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PROGRAM DIDIK CEMERLANG AKADEMIK SPM MODEL SPM QUESTIONS ( PAPER 1 ) ORGANISED BY: JABATAN PELAJARAN NEGERI PULAU PINANG ADDITIONAL MATHEMATICS MODULE 19 http://mathsmozac.blogspot.com http://sahatmozac.blogspot.com

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SPM

MODEL SPM QUE 1 )

ORGA

JABATAN PELAJARA

MODU

http://maths

http://sahatmozac.blogspot.comSTIONS ( PAPER

NISED BY:

LE 19N NEGERI PULAU PINANG

mozac.blogspot.com

• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 2

2 Hours

JABATAN PELAJARAN NEGERI PULAU PINANG

Paper 1

Two Hours

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

2. Calon dikehendaki membaca arahandi halaman 2.

Kod PemeriksaQuestions Marks Actual Marks

1 22 33 34 35 36 37 38 39 310 211 412 413 414 215 216 317 418 419 420 421 322 423 324 325 4

Total

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 3

INFORMATION FOR CANDIDATES

1. This question paper consists of 25 questions.

3. Give only one answer for each question.

4. Write your answer clearly in the spaces provided in the question paper.

6. If you wish to change your answer , cross out the work that you have done. Then write down the

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

8. The marks allocated for each question and sub-figure mathematical tables is provided .

9. You may use a non-programmable scientific calculator .

10.A booklet of four-figure mathematical tables is provided.

11.You may use a non programmable scientific calculator.

12.This question paper must be handed in at the end of examination.

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 4

1 . Diagram 1, the function h maps x to y and the function k maps y to z.

DIAGRAM 1

Determine

(a) hk 1 ( 4),

(b) kh 1 ( 2). [2 marks]

(b) ___________

2. The function p1 is defined as p1 (x) =x

x43 , x 4.

Find

(a) p(x),

(b) p(5). [3 marks]

(b) ___________

x y z

4

3

2

hk

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pina

3. The following information refers to the functions h and g.

Find f (x). [3 marks]

4. The straight line y = t intercept with the curve y = 3 + 5x 4x2 at the two points A and B .

Find the range of values of t . [3 marks]

Jawapan : ___________

23

12 2

places . [3 marks]

g (x) = 4 3 x

fg (x) = 2 x + 5

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 6

6. Diagram 2 shows the graph of a quadratic functions g(x) = 4 2(x + h)2 where h is constant.

DIAGRAM 2

The curve y = g(x) has maximum point (3, k) , where k is a constant .State

(a) the value of h,

(b) the value of k,.

(c) the equation of the axis of symmetry .[3 marks]

Answer : (a) h = ___________

(b) k = ___________

(c) ___________

7. Solve the equation .)4)(8(

164 13

xx

x [3 marks]

y = g(x)

(3,k)

x

y

O

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 7

8. Solve the equation log2 (x 1) + 2 = 2 log2 x [3 marks]

9. Given that log2 x = p and log2 y = r, express

2

3

232log

yx in term p and r.

[3 marks]

10. The sum of the first n term of an arithmetric progression is given by Sn= 5n 3. Find the

fifth term . [2 marks]

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 8

11. The first three terms of an arithmetic progression are 21 , 1, 2 ,

Find

(a) the common ratio ,

(b) the sum of the first 10 terms after the 5th term .

[ 4 marks]

(b) ___________

12. The sum of the first n terms of an arithmetric progression 47, 44, 41, is 1325. Find

(a) the common difference of the progression ,

(b) the value of n. [4 marks]

(b) n = ___________

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajara

13. Diagram 3 shows a straight line graph of log10 y againts log10 x.

The variables x and y are related by equation y = p x q, where p and q are contants .

(a) Calc

(b) Find

14. The follow

parallel to e

Express p

log10 y

log10 x

2

4 O

http://sahatmozac.blogspot.comDIAGRAM 3

ulate the value of p and q,n Pulau Pinang 9

the value of y if x = 10. [4 marks]

Answer : (a) p = ___________

q = ___________

(b) y =___________

ing information refers to the equations of two straight lines , AB and CD , which

ach other.

in terms q. [2 marks]

AB : 2y = p x + q

CD : 3y = (q + 1) x + 2

Where p and q are constants

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 10

15. Given that B point is (8, 5) and O is origin.

(a) ExpressOB in terms of

~i and

~j .

(b) Find the unit vector in the direction ofOB . [2 marks]

(b) ___________

16. Given thatOA = 2

~i + 3

~j ,

OB = 10

~i + 6

~j and R is a point on AB such that AR :

AB = 2 : 3. Find

(a)AB ,

(b)OR . [3 marks]

(b) ___________

17. Solved the equation 3cot

1 22 xsekx

for 0 x 360.

[4 marks]

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran P

18. Diagram 4 shows the sector OPQ, centre O with a radius of 5 cm . Line PR is perpendicular tothe line OQ and QR = 1 cm.

[4 marks]

Find ( a ) POR in radians ,

( b ) the perimeter of the shaded region .

Answer : ( a ) .

( b ) .

19. Given that 2)25(4)( xxxf , find )(" xf [4 marks]

RAJAH 4

Q

P O

R

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 12

20. Given that x = t + 3t 2 and y = 2t 1

(a) finddydx in term of t.

(b) If y decreases from 4.0 to 3.98, Find the corresponding small change in t .

[4 marks]

(b) ___________

21. Given that 2321

xxy and )(4 xf

dxdy

with )(xf is a function in x .

Calculate the value of dxxf )(32

2 . [3 marks]

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 13

22. A chess team consists that of 5 students . The team will be chosen from a group of 6 boys

and 4 girls . Calculate the number of teams that can be formed such that each team consists

of

(a) 4 boys,

(b) Not more than 2 girls.[4 marks]

(b) ___________

23. The mean of five numbers is m. The sum of the squares of the numbers is 720 and the

standard deviation is 9h2. Express m in term of h.

[3 marks]

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 14

24. Ali has 6 accessories of the item which consists of P, Q, R, S, T and U. He wants to arrange

4 of the items in a row . Find the probability that

(a) the arrangment is TUPS ,

(b) the arrangment does not incule P item

[3 marks]

(b) ___________

25. X is a random variable of normal distribution with a mean of 10 and a variance 9 , find the

value of r such that P ( X < r ) = 0 . 9 7 5.

[4 marks]

END OF QUESTION PAPER

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 15

1. ( a ) h k 1 ( 4) = 2

( b ) k h 1 ( 2) = 4

2 . ( a ) p 1 ( x ) =x

x43

p 1 ( y ) = yy43

x =y

y43

x ( 4 y ) = 3 y

4 x x y = 3 y

y ( x + 3 ) = 4 x

y =3

4xx

p ( x ) =3

4xx , x 3,

( b ) 35)5(4)5(

p

=25

3 . g ( x ) = 4 3 x

y = 4 3 x

3 x = 4 y

x =3

4 y

g 1(x) =3

4 x

f ( x ) = f g g 1 ( x ) = f g

34 x

= 2 53

4

x

=3

223 x

4 . y = t , y = 3 + 5 x 4 x 2

3 + 5 x 4 x 2 = t

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• Additional Mathematics ( Paper 1) SPM

Jabatan Pelajaran Pulau Pinang 16

4 x 2 5 x + t 3 = 0

Intercept at two points , use b 2 4 a c > 0

( 5 ) 2 4 ( 4 ) ( t 3 ) > 0

1 6 t < 7 3

t