77189458 form 4 modern mathematics syllabus

8/12/2019 77189458 Form 4 Modern Mathematics Syllabus

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SEKOLAH MENENGAH TEKNIK SEPANG, 43800 DENGKIL, SELANGOR

FORM 4 MATHEMATICS SCHEME OF WORK 2009

LEARNING AREAS ANDLEARNING OBJECTIVES

LEARNING OUTCOME

1 STANDARD FORM

1.1 Understand and use theconcept of significant

figure;

i. Round off positive numbers to a given number of significantfigures when the numbers are: (a) greater than 1; (b) less

than 1;ii. Perform operations of addition, subtraction, multiplication

and division, involving a few numbers and state the answerin specific significant figures;

iii. olve problems involving significant figures;

1.! Understand and use theconcept of standard form

to solve problems.

i. tate positive numbers in standard form when the numbersare:

a) greater than or e"ual to 1#;

b) less than 1;

ii. $onvert numbers in standard form to single numbers;

iii. Perform operations of addition, subtraction, multiplication

and division, involving an% two numbers and state theanswers in standard form;

iv. olve problems involving numbers in standard form.

2 !UADRATICE"PRESSIONS AND

E!UATIONS

!.1 Understand the conceptof "uadratic e&pression;

i. 'dentif% "uadratic e&pressions;

ii. orm "uadratic e&pressions b% multipl%ing an% two lineare&pressions;

iii. orm "uadratic e&pressions based on specific situations;

!.! actorise "uadratice&pressions

i. actorise "uadratic e&pressions of the form cbxax ++2 ,

where b # or c #;

ii. actorise "uadratic e&pressions of the form px ! − q, p and qare perfect s"uares;

iii. actorise "uadratic e&pressions of the form cbxax ++2 ,

where a, b and c not e"ual to *ero;

iv. actorise "uadratic e&pressions containing coefficients withcommon factors;

!.+ Understand the conceptof "uadratic e"uation;

i. 'dentif% "uadratic e"uations with one unnown;

ii. -rite "uadratic e"uations in general form i.e.

02

=++ cbxax

iii. orm "uadratic e"uations based on specific situations;

!. Understand and usethe concept of roots of"uadratic e"uations tosolve problems.

i. /etermine whether a given value is a root of a specific"uadratic e"uation;

ii. /etermine the solutions for "uadratic e"uations b%: a) trialand error method; b) factorisation;

iii. olve problems involving "uadratic e"uations.

FIRST MID#TERM BREAK

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LEARNING AREAS ANDLEARNING OBJECTIVES

LEARNING OUTCOME

3 SET

+.1 Understand theconcept of set;

i. ort given ob0ects into groups;

ii. /efine sets b%: (a) descriptions; (b) using set notation;

iii. 'dentif% whether a given ob0ect is an element of a set use

the s%mbol ∈ or ∉;

iv. Represent sets b% using 2enn diagrams;

v. 3ist the elements state the number of elements of a set;

vi. /etermine whether a set is an empt% set;

vii. /etermine whether two sets are e"ual;

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+.! Understand and usethe concept of subset,universal set and thecomplement of a set;

i. /etermine whether a given set is a subset of a specific set

and use the s%mbol ⊂ or ⊄ ;

ii. Represent subset using 2enn diagram;

iii. 3ist the subsets for a specific set;

iv. 'llustrate the relationship between set and universal setusing 2enn diagram;

v. /etermine the complement of a given set;

vi. /etermine the relationship between set, subset, universalset and the complement of a set;

+.+ Perform operations onsets:

• the intersection of sets;

• the union of sets.

i. /etermine the intersection of: (a) two sets; (b) three sets;

and use the s%mbol ∩ ;

ii. Represent the intersection of sets using 2enn diagram;

iii. tate the relationship between (a) 4 ∩ 5 and 4 ; (b) 4 ∩ 5and 5 ;

iv. /etermine the complement of the intersection of sets;

v. olve problems involving the intersection of sets;

vi. /etermine the union of: (a )two sets; (b) three sets; and

use the s%mbol ∪ ;

vii. Represent the union of sets using 2enn diagram;

viii. tate the relationship between (a) 4 ∪ 5 and 4 ; (b) 4 ∪ 5and 5 ;

i&. /etermine the complement of the union of sets;

&. olve problems involving the union of sets;

&i. /etermine the outcome of combined operations on sets;

&ii. olve problems involving combined operations on sets.

TEST 1

4 MATHEMATICALREASONING

.1 Understand theconcept of statement

i. /etermine whether a given sentence is a statement;

ii. /etermine whether a given statement is true or false;iii. $onstruct true or false statement using given numbers and

mathematical s%mbols;

.! Understand theconcept of "uantifiers6all7 and 6some7;

i. $onstruct statements using the "uantifier:(a) all; (b) some;

ii. /etermine whether a statement that contains the "uantifier6all7 is true or false;

iii. /etermine whether a statement can be generali*ed tocover all cases b% using the "uantifier 6all7;

iv. $onstruct a true statement using the "uantifier 6all7 or6some7, given an ob0ect and a propert%.

.+ Perform operationsinvolving the words

6not7 or 6no7, 6and7 and6or7 on statements;

i. $hange the truth value of a given statement b% placing theword 6not7 into the original statement;

ii. 'dentif% two statements from a compound statement thatcontains the word 6and7;

iii. orm a compound statement b% combining two givenstatements using the word 6and7;

iv. 'dentif% two statement from a compound statement thatcontains the word 6or7 ;

v. orm a compound statement b% combining two givenstatements using the word 6or7;

vi. /etermine the truth value of a compound statement which

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is the combination of two statements with the word 6and7;

vii. /etermine the truth value of a compound statement whichis the combination of two statements with the word 6or7.

. Understand theconcept ofimplication;

i. 'dentif% the antecedent and conse"uent of an implication6if p, then q7;

ii. -rite two implications from a compound statementcontaining 6if and onl% if7;

iii. $onstruct mathematical statements in the form of

implication: (a) 'f p, then q; (b) p if and onl% if q;iv. /etermine the converse of a given implication;

v. /etermine whether the converse of an implication is true orfalse.

.8 Understand theconcept of argument;

i. 'dentif% the premise and conclusion of a given simpleargument;

ii. 9ae a conclusion based on two given premises for: (a)4rgument orm '; (b) 4rgument orm ''; (c) 4rgument orm''';

iii. $omplete an argument given a premise and the conclusion.

. Understand and use theconcept of deduction and

induction to solveproblems.

i. /etermine whether a conclusion is made through: (a)reasoning b% deduction; (b) reasoning b% induction;

ii. 9ae a conclusion for a specific case based on a givengeneral statement, b% deduction;

iii. 9ae a generali*ation based on the pattern of a numericalse"uence, b% induction;

iv. Use deduction and induction in problem solving.

$ THE STRAIGHT LINE

8.1 Understand theconcept of gradient of astraight line;

i. /etermine the vertical and hori*ontal distances betweentwo given points on a straight line.

ii. /etermine the ratio of vertical distance to hori*ontaldistance.

. Understand the concept of

gradient of a straight line in$artesian coordinates;

i. /erive the formula for the gradient of a straight line;

ii. $alculate the gradient of a straight line passing throughtwo points;

iii. /etermine the relationship between the value of thegradient and the: (a) steepness, (b) direction of inclination,of a straight line;

8.+ Understand theconcept of intercept;

i. /etermine the x intercept and the y intercept of a straightline;

ii. /erive the formula for the gradient of a straight line interms of the x intercept and the y intercept;

iii. Perform calculations involving gradient, x intercept and y intercept;

8. Understand and usee"uation of a straight line;

i. /raw the graph given an e"uation of the form y mx < c ;ii. /etermine whether a given point lies on a specific straight

line;

iii. -rite the e"uation of the straight line given the gradientand y intercept;

iv. /etermine the gradient and y intercept of the straight linewhich e"uation is of the form: (a) y mx < c; (b) ax < by c;

v. ind the e"uation of the straight line which: (a) is parallel tothe y a&is; (b) passes through a given point and has a

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specific gradient; (c) passes through two given points;

vi. ind the point of intersection of two straight lines b%: (a)drawing the two straight lines; (b) solving simultaneouse"uations.

8.8 Understand and use theconcept of parallel lines.

i. 2erif% that two parallel lines have the same gradient andvice versa;

ii. /etermine from the given e"uations whether two straightlines are parallel;

iii. ind the e"uation of the straight line which passes througha given point and is parallel to another straight line;

iv. olve problems involving e"uations of straight lines.

MID%EAR E"AMINATION

FIRST TERM BREAK

& STATISTICS III

.1 Understand the concept ofclass interval;

i. $omplete the class interval for a set of data given one ofthe class intervals;

ii. /etermine: (a) the upper limit and lower limit; (b) the upperboundar% and lower boundar% of a class in a grouped data;

iii. $alculate the si*e of a class interval;

iv. /etermine the class interval, given a set of data and thenumber of classes;

v. /etermine a suitable class interval for a given set of data;

vi. construct a fre"uenc% table for a given set of data.

.! Understand and use theconcept of mode and mean

of grouped data;

i. /etermine the modal class from the fre"uenc% table ofgrouped data;

ii. $alculate the midpoint of a class;

iii. 2erif% the formula for the mean of grouped data;

iv. $alculate the mean from the fre"uenc% table of groupeddata;

v. /iscuss the effect of the si*e of class interval on theaccurac% of the mean for a specific set of grouped data..

.+ Represent andinterpret data inhistograms with class

intervals of the samesi*e to solve problems;

i. /raw a histogram based on the fre"uenc% table of agrouped data;

ii. 'nterpret information from a given histogram;

iii. olve problems involving histograms.

. Represent andinterpret data infre"uenc% pol%gons to

solve problems.

i. /raw the fre"uenc% pol%gon based on: (a) a histogram; (b)a fre"uenc% table;

ii. 'nterpret information from a given fre"uenc% pol%gon;

iii. olve problems involving fre"uenc% pol%gon.

.8 Understand theconcept of cumulativefre"uenc%

i. $onstruct the cumulative fre"uenc% table for(a) ungroupeddata; (b) grouped data;

ii. /raw the ogive for: (a) ungrouped data; (b) grouped data;

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. Understand and usethe concept ofmeasures of dispersion to

solve problems.

i. /etermine the range of a set of data.

ii. /etermine:the median; (a) the first "uartile;(b) the third"uartile;(c) the inter"uartile range; from the ogive.

iii. 'nterpret information from an ogive;

iv. olve problems involving data representations andmeasures of dispersion.

' PROBABILIT%

=.1 understand the

concept of samplespace

i. /etermine whether an outcome is a possible outcome of an

e&periment;ii. 3ist all the possible outcomes of an e&periment: (a) from

activities; (b) b% reasoning;

iii. /etermine the sample space of an e&periment;

iv. -rite the sample space b% using set notations.

=.! Understand theconcept of events.

i. 'dentif% the elements of a sample space which satisf% givenconditions;

ii. 3ist all the elements of a sample space which satisf% certainconditions using set notations;

iii. /etermine whether an event is possible for a sample space.

=.+ Understand and use the

concept of probabilit% of anevent to solve problems.

i. ind the ratio of the number of times an event occurs to the

number of trials;ii. ind the probabilit% of an event from a big enough number

of trials;

iii. $alculate the e&pected number of times an event willoccur, given the probabilit% of the event and number oftrials;

iv. olve problems involving probabilit%;

v. Predict the occurrence of an outcome and mae a decisionbased on nown information.

TEST 2

>. CIRCLES III

>.1 understand and usethe concept oftangents to a circle.

i. 'dentif% tangents to a circle;

ii. 9ae inference that the tangent to a circle is a straight lineperpendicular to the radius that passes through the contactpoint;

iii. $onstruct the tangent to a circle passing through a point:(a) on the circumference of the circle; (b) outside the circle;

iv. /etermine the properties related to two tangents to a circlefrom a given point outside the circle;

v. olve problems involving tangents to a circle.

>.! Understand and use theproperties of anglebetween tangent and chord

to solve problems.

i. 'dentif% the angle in the alternate segment which issubtended b% the chord through the contact point of thetangent;

ii. 2erif% the relationship between the angle formed b% thetangent and the chord with the angle in the alternatesegment which is subtended b% the chord;

iii. Perform calculations involving the angle in alternatesegment;

iv. olve problems involving tangent to a circle and angle inalternate segment.

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>.+ Understand and use theproperties of commontangents to solve problems.

i. /etermine the number of common tangents which can bedrawn to two circles which: (a) intersect at two points; (b)intersect onl% at one point; (c) do not intersect;

ii. /etermine the properties related to the common tangent totwo circles which: (a) intersect at two points; (b) intersectonl% at one point; (c) do not intersect;

iii. olve problems involving common tangents to two circles;

iv. olve problems involving tangents and common tangents.

?. TRIGONOMETR% II?.1 understand and usethe concept of the

values of sin θ , cos θ and

tan θ (#° ≤ θ ≤ +#°)to solve problems.

i. 'dentif% the "uadrants and angles in the unit circle;

ii. /etermine: (a) the value of y coordinate; (b) the value of x coordinate; (c) the ratio of y coordinate to x coordinate; ofseveral points on the circumference of the unit circle;

iii. 2erif% that, for an angle in "uadrant ' of the unit circle : (a)

sin θ y coordinate ; (b) cosθ x coordinate; (c)

coordinate

coordinatetan

−

−=

x

yθ ;

iv. /etermine the values of (a) sine; (b) cosine; (c) tangent; ofan angle in "uadrant ' of the unit circle;

v. /etermine the values of (a) sinθ

; (b) cosθ

;( c) tanθ

; for?#° ≤ θ ≤ +#°;

vi. /etermine whether the values of (a) sine; (b). cosine; (c).tangent, of an angle in a specific "uadrant is positive ornegative;

vii. /etermine the values of sine, cosine and tangent forspecial angles;

viii. /etermine the values of the angles in "uadrant ' whichcorrespond to the values of the angles in other "uadrants;

i&. tate the relationships between the values of: (a) sine; (b).cosine; (c) tangent, of angles in "uadrant '', ''' and '2 withtheir respective values of the corresponding angle in

"uadrant ';x. ind the values of sine, cosine and tangent of the angles

between ?#° and +#°;

xi. ind the angles between #° and +#°, given the values ofsine, cosine or tangent;

&ii. olve problems involving sine, cosine and tangent.

?.! /raw and use the graphs ofsine, cosine and tangent.

i. /raw the graphs of sine, cosine and tangent for angles

between #° and +#°;

ii. $ompare the graphs of sine, cosine and tangent for angles

between #° and +#°;

iii. olve problems involving graphs of sine, cosine andtangent.

SECOND MID#TERM BREAK

10 ANGLES OFELEVATION ANDDEPRESSION

1#.1 Understand and usethe concept of angle ofelevation and angle of

depression to solve

i. 'dentif%: (a) the hori*ontal line; (b) the angle of elevation;(c) the angle of depression, for a particular situation;

ii. Represent a particular situation involving: (a) the angle ofelevation; (b) the angle of depression, using diagrams;

iii. olve problems involving the angle of elevation and theangle of depression.

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problems.

11. LINES AND PLANESIN 3 DIMENSION

?.! Understand and use theconcept of angle betweenlines and planes to solve

problems.

i. 'dentif% planes;

ii. 'dentif% hori*ontal planes, vertical planes and inclinedplanes;

iii. etch a three dimensional shape and identif% the specificplanes;

iv. 'dentif%:

v. 3ines that lies on a plane;

vi. 3ines that intersect with a plane;

vii. 'dentif% normals to a given plane;

viii. /etermine the orthogonal pro0ection of a line on a plane;

ix. /raw and name the orthogonal pro0ection of a line on aplane;

x. /etermine the angle between a line and a plane;

xi. olve problems involving the angle between a line and aplane.

11.! Understand and usethe concept of anglebetween two planes to solve

problems.

i. 'dentif% the line of intersection between two planes;

ii. /raw a line on each plane which is perpendicular to the lineof intersection of the two planes at a point on the line ofintersection;

iii. /etermine the angle between two planes on a model and agiven diagram

iv. olve problems involving lines and planes in +dimensionalshapes.

38 HARI RA%A AIDILFITRI ( EVENT HOLIDA%

39 #42

REVISION )PREPARATION FOR FINAL E"AMINATION*

43 (44

FINAL E"AMINATION

4$ #4&

DISCUSSION OF FINAL E"AMINATION PAPER ( INTODUCTION TO FORM FIVE TOPICS

4' #$2

SCHOOL HOLIDA%S

Prepared b%

Pn. @uriah 5inti 'brahim

Aead of 9athematics Panel

9Beni epang

$heced b%

Pn. Cainab bt. 9ohd hah

Aead of cience and 9athematics/epartment

9Beni epang

$ertified b%

Pn. Aa0ah iti atimah bt. 4bd.9anan

enior 4ssistant of 4dministration

9Beni epang

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9

77189458 form 4 modern mathematics syllabus

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