smc addmath mocks 2010

8/8/2019 SMC Addmath Mocks 2010

http://slidepdf.com/reader/full/smc-addmath-mocks-2010 1/5

SULIT

3472

Aug

2010

2.5 hours

DO NOT OPEN THE QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO.

Instructions :

1 This question paper consists of two sections : Section A and Section B .

2 Answer ALL questions in Section A , and TWO questions from Section B .

3 The figures / diagrams given in a problem would provide useful information to solve the problem.

However, it might not be drawn to scale.

4 All solution methods must be clearly shown. You may loose marks if important working steps are

not properly shown.

5 The marks allocated for each question or sub question are shown in brackets.

6 A list of formulae is provided.

7 You may use a non-programmable scientific calculator or a booklet of four-figure mathematical tables.

2 Hours 30 Minutes

This question paper consists of 5 pages

~ ALL THE VERY BEST ~

LEMBAGA PEPERIKSAAN MALAYSIA

SRI MURUGAN CENTRE MALAYSIA

PEPERIKSAAN MOCKS SPM 2010

ADDITIONAL MATHEMATICS



The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

[ See over

SULIT

ALGEBRA STATISTICS TRIGONOMETRY

GEOMETRY

CALCULUS



9. (a) The first three terms of an arithmetic progression are 51 , 47 and 43 . The nth

term of the progression is

negative. Find the minimum value of n . [ 2m ]

(b) The first three terms of a geometric progression are x + 1 , x - 3 and 2 . Calculate the sum to infinity of

the progression. [ 5m ]

10. Diagram 3 shows a straight line when log2 y plotted against x .

(a) Express log 2 y in terms of x , [ 1m ]

(b) By expressing y in the form amx - 2c

, find the values of a , m , and c . [ 3m ]

11. (a) X is a random variable of a normal distribution with a mean of 4.8 and a variance of 1.44 .

Find the value of P(4.8 < X < 5.2 ). [ 2m ]

(b) Solve 4 sin A cos A - 1 = 0 for 0o

< A < 200o

. [ 4m ]

12. Solve the simultaneous equations 4x + y = -8 and x 2

+ x - y = 2 . [ 4m ]

13. There are 6 cans of paint, each consisting of red, blue, green, yellow, black and white.(a) Find the number of ways to arrange 4 cans in a row. [ 1m ]

(b) If the red, blue, yellow and white paints are selected, find the number of possible mixtures. [ 2m ]

14. (a) Five letters from the word ' INTEGRAL ' are to be arranged. Calculate the number of possible arrangements

if they must begin and end with a vowel. [ 2m ]

(b) A test paper consists of 40 questions. Each question is followed by 4 choices of answer, where only

one answer is correct. Murugan answers 30 questions correctly and randomly chooses an answer for each

of the remaining 10 questions. Find the probability that he obtains at least 82.5% for the test. [ 4m ]

15. Diagram 4 shows a quadrilateral. Given that is parallel with , h and k are constants.

Find

(a) the value of h and of k ,

(b) the area of triangle ABC , if the area of the triangle ABD is 20 unit 2

.

[ 5m ]

16. Based on the Diagram 5 , answer the following questions.

Given that the curve y = (x - 4)2

is symmetrical about the line x = 4 .

Calculate

(a) the area of the region R . [ 4m ]

(b) the volume generated when the shaded region is revolved 180o

about the line x = 4. [ 5m ]

17. Given that x = 3 is the equation of the normal to the curve y = hx 2

- 4x + 1 at its turning point. Find

(a) the value of h , [ 2m ]

(b) the equation of the tangent to the curve at the same turning point. [ 2m ]

18. (a) Prove that 2 cosec 2A - cot A = tan A . [ 3m ]

(b) Sketch the graph y = 2 - | 3 sin 2x |, for 0 ≤ x ≤ π . Hence, find the value of k such that

| 3 sin 2x | = 3k has only two solutions for 0 ≤ x ≤ π . [ 5m ]

[ See over

SULIT

If ,

x O

log2 y

(3, 2 )

(0, 1 )

Diagram 3

.

.

y

x

O

AD

C B

k x

hx

hy

>

>

Diagram 4

Diagram 5

x = 4

R

y = 1

y = (x - 4)2

y

k

x AB 2

1

2

AD BC



Section B : Answer TWO questions. [ 20 marks ]

19. (a) A point T(x, y) moves along the circumference of a circle with centre C(4, 6) . Points A(0, 3) and B(7, h)

are on the circumference. Find

(i) the equation of the locus of the point T . [ 3m ]

(ii) the values of h . [ 2m ]

(b) Diagram 6 shows a semicircle ABCD with AB as the diameter.

The radius of the semicircle is 5 cm . Find(i) the length of the arc AD , [ 2m ]

(ii) the perimeter of the shaded region. [ 3m ]

[ Use π = 3.142 ]

[ Give your answers correct to 3 decimal places ]

20. (a) Diagram 7 shows a triangle PQR . Calculate

(i) the obtuse angle PRQ , [ 2m ]

(ii) the area of the new triangle PQR' if PR is lengthened to point R' while the

length of PQ , the length of QR and angle QPR are maintained.

[ Give your answers correct to 2 decimal places ] [ 4m ]

(b) The roots of the quadratic equation x 2

- 10x + 3 - 3m = 0 are in the ratio of 2 : 3. Find the roots and the

value of m . [ 4m ]

21. (a) A dice is tossed 50 times. The table below shows the scores obtained.

1 2 3 4 5 6

5 8 x 10 7 y

If the modal score is 3, find the range of values of x and of y. Hence, for the smallest value of x,

find the median score and the mean. [ 5m ]

(b) The table below shows the prices of four items in the year 2006 and 2009.

(i) Calculate the composite price index for the year 2009 based on the year 2006. [ 3m ]

(ii) If the composite price index continues to increase at the same rate from 2009 to

2010, calculate the composite price index in the year 2010 based on the year 2006. [ 2m ]

22. A particle moves along a straight line from a fixed point, O . Its velocity, V = (3t 2

- 12t - 15) ms-1

, where t is

the time in second. Given that after 1 second, the particle is 22 m on the left hand side of O .

[ Assume positive direction is towards the right ]

Find the

(a) initial velocity, [ 1m ]

(b) initial acceleration, [ 1m ]

(c) minimum velocity, [ 2m ]

(d) range of the values of t when the particle decelerates, [ 2m ]

(e) total distance travelled by the particle in the first 6 seconds. [ 4m ]

280

A

B

C

D

8.00

18.00

24.00

2.60

10.00

21.60

33.60

[ The End

SULIT

Score

Frequency

Price in2006 ( RM )

Price in2009 ( RM )

MonthlyExpenses (RM )

Item

2.00 200

160

360

Diagram 6 A B

C D

40o

P

Q

R28o

Diagram 7

smc addmath mocks 2010

Documents