Pmr Mathematics

PMR MATHEMATICS

2011

PAPER 1

A. GENERAL GUIDE – Paper 1

Covers all topics from Form 1 to Form 3 and requires skill higher than BASIC SKILL.

Consist of objective questions with 4 choices of answer.

Candidates have to do complete revision covering all topics and do not at all choose certain topics only.

Contains topics covering NUMBERS, SHAPES and ALGEBRAIC themes.

Skills related to NUMBERS, SHAPES and ALGEBRA complement each other ; without any one of the skill, others can’t be acquired. For example, questions on SHAPES require a lot of ALGEBRAIC and NUMBERS skills whilst questions on ALGEBRA require skills on NUMBERS or vice versa.

Skills related to NUMBERS should be built first whilst skills on ALGEBRA are very important to solve many problems.

Paper 1 will take place after Paper 2 has been executed.

B. EXAMINATION FORMAT – Paper 1Syllabus Scope Duration Form of

QuestionTotal

QuestionNumber of

QuestionRequired To Be

Answered

Total Marks

Notes

All topics in the KBSM Syllabus (Form 1 – 3) with skill higher than basic skill

75 min Objective 40 All 40 % 4 choice of answers are prepared for each question

• Use the final 5 to 10 minutes to recheck answers.• Do not wait till all questions are answered and only then transfering them to the OMR answering paper. Transfer each answer after each question has been answered.• Each question needs more or less 1 to 2 minutes to solve. If it can’t be solved, shift to other question.• If there are still questions that can’t be answered for the second time, you may have to guess the answer. Do so but after all distractors have been removed.

C. ANALYSIS PAPER 1 TOPICS 2004 2005 2006 2007 2008 2009 2010 2011 2012

FORM 1 1.Whole Numbers2.Number Patterns & Sequences3.Fractions4.Decimals5.Percentages6.Integers7.Algebraic Expressions I8.Basic Measurements9.Lines and Angles I10.Polygons I11.Perimeter and Area 12.Solid Geometry I

-31111-2-11-

13--11---3--

122-1--1112-

12111--1-21-

111111-3-11-

12-1---2-321

TOTAL 11 9 11 10 11 12

FORM 21.Directed Numbers2.Squares,Sq.Rt,Cubes,Cube Rt3.Algebraic Expressions II4.Linear Equations I5.Ratios, Rates & Proportions I6.Pythagora’s Theorem7.Geometrical Constructions8.Coordinates9.Loci in Two Dimensions10.Circles I11.Transformations I12.Solid Geometry II13.Statistics I

----23-213-12

----23-213-11

----11-313-31

1---13-213-31

----23-213-12

1---22-212-13

TOTAL 14 13 13 15 14 14

FORM 31.Lines and AnglesII2.Polygons II3.Circles II4.Statistics II5.Indices6.Algebraic Expressions III7.Algebraic Formulae8.Solid Geometry III9.Scale Drawings10.Transformations II11.Linear Equations II12.Linear Inequalities13.Graphs of Functions14.Ratios, Rates & Proportions II15.Trigonometry

1133---111-112-

1233---2-11122-

1223---1-11122-

-223---1-11122-

1233---1-1112--

1223--11-1-111-

TOTAL 15 18 16 15 15 14

D. FORMS OF QUESTION – Paper 1

“COMMON SENSE” QUESTIONS (NEEDS NO CALCULATION)

EXAMPLE 1 : Mrs Kasmah brings along RM 30 to the market. She used 5 / 10 of her money to buy

1⅔ kg of prawns. What is the price of 1 kilogram of those prawns ?

A. RM 9 B. RM 15

C. RM 16 D. RM 21

C. FORMS OF QUESTION – Paper 1

QUESTIONS THAT CAN BE ANSWERED USING OTHER QUESTION BEFORE OR AFTER IT AS A GUIDE

Example 2 below can be answered using Example 3 as a guide.

EXAMPLE 2 : EXAMPLE 3 :

Amir Amsyar bought a pair of pants Solve the following equation

at a price of RM 42 after discount. 6 – 2x = 4The original price is RM 60. Calculate 3The percentage of discount given.

A. 20 % C. 30 % A. – 2 C. 4B. 25 % D. 35 % B. 3 D. - 3


QUESTIONS THAT CAN BE ANSWERED BY TRYING OUT EACH

CHOICE GIVEN (If possible, try not using this method because it

is time consuming)

EXAMPLE 4 :

An electrical appliance company offers

25 % discount to its clients for certain

electrical appliances. Encik Ngapan bought

a refrigirator at an offer price of RM 1080.

What is the original price of the refrigirator ?

A. RM4320 C. RM810

B. RM1440 D. RM2400

Try whether 4320 – 25 x 4320 is 100equal to 1080. If not the same, repeat with other choices. (If possible make a RANDOM choice because we might succeed at first try)


QUESTIONS THAT CAN BE SOLVED USING ALGEBRAIC METHOD

EXAMPLE 5 :The interior angles of a hexagon are 2xo, 2xo, 3xo, 3xo, 4xo dan 4xo. The value of x is A. 40o C. 80o

B. 70o D. 90o

Form the equation2x + 2x + 3x + 3x + 4x + 4x = 4(180)and solve the equation.


QUESTIONS THAT CAN BE SOLVED USINGALGEBRAIC METHOD

EXAMPLE 6 : In the following diagram, calculate the height of the cylinder, h, given surface area of the cylinder is 330 cm2 and its radius is 3.5 cm. r A. 11.5 cm C. 15 cmB. 13.25 cm D. 26.5 cm h

Form the equation2π(3.5)2 + 2π(3.5)h = 330and solve the equation. (Subtitute π = 22 / 7)


QUESTIONS THAT CAN BE SOLVED USING

ALGEBRAIC METHOD

EXAMPLE 7

Given M (k, 2) is the mid point for the

line that connects points P (-8, a) and

Q (2a, a). The value of k is

A. 2 C. - 2

B. 3 D. – 3

Form the simultaneous equation a + a = 2 dan – 8 + 2a = k 2 2 and solve them.


QUESTIONS THAT HAD TO BE GUESSEDBefore guessing, eliminate all the distractors first.

EXAMPLE 8 :

Which of the following is not true ?

A. – 120 ÷ (- 5) = 24 May be true because (-) ÷ (-) = (+)B. 843 ÷ (- 3) = - 281 May be true because (+) ÷ (-) = (-)C. – 365 ÷ 5 = - 73 May be true because (-) ÷ (+) =

(-)

D. – 405 ÷ (- 9) = - 45 Not possible ! (-) ÷ (-) ≠ (-)

TRY THE FOLLOWING QUESTIONS RELATING TO NUMBERS :

1. 2 2 – 7 ÷ 4 1 + 1

9 15 5 3

A. 79 C. 2 2

204 9

B. 1 7 D. 2 4

9 9

2. 0.55 x 8.1

45

A. 99 C. 0.99

B. 9.9 D. 0.099

3. –10 + 6 + (-11) =

A. –15 C. 6 B. – 6 D. 11

4. 100.1 – (- 0.5) ÷ 0.005 =

A. 0.1 C. 200.1

B. –110.1 D. – 90.1

5. ¾ - (- 0.9 ÷ 0.003) ÷ 100

A. - ¼ C. 3 ¾

B. – 2 ¼ D. – 1 ¼

SQUARES, SQUARE ROOT, CUBE, CUBE ROOT, PERCENTAGES, DIRECTED NUMBERS, WHOLE NUMBERS, NUMBER PATTERNS, FRACTIONS, DECIMALS, INDICES……..

TRY THE FOLLOWING QUESTIONS RELATING TO ALGEBRA :

1. An egg cost 15 cent. If x eggs cost RM 1.80, find the value of x. A. 6 C. 10 B. 8 D. 12

2. Factorize 6pq – 4q2

A. 2q(4p – 4q) C. 6p(p – 4q2) B. 6q(p – 4q2) D. 2q(3p – 2q)

3. Simplify 25x2y .

5xy + 15xy2

A. 5 C. 5x .

5xy + 3 1 + 3y

B. 5x D. 5xy .

x+ 3y 1 + 5x

4. If x + 2 = 3x then x =

5

A. – 1 / 3 C. – 5 B. – 2 / 5 D. 1

TRY THE FOLLOWING QUESTIONS RELATING TO SHAPES :

1.

2x

x

3x

In the above diagram, x in degrees is

A. 20o C. 30o

B. 50o D. 35o

2.

x cm

5 cm

10 cm

Diagram shows a cuboid fill with water

to a height of x cm. Calculate the

value of x if the water’s volume is 75

cm3.

A. 1.5 cm C. 1 cm

B. 2 cm D. 3 cm

PMR MATHEMATICS

2010

PAPER 2

A. GENERAL GUIDE – Paper 2

Paper 2 is in the form of written subjective. Questions are constructed according to KBSM syllabus at

minimum to high capability level. Skills tested are basic to high level skills in certain topic

listed in the syllabus . Concepts tested are basic Mathematical concepts that all

Form 3 students should have acquire from certain topic. Questions are phrased in short and moderate sentences

not using long and difficult words. Questions are focused to types that have certain difficulty

level. This allows differentiation between students that acquired basic skill with those that acquired minimum level skill.

B. EXAMINATION FORMAT – Paper 2

Syllabus Scope

Duration Form of Question

Total Question

Number of Question

Required To Be Answered

Total Marks

Notes

Minimum to

High Level Skill’s

Component

(Multi Skill)

1 hour

45 min

Subjective 20 All 60 % Answers must be written in the space provided in the question paper.

Marks are awarded according to working method and precision of answers.

Paper 2 will take place after Paper 1 has been executed.1. Use the final 5 to 10 minutes to recheck answers.2. Each question needs more or less 2 to 3 minutes to solve. If it can’t be solved, shift to other question.3. Usually marks are awarded straight to the precise answer given. If there are any mistake, only then marks are awarded to the working method written.

C. ANALYSIS PAPER 2

TOPICS 2004 2005 2006 2007 2008 20092M 3M 4M 5M 6M 2M 3M 4M 5M 2M 3M 4M 5M 2M 3M 4M 5M 2M 3M 4M 5M 6M 2M 3M 4M 5M

FORM 1 1. Whole Numbers3. Fractions4. Decimals

11

11

1

TOTAL 1 1 1 1 1

FORM 21. Directed Numbers2. Sq, Sq.Rt, Cubes, Cube Rt3. Algebraic Expressions II4. Linear Equations I7. Geometrical Constructions9. Loci in Two Dimensions11. Transformations I12. Solid Geometry II13. Statistics I

1

2

1

1

11

11

1

1

1

1

1

11

1

2

1

1

1

11

1

1

1

1

11

11

1

3

1

1

11

2

1

111

1

1

1

TOTAL 3 4 1 1 2 2 1 2 3 2 1 2 2 3 1 2 4 2 1 1 3 4 1

FORM 34. Statistics II5. Indices6. Algebraic Expressions III7. Algebraic Formulae9. Scale Drawings10. Transformations II12. Linear Inequalities13. Graphs of Functions15. Trigonometry

11

1

1121

11

11

1

2

1211

1

112

1

111

1

11

1

1

2

113

1

11

1

1

1

12

111

1

1

1211

21

1

1

1

TOTAL 3 5 2 5 5 1 1 4 5 1 1 3 7 1 3 6 1 1 1 8 2

C. CONTENT – Paper 2 THEMES TOPICS

NUMBERS

1. WHOLE NUMBERS 2. FRACTIONS

3. INDICES 4. DIRECTED NUMBERS

5. SQUARES, SQUARE ROOTS, CUBE, CUBE ROOTS

SHAPES

1. PERIMETER AND AREA 2. SOLID GEOMETRY

3. TRANSFORMATIONS 4. TRIGONOMETRY

5. GEOMETRICAL CONSTRUCTIONS

6. LOCI IN TWO DIMENSIONS

ALGEBRA

1. LINEAR EQUATIONS 2. ALGEBRAIC FORMULAE

3. ALGEBRAIC EXPRESSIONS 4. LINEAR INEQUALITIES

5.STATISTICS I AND II

D. ANSWERING METHODS – Paper 2

SHOW CLEAR WORKING METHOD.

EXAMPLE 1 :

Cik Nurul’s monthly salary is RM 470. How much is her annual salary?

Answer : _____________

Show working method in the space provided.


IF NO WORKING METHOD CAN BE WRITTEN, JUST WRITE DOWN THE ANSWER.

EXAMPLE 2 :Between translation, rotation, reflection and enlargement, which one involves change of size.

Answer : ______________

No working method can be shown.


DRAW DIAGRAM REQUESTED USING GEOMETRICAL

INSTRUMENT (PROTRACTOR, RULER, COMPASS etc)

EXAMPLE 3 :

Using ruler and compass, construct a 30o angle.

Make sure there are signs of “intersection of 2 cicles” to prove you used the compass.

You can use the protractor to double check it is a 30o angle.

Pmr Mathematics

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