Trial Spm p1 Smk St Anthony 2013

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3472/1

mathematics

September 2013

2 Hours

Name: ________________________

Form :_________________________

SPM TRIAL EXAMINATION 2013

Paper 1

Two Hours

1. This question paper consists of 25questions.

Given only one answer for eachquestion.

4. Write your answers clearly in thespaces provided in the question paper.

Then write down the new answer.

7. The diagrams in the questions providedare not drawn to scale unless stated.

8. The marks allocated for each questionand sub-part of a question are shown in

brackets.

9. A list of formulae and normaldistribution table are provided.

10.You may use a non-programmablescientific calculator.

11.This question paper must be handed inat the end of the examination.

For examiners use only

Question Total marks Marks Obtained

1 3

2 3

3 2

4 3

5 3

6 3

7 3

8 4

9 4

10 3

11 3

12 3

13 2

14 3

15 3

16 3

17 4

18 4

19 4

20 3

21 3

22 4

23 4

24 3

25 3

Total

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1. Diagram 1 shows the relation between set A and set B

State

(a) the range of the relation

(b) the image of 4 [ 3 marks ]

b) _______________

2

4

6

5

6

78

9

1

3

2. The function is defined as and , Find

(a) the value of

(b) composite of [ 3 marks ]Answer: a) _______________

b) _______________

3. The function is defined as , Find [ 2 marks ]

2

3

3

2

{ 6, 7, 9 } 7

{ 6, 7, 9 }

7

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4. Given that the quadratic equation will intersect the exactly one

point, find the value of.[ 3 marks ]

5. Given that the quadratic equation has two distinct root, find the range of.[ 3 marks ]

6. Solve the equation [3 marks ]

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8. Given that and , express in term of and . [4 marks ]

8

4

9

4

7. Given a quadratic function has the minimum point , where and areconstant. State

(a) the value of(b) the value of(c) the equation of the axis of symmetry [3 marks]

(b) __________________

(c) __________________

7

3

9. An Arithmetic Progression contains 20 terms. Given that the term is and the sum of the last terms is , calculate(a) the first term and common difference(b)the sum of the first terms [4 marks ]

(b) ______________________

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10. In a geometric progression, the first term is and the fourth term is .

Calculate

a) the common ratiob) the sum to infinity of the geometric progression. [ 3 marks ]

11. The diagram shows the parallelogram . Finda) the value ofb) area of the parallelogram [ 3 marks ]

b) __________________

10

1

12.In the diagram, the straight line has an equation of . intersects the at point and the at point .

Point lies on such that . Finda) The coordinates of and b) The coordinates of [ 3 marks ]

b) __________________

1

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13. Diagram below shows two vectors, and . Express

(a) in the form

(b) in the form [2 marks]

(b) __________________

13

2

14. Given that and , find the possible value (or values) of for followingcases,

(a) and are parallel(b) [3 marks]

(b) __________________

14

3

15. Diagram 1 shows part of a straight line graph drawn to represent . Find the values ofand . [3 marks]

15

3

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16. Given is an acute angle and , Express each of the following in terms of.

a) b) [3 marks]

1

17. Solve the equation for . [4 marks]

1

18. Diagram shows a circle with center.The length of the minor arc is 16cm and the angle of the majorsector is . Using ,find (Give your answer correct to four significant figures)

(a)The value of, in radians(b)The length, in cm, of the radius of the circle [3 marks]

(b) __________________

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19. Given that a curve . Find value of, if

(a) the turning point when (b) the tangent of the curve is when [4 marks]

(b) _________________

19

4

20. Given that . Find(a)

(b) [3 marks]

(b) _________________

20

321. A set of data has a mean of and a standard deviation of. If each value in the set of data is addewith and multiplied by , find

(a) the new mean

(b) the new variance [3 marks]

(b) __________________

21

3

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22.

Diagram shows six different letters.

a) Find the number of possible arrangementsb) Find the number of these arrangements . beginning with Vowels. [4 marks]

23. Charm, Ali, and Murugen will be taking part in badminton competition. The probability that

Charm, Ali, and Murugen will win the competition is,

, and

respectively. Find the probability that

a) Only Charm will win in the competition.

b) Only two of them will win the [4 marks]

M O B I L E

(b) __________________

24. A pack of present containing three pens are chosen from 3 blue pens and 4 black pens. Find theprobability of getting at least one black pen in the pack of present. [3 marks]

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25. is random variable which is normal distributed with a mean of, and standard deviation of 2.

Find

a) the value of, if the is 1.3 when b) [3 marks]

25

3

(b) __________________

Prepared by :

________________________

(Thong Shiau Chuan)

Checked by:

________________________

Verified by :

______________________

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Schema Add Math, SPM TRIAL EXAMINATION 2013

Question Solution Marks

1 a) {6 , 7, 9 }b) 7

2 ( 1 marks if 2 of 3 correct answer)

1

2 a) K=3b)

1

1

1

3 Lets or

1

1

4

1

1

1

5

1

1

1

6

1

1

1

7

1

1

1

8

1

1

1

19 a)

b)

1

1

1

1

10 a)

1

1

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b) 1

11a)

b)

1

1

1

12 a)

b)

1

1

1

13

1

1

14 a)

b)

1

1

1

15

1

1

1

16 Drawing of triangle

a) b)

1

1

1

17

and

1

1

1

1

18 a) b)

1

1

1

19 a)

b)

1

1

1

1

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K=1

20 a) b)

1

1

1

21 a) b)

1

1

1

22 a)

b)

1

1

1

1

23 a)

b)

1

1

1

1

24

1

1

1

25 a)

b)

1

1

1