MOCK 12 MATH COMPULSORY PART PAPER 2

QUEEN'S COLLEGE

MOCK EXAMINATION 2011 - 2012

MATHEMATICS Compulsory Part

PAPER 2

Date: th February 2012

Time: 11 :30 am - 12:45 pm

Time allowed: 1 hour 15 minutes

1. Read carefully the instructions on the Answer Sheet and insert the infonnation required in the spaces provided.

2. When told to open this book, you should check that all the questions are there. Look for the words 'END OF

PAPER' after the last question.

3. All questions carry equal marks.

4. ANSWER ALL QUESTIONS. You are advised to use an HB pencil to mark all the answers on the Answer Sheet,

so that wrong marks can be completely erased with a clean rubber.

5. You should mark only ONE answer for each question. If you mark more than one answer, you will receive NO

MARKS for that question.

6. No marks will be deducted for wrong answers.

There are 30 questions in Section A and 15 questions in Section B.

The diagrams in this paper are not necessarily drawn to scale.

Choose the best answer for each question.

Section A

{a3b-1t1. Simplify

(a-1b2 t I

A. ab 3

1B.

a2b3

1C.

a 2b6

ID.

a 2b9

2. x 2 _ y2 -x+ Y =

A. (x- yXx- y-l)

B. (x- yXx+ y-l)

C. (x-yXx+ y+I)

D. (x+ yXx- y+ 1)

3. If 4x =a , then 16 x ==

A. 4a.

B. a2 •

4C. a .

D. 2° .

{Y~X2 -4x-444. If , then y=

y == -2x+ 4

A. -32 or 52.

B. -12 or 16.

C. -12 or 96.

D. -8 or 20.

2

5. The figure shows the graph of y == ax2 + bx +c . Detennine the signs of a and c.

A. a < 0, c < 0 Y

Y= ax 2 + bx+ c

B. a> 0, c < 0

C. a < 0, c> 0

--J.------4--+-..,. xD. a> 0, c > 0

6. Let f{x) = x 3 - 2X2 - 5x +6 . It is known that f(1) = 0 . f{x) can be factorized as

A. (x-lY(x+6).

B. (x-1Xx+1Xx+6)

C. (x-1Xx-2Xx+3)

D. (x-1Xx+2Xx-3)

7. If 3X2+ax+7=3(x-2y+b ,then

A. a =-12 b = -5.

B. a=-12 b=7.

C. a = -4 , b = 3 .

D. -a = 0 , b = -5 .

8. Solve the equation (x+2)=(x-3)(x+2).

A. x=3

B. x=4

C. x= -2 or x = 3

D. x = -2 or x = 4

9. If the equation x 2 + 3x + (k + 2) = 0 has no real roots, find the range of values of k.

1A. k<-­

4

1B. k<­

4

1C. k>-­

4

1D. k>­

4

3

10. If P is a root of the equation ax2 +bx + c = 0, which of the following must be a root of the equation

x-3 x-3a(__)2 +b(--)+c =O? 2 2

p+3A.

2

p-3B.

2

C. 2p+3

D.' 2p-3

11. In the figure, ABCD is a rectangle formed by four squares each of area 1 cm2 • DB is a diagonal. Find

the area of the shaded region.

9 A. - cm2

A D10

7B. cm2 ~ 8 B C

5C. cm2

6

4D. cm2

5

12. The solution of 3x-l > 5 or 3-2x<5 IS

A. x>-l.

B. x>2.

C. -1 <x<2.

D .. x <-1 orx> 2.

13. VCa-2 )Ca3 ) =

7

A. a3 •

1

B. a-3 •

C. a -1 .

D. a-2 .

4

14. The following is the graph of y = 3a x where a> O. Find the value of a.

y3A. 2

2B. ­

3

1C. ­

3

2D. ­

9

15. If log x=m , then logif;2 =

A . Vm 2 •

.logv;;1B. m .

2m C. ­

3

2logmD. ---­

3

16. Which of the following equations show(s) that y varies directly as x?

II. xy=10

III. x + y =10

A. I only

B. II only

C. I and III only

D. II and III only

17. If x varies inversely as y and directly as Z2, then

A. is a constant.

xyB. is a constant.

Z2

XZ2 C. is a constant.

y

'Z2 D. is a constant.

y

5

18. In ,a class, students study either History or Geography, but not both. If the number of students studying Geography is 50% more than those studying History, what is the percentage of students studying History?

A. 25%

B. 33!% 3

C. 40%

D. 60%

19. If x:y=I:2 and y : z = 3 : 2 , which of the following must be true?

I. x varies inversely as y.

II. y varies directly as z.

III. z varies directly as x.

A. I only

B. III only

C. I and II only

D. II and III only

20. In the figure, ABCD is a parallelogram. E is a point on AB such that AE: EB = I : 3. AC and DE

intersect at F. If the area of the parallelogram ABCD is 40 cm2, then the area of ,6DFC is

A. 10 cm2• C

B. 12 cm2•

C. 15 cm2•

D. 16 cm2•

A E

21. In the figure, CD is the tangent to the circle at D, LBAD = 34°, DB = DC and CBA is a straight line.

Find LBDA.

c

6

22. In the figure, AB is the tangent to the circle at P. Find x.

A

C. 73°

B

23. In the figure, PQ and RS are two vertical poles standing on the horizontal ground. The. angle of

elevation of R from P is 20° and the angle of depression of S from P is 40°. If

RS = 5m, then PR=

5sin40°A. m.

sin 70°

5sin50°B. m.

sin 60°

5sin60°C. m. sin50°

5 sin 70° D. m.

sin 40°

224. Find the maximum value of y - --- ­

- 5 - 3sinx .

'2 A.

3

1B.

4

2C.

5

D.

. e 325. If sm =- and e lies in the first quadrant, then sin (90° - e) + sin(180° + e) = 5

1A.

5

.-1B.

5

7C.

5

-7D.

5

R

p

s

7

26. Which of the following could be a geometric sequence/geometric sequences?

o

I. 3, 33 , 3s, 37 , •••

II. 9 , 99 , 999 , 9999 , ...

III. 10 , -100 , 1 000 , --10 000 , ...

A. III only

B. I and II only

C. I and III only

D. II and III only

27. In the figure, LADB = 40°, LBDC = 60° and AB = a, then AC=

a sin 40° A.

sin 60°

a sin 40° B.

sin 80°

a sin 60° C.

sin 40°

a sin 80° D.

sin 40°

128. TO?1 and Mary each throws a dart. The probability of Tom's dart hitting the target is while that of

3

2Mary's is . Find the probability of only one dart hitting the target.

5

2A. 15

3B.' ­

15

7C.

15

11D.

15

29. Which of the following can be negative?

A. Range

B. Inter-quartile range

C. Standard deviation

D., Median

8

30. Consider the following box-and-whisker diagram.

I I I I 108 b c d e 90

Which of the following must be true?

1. Inter-quartile range = d - b

II. Mean = c

III. Range = a - e

A. I only

B. I and III only

C. II and III only

D. I, II and III

Section B

1 .)201131. The complex number ( ~ =

1-1

A. ~i.

B. i .

C. -1.

D. 1.

32. Let a and b be constants. If the figure shows the graph of y = a sin(2x° + 30°) + b, then

A. a = 1 and b = 3.

B. a = 2 and b = 1.

C. a = 2 and b = 2.

D. a= 3 and b = 4.

o 30 120 180 x

9

33. In the figure, the graphs of y = 2X2 +3x -1 and y = 1 intersect at A(a, 1) and B(b, 1). Which

of the following is true?

2X2 + 3x > -2 , where x < a or x > b A. {

2X2 +3x5-2, where a5x5b

2X2 > -3x + 2, where x < a or x> b B. {

2X2 5-3x+2, where a5x5b

2X2 + 3x - 2 < 0 , where x < a or x > b C. {

2X2 +3x - 2 ~ 0, where a 5 x 5 b

2(x 2 +1) < - 3x , where x < a or x > b D. {

2(x 2 + 1) ~ -3x, where a 5 x 5 b

34. In the figure, AB = BC = 6 cm, BD = 5 em, CD = 7 cm and .6.ABC is a straight line. Find, to the nearest

integer, the area of .6.ABD. 0

A. 13 cm2

B. 14cm2

C.' 15 cm2 A C6 B 6

D. 16 cm2

35. In the figure, find the minimum value of c = x +y subject to the following constraints:

4X+3Y 2:12 { x + 2y 2: 6

x and yare positive integers.

A. 3

B. 3.6

C. 4

D.' 6

36. It is given that x varies directly as l and inversely as ..Jz. If y is increased by 10% and Z 1S

decreased by 19%, find the percentage increases in x correct to 3 significant figures.

A. 22.2%

B.' 34.4%

C. 35.8%

D. 49.4%

10

37. If x oc Z2 and yoc-1

, which of the following must be true? Z

1 xoc-L

y2

x 3II. -ocz

Y

III. (x- Y)OC(Z2 -~)

A. I and II only

B. I and III only

C. II and III only

D. I , II and III

38. Let a and b be two consecutive positive integers. Which of the following must be true?

I. a+b is odd.

II. ab is odd.

III. a2 +b2 is odd.

A. III only

B. I and II only

C. I and III only

D. II and III only

39. In the figure, ABCD is a trapezium. Which of the following must be true?

I. AED is an equilateral triangle D C

II. EBCD is a parallelogram

III. AB=2DC

A. I only A 8E

B. II only

C. I and II only

D. I and III only

II

2 4 8 40. FiJ?d the sum of all positive tenns in the geometric sequence 3'-}5' 75 , ...

5A. 21

10B.

21

50C. ­63

50D.

87

941. In a geometric series, if the sum of the frrst three tenns is and the sum to infinity is 2, find the first

4

tenn of the series.

4A.

3

B. 3

c. 4

D: 1

2

42. The mean, standard deviation and inter-quartile range of n numbers are m, s and q

respectively. If each number is decreased by 3, what will be their new means, standard deviations and

inter-quartile range?

~ean Standard Inter-guartile

Deviation Range

A. m s q

B. m s-3 q-3

C. m-3 s q

D." m-3 s q-3

43. In the figure, find the point (x,y) in the shaded region (including the boundary) at which bx-ay+3 attains its greatest value.

A. (a,b)

B. (-a,b)

c. (b,a)

D. (b,-a) (b. -a)

x

12

44. In the figure, P and Q are two right cylindrical vessels each containing some water. The two vessels

are placed on the same horizontal surface. The internal base radii of P and Q are in the ratio 1:3.

A and B are two cubes with sides in the ratio 1:2. A and B are put into P and Q respectively. Suppose both cubes are totally immersed in water without any overflow. If the rise in water

level-in P is 1 cm , then the rise in water level in Q is

- - -- ­ - - -- - -- ­ - - ­- - ---- ­ -

EO I

A. 2

em. 3

B. 9

cm. 8

C. 8 cm.

9

D. 8 cm.

27 45. The equations of two circles are

Which of the following must be true?

I. The two circles have the same centre.

II. The two circles have equal radii.

III. The line joining two centres of the two circles passes through the origin.

A. I only

B. II only

C. III only

D. II and III only

END OF PAPER 13