MA JUJ Pahang 09

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MATHEMATICS SPMThis module aims to prepare the Form five students for the SPM examination and also for the Form four students to reinforce as well as to enable them to master the selected topics. It also serves as a guidance for effective acquisition of the various mathematical skills. At the end of each topic, sample answers are given. Discussions on common mistakes that result in the students failure to obtain full mark are included as well. This module suggests specific strategies for each chosen topic and strategies which can help the students in problem solving. It is hoped that this module can benefit all the Pahang students as well as helping them towards achieving excellent results in SPM Mathematics.

TABLE OF CONTENTS 1.1 1.2 1.3 1.4 1.5 Authentic Examination Format Topical Analysis of SPM Paper 1 Topical Analysis of SPM Paper 2 Selected topical (BONUS) 4 full sets of Paper 1 and 3 sets Paper 2 questions with marking scheme

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FORMAT OF ASSESSMENT INSTRUMENT MATHEMATICS 1449 NO 1 2 3 TOPIC Instrument type Item type Number of Questions PAPER 1 (1449/1) Objective questions Multiple Choice Questions 40 questions ( answer all) PAPER 2 (1449/2) Subjective questions Open ended structure and limited response Section A 11 questions (answer all) Section B 5 questions (choose 4) Section A Total marks : 52 Section B Total marks : 48 (Each question 12 marks) Overall Total :100 5 6 Test Duration Constructs Weights 1 hour 15 minutes Knowledge - 45% Skills - 55% 2 hours 30 minutes Knowledge - 25% Skills - 70% Values - 5% Lower secondary school scope with continuation in the upper secondary. All aspects of learning from Form 4 and Form 5.

4

Total Marks

40

7

Context Scope

Lower secondary school scope with continuation in the upper secondary. All aspects of learning from Form 4 and Form 5. L:M:H = 5:3:2

8

9

Difficulty level Low - L Medium - M High - H Additional Tools

L:M:H = 5:3:2

a. Scientific Calculator b. Four-figure Mathematical table b. Geometry Set

a. Scientific Calculator b. Four-figure Mathematical table b. Geometry Set

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2. LIST OF MATHEMATICS TOPICS 1449 No. FORM 1 3 1 2 3 4 5 6 7 8 9 10 11 12 13 Circles I and II Polygons I and II Solids and Volumes Transformations I and II Trigonometry I Algebraic Expressions I and II Algebraic fractions Algebraic Formulae Linear Equations(1 and 2 unknowns) Indices Linear Inequalities Statistics I and II Arc Length & Area of Sector FORM 4 Standard Form Quadratic Expressions and Equations Sets Mathematical Reasoning The Straight Line Statistics III Probability I Circles III Trigonometry II Angles of Elevation and Depression Lines and Planes in 3 Dimensions FORM 5 Number Bases Graphs of Functions II Transformations III Matrices Variations Gradient and Area under a Graph Probability II Bearing Earth as a Sphere Plans and Elevations

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1.2 .

TOPICAL ANALYSIS OF SPM MATHEMATICS PAPER 1 TOPICS FORM 4 5 3 4 4 4 4 5 5 2 2 2 3 3 3 3 5 5 4 4 5 4 2 3 3 3 5 4 NUMBER OF QUESTIONS 2004 2005 2006 1,2,3,4 1,2,3 1,2,3,4 5,6 4,5 5,6 7 6,7 7 8 8 8 15,16 15 15,16 11,12 14 18 17 10 20 22 19 21 23,24 25,26 40 29 33,34 30,31,32 38,39 35,37 27 28 9 13 36 11,12,13 14 16 17,18 9,10 19 22 20 21 23,24 25 39,40 28 32,33 29,30,31 36,37,38 34 27 35 26 11,12,13 14 17 18 9,10 19,20 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Standard Form Number Bases Polygon II Circles III Angles of Elevation & Depression Trigonometry II Lines and Planes in 3 Dimensions Bearing Earth as a Sphere Transformations I Algebraic Expressions II Linear Equations I Algebraic Expressions III Algebraic Formulae Indices Linear Inequalities Matrices Graph of Function II The Straight Line Sets Variations Probability I Statistics I Statistics II Transformations II Trigonometry I Probability II Statistics III

2003 1,2,3,4 5,6 7,8 9 10 11,12 13 14 15 16,17,18 19 3,20 21 22 23,24 25,26 27,28,29 30 31 32,33,34 35,36 37,38 39 40 -

2007 1,2,3 4,5 6,7 8 15 11,12,13 14 16 17,18 9,10 19 22 21 20 23,24 25 39,40 28 32,33 29,30,31 36,37,38 34,35 26,27

2008 1,2,3,4 5,6 7 8 15,16 11,12,13 14 17 18 9,10 19 22 21 20 23,24 25 39,40 28 32,33 29,30,31 36,37,38 34,35 26 27

21 23 24 39,40 28 32,33 29,30,31 36,37,38 34,35 26,27 25 -

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1.3 TOPICAL ANALYSIS OF SPM MATHEMATICS PAPER 2 Total Question No. Form Topic 05 06 07 Part A (Question 1 to Question 11) 1. 1-3 Linear Simultaneous Equations 1 1 1 2 4 Quadratic Equation 1 1 1 3.a 4 Sets (Shade Venn diagrams) 1 3.b 5* Region for Inequalities 1 1 4. 4 Mathematical Reasoning( Statement, implication, 1 1 1 argument, mathematical induction, converse ) 5. 4 The Straight Line parallel, equation, y-intercept 1 1 1 6. 5 Probability II 1 1 1 7. 1-3 Arc Length & Area of Sector 1 1 1 8. 1-3 Volume of Solids a. Pyramids and half cylinders b. Cones and Cylinders 1 c. Cones and cuboids d. Pyramid and prism 1 1 e. Right prism and half cylinders 9. 5 Matrices ( Inverse, matrix equation ) 1 1 1 110. 5 Gradient and Area Under a Graph a. Speed-Time Graph 1 1 * b. Distance-Time graph 1 11. 4 Lines & Planes in 3 Dimensions (angle between 1 1 1 2 planes) Part B (Question 12 to 16 - Choose any four) 12. 5 Graphs of Functions II * a. Quadratic 1 1 b. Cubic 1 c. Reciprocal 13. 5 Transformations III ( combined ) 1 1 1 14. 5 Earth as a Sphere 1 1 1 15. 5 Plans and elevations a. Right Prism and cuboids b. Cuboids and half cylinder, prism 1 1 c. Prism and prism 1 16. 4 Statistics III a. Raw data, frequency table, mean, frequency 1 polygon, modal class 1 1 * b. Ogive 1 c. Histogram 1 1 d. Frequency Polygon e. Communication 1 Total Questions 16 16 16 * FOCUS IN 2009

08 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 16

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Question Allocation (Mathematics SPM 2006) Number of questions Paper 1 % 10 25.00 21 52.00 9 22.50 40 100.00

Form 3 4 5 Total

Paper 2 3 6 7 16

Marks 14 33 65 112

% 12.50 29.46 58.04 100.00

Total % 18.75 40.98 40.27 100.00

Question Allocation (Mathematics SPM 2007) Number of questions Paper 2 Marks % 3 14 12.5 6 33 29.5 7 65 58 16 112 100.00

Form 3 4 5 Total

Paper 1 13 16 11 40

% 32.5 40.0 27.5 100.00

Total % 28.57 39.28 32.14 100.00

Question Allocation (Mathematics SPM 2008) Number of questions Paper 1 % 12 30.00 19 47.50 09 22.50 40 100.00

Form 3 4 5 Total

Paper 2 3 6 7 16

Marks 14 33 65 112

% 12.50 29.46 58.04 100.00

Total % 18.75 40.98 40.27 100.00

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TOPICAL EXERCISE 1. Simultaneous Linear EquationsEXERCISE 1. 1.Calculate the value of v and w that satisfy the following simultaneous linear equation: Hitungkan nilai bagi v dan w yang memuaskan persamaan linear serentak berikut:2v 3w = 10 4v + w = 1 [4 marks]

2.Calculate the value of p and q that satisfy the following simultaneous linear equation: Hitungkan nilai bagi p dan q yang memuaskan persamaan linear serentak berikut: 1 p + q =1 3 2p q = 7 [4 marks]

3.Calculate the value of m and n that satisfy the following simultaneous linear equation: Hitungkan nilai bagi m dan n yang memuaskan persamaan linear serentak berikut:

m + 3n = 11 1 mn =3 2 [4 marks]

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4.Calculate the value of a and b that satisfy the following simultaneous linear equation: Hitungkan nilai bagi a dan b yang memuaskan persamaan linear serentak berikut: 3a + 2b = 14 a 3b = 7 [4 marks]

5.Calculate the value of x and y that satisfy the following simultaneous linear equation: Hitungkan nilai bagi x dan y yang memuaskan persamaan linear serentak berikut:5 x + 4 y = 13 4 x + 2 y = 8 [4 marks]

ANSWERS:8

Q 1.

2.

Marking Scheme 4v 6 w = 20 or 12v + 3w = 3 -7w = 21 or 14v = 7 OR 1 3 10 1 (2 marks) 2(1) (3)(4) 4 2 1 w = 3 1 v= 2 3 p + q = 3 or equivalent 5 p = 10 OR 1 1 1 1 (2 marks) 3 7 1 1(1) (2) 2 1 3 p=2

Mark 1 1

Total Marks

1 1 1 1

4

3.

q = 3 m 2n = 6 5n = 5 OR

1 11 1

4

or equivalent

4.

5.

1 3 11 1 1 3 1 1(1) 3 2 2 m=8 n =1 3a 9b = 21 or equivalent 7b = 7 OR 3 2 14 1 (3)(3) 2(1) 1 3 7 a = 4 b =1 8 x + 4 y = 16 or equivalent 3x = 3 OR 2 4 13 1 5(2) 4(4) 4 5 8 x = 1 y = 2 1

(2 marks)1 1 1 1

4

(2 marks) 1 1 1 1 (2 marks)1 1

4

4

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2. Quadratic Expressions and Quadratic EquationsEXERCISE 2 1.By using factorisation, solve the quadratic equation: Dengan menggunakan pemfaktoran, selesaikan persamaan kuadratik: 3x 2 = 2( x 1) + 7 [4 marks] 2.By using factorisation, solve the quadratic equation. Dengan menggunakan pemfaktoran, selesaikan persamaan kuadratik: 2y2 6 + y =1 3

[4 marks]

3.By using factorisation, solve the quadratic equation. Dengan menggunakan pemfaktoran, selesaikan persamaan kuadratik: 1 4 x x + = 18 4 [4 marks]

4.By using factorisation, solve the quadratic equation. Dengan menggunakan pemfaktoran, selesaikan persamaan kuadratik:p +1 = 2 p2 +1 5

(

)[4 marks]

5.By using factorisation, solve the quadratic equation. Dengan menggunakan pemfaktoran, selesaikan persamaan kuadratik: 1 p 2 = (3 5 p ) 2 [4 marks]

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ANSWER: Q 1. Marking Scheme 3x 2 2 x 5 = 0 (3x 5)(x + 1) = 0 5 3 -1 Mark 1 11 1

Total Marks

4

2.

2y 2 + 3y 9 = 0 (2 y 3)( y + 3) = 0 3 2 -3 4 x 2 + x 18 = 0 (4 x + 9)(x 2) = 0 9 4 2 2 p2 5 p 3 = 0 (2 p + 1)( p 3) = 0 1 2 32 p2 + 5 p 3 = 0 (2 p 1)( p + 3) = 0 1 2 -3

1 1 1 1 1 1 1 1 1 1 1 11 1 1 1

4

3.

4

4.

4

5.

4

11

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VOLUME OF SOLID GEOMETRYEXERCISE 31. Diagra