b) grouped data ;

ii. draw the ogive for :a) unrouped data

b) grouped data ;

i. determine the range of a set of data ;

ii. determine :a) the median ;b) the first quartile ;c) the third quartile ;d) the interquartile range ;from the ogive.

iii. interpret information from ogive ;

iv. solve problems involving data representations

and measures of dispersion.

Corporation

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12/20


OBJECTIVES


AIDS/ CCT

24,25,26

CHAPTER 7 :

PROBABILITY

7.1 Understand the

concept of

Sample space

7.2 Understand the

concept of events

7.3 Understand anduse the concept of

Probability of an

event to solve

problems.

Student will be able to:i. determine whether the outcome is a possible

outcome of an experiment;

ii. list all the possible outcomes of an experiment :

a) from activities ;b) by reasoning ;

iii. determine thesample space of an experiment ;iv. write the sample space by using set notations.

i. identify the elements of asample space which

satisfy given condisions ;

ii. list all the elements of asample space whichsatisfy certain condisions using set notations ;

iii. determine whether an event is possible for a

sample space.

i. find the ratio of the number of times an eventoccurs to the number of trials ;

ii. find the probability of an event from a big enoughnumber of trials ;

iii. calculate the expected number of times an event

will occur, given the probability of the event andnumber of trials ;

iv. solve problems involving probability ;

v. predict the occurrence of an outcome and make adecision based on known information.


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13/20


OBJECTIVES


AIDS/ CCT

27,28 CHAPTER 8 :

CIRCLES III

8.1 Understand and

use the concept of

tangents to a

circle

8.2 Understand and

use the properties of

an angle between

tangent and chord to

solve problems

Student will be able to:i. identify tangents to a circle ;ii. make inference that the tangent to a circle is a

straight line perpendicular to the radius that

passes through the contact point ;

iii. construc the tangent to a circle passing through apoint :

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 ;

vi. solve problems involving tangents to a circle

i. identify the angle in the alternate segment which

is sustended by the chord through the contact

point of the tangent ;

ii. verify the relationship between the angle formedthe tangent and the chord with angle in the

alternate segment which is sustended by thechord ;

iii. perform calculations involving the angle in

alternate segment ;iv. solve problems involving tangents to a circle and

angle in alternate segment ;

Corporation

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14/20

WEEK TOPICS LEARNINGOBJECTIVES

LEARNING OUTCOMES VALUES TEACHINGAIDS/ CCT

29 CHAPTER 8 :

CIRCLES III

8.3 Understand and

use the properties of

common tangent to

solve problems

Student will be able to: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 points ;c) do not intersect ;

ii. determine the properties related to the commontangent to two circles which :

a) intersect at two points ;b) intersect only at one points ;c) do not intersect ;

iii. solve problems involving common tangent to

two circles ;

iv. solve problems involving tangent and commontangent.

Corporation

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15/20


OBJECTIVES


AIDS/ CCT

30,31 CHAPTER 9 :

TRIGONOMETRY

II

9.1 Understand and

use the concept of

values of sin ,cos , and tan (0

0 3600)to solve problems.

Student will be able to:i. identify the quadrant and angle in the unit circleii. determine :

a) the value of y-coordinate ;b) the value of x-coordinate ;c) the ratio of y-coordinate to x-coordinate;of several points on the circumference of the unit

circle.

iii. verify that, for an angle in quadrant I of the unitcircle :

a) sin = y-coordinate

b) cos = x-coordinate

c) tan = y-coordinatex-coordinate

iv. determine the values of :a) sine ;b) cosine ;c) tangent ;of an angle in quadrant I of the unit circle ;

v. determine the values of :

a) sin ;

b) cos ;

c) tan ;

for 900

3600

vi. determine whether the values of :

a) sin ;

b) cos ;

c) tan ;of an angle in specific quadrant is positive or

negative.

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16/20


OBJECTIVES


AIDS/ CCT

32,33 CHAPTER 9 :

TRIGONOMETRY

II

9.1 Understand and

use the concept of

values of sin ,cos , and tan (0

0 3600)to solve problems.

9.2 Draw and use the

Graphs of sine,

cosine and tangent.

Student will be able to:vii. determine the values of sine, cosine, and

tangent for special angles ;

viii. determine the values of the angles in quadrant I

which correspond to the values of the angles in

other quadrants;ix. state the relationships between the values of :

a) sine ;

b) cosine ;c) tangent ;

of an angle in quadrant II, III and IV with their

respective values of the corresponding angle inquadrant I ;

x. find the values of sine, cosine and tangent of the

angles between900 and3600

xi. find the angles between 00 and3600 ,given the

values of sine, cosine or tangent ;

xii solve problems involving sine, cosine and

tangent.i. draw the graphs of sine, cosine and tangent for

angles between 00 and3600

ii. compare the graphs of sine, cosine and tangentfor angles between 00 and3600

iii. solve problems involving graphs of sine, cosine

and tangent .

Corporation

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Kementerian Pendidikan Malaysia Page 16 11/7/2008


17/20


OBJECTIVES


AIDS/ CCT

34, 35 CHAPTER 10 :

ANGLES OF

ELEVATION

AND

DEPRESSION

10.1 Understand and

use the concept of

angle of elevation

and angle of

depression to solve

problems.

Student will be able to: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 elevation ;b) the angle of depression ;using diagrams ;

iii. solve problems involving the angle of elevation

and the angle of depression.

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18/20

WEEK TOPICS LEARNINGOBJECTIVES LEARNING OUTCOMES VALUES TEACHINGAIDS/ CCT

36

37, 38

CHAPTER 10 :

ANGLES OF

ELEVATION

AND

DEPRESSION

CHAPTER 11 :

LINES AND

PLANES IN

3-DIMENSIONS

10.1 Understand and

use the concept of

angle of elevation

and angle of

depression to solve

problems.

11.1 Understand anduse the concept of

angle between lines

and planes to solve

problems.

Student will be able to: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 :c) the angle of elevation ;d) the angle of depression ;using diagrams ;

iii. solve problems involving the angle of elevation

and the angle of depression.

i. identify planes ;

ii. identify horizontal planes, vertical planes and

inclined planes ;iii. sketch a three dimensional shape and identify the

specific planes ;iv. identify :

a) lines that lies on a plane ;b) lines that intersect with a plane ;

v. identify normals to a given plane ;

vi. determine the orthogonal projection of a line on

a plane ;vii. draw and neme the orthogonal projection of a

line on a plane ;

viii. determine the angle between a line and a plane ;

ix. solve problems involving the angle between aline and a plane ;

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OBJECTIVES


AIDS/ CCTS

39, 40 CHAPTER 11 :

LINES AND

PLANES IN

3-DIMENSIONS

11.2 Understand and

use the concept of

angle between two

planes to solve

problems.

Student will be able to:i. identify the line of intersection between two

planes ;

ii. draw a line in each plane which is perpendicular

to the lilne of intersection of the two planes at apoint 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 3-

dimensional shapes.

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20/20

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