QUEEN’S COLLEGE

Yearly Examination, 2007-2008

Mathematics II

Date: 25 - 6-2008

Secondary 4Time:8:30- 9:30

Instructions:

1.Answer ALL questions on the answer sheet.

  1. You should mark only ONE answer to each question. Two or more answers will score

no marks.

  1. Each question carries 2 marks. No marks will be deducted for wrong answers.
  2. The diagrams in this paper are not necessarily drawn to scale.

- 1 -

  1. If , then

A.b = 2, c = 8

B. b = 2, c = 5

C. b = 3, c = 5

D. b = 2, c = 2

  1. If , then
  1. 1 .
  2. 7 .
  3. 8 .
  4. 9 .
  1. It is given that f(x) = and g(x) = . Find g(4) – f(2) .
  1. 2
  2. 13
  3. 14
  4. 15
  1. When is divided by x+ 1 , the remainder is
  1. 0 .
  2. –1 .
  3. 1 .
  4. –2 .
  1. Which of the following is/are an identity/identities?

I.

II.

III.

A.I only

B. II only

C. III only

D. I and II only

  1. The number of solutions of the equation for is

A.0

B.1

C.3

D.4

  1. In the figure, a : b : c =

A.

B.

C.

D.

  1. If and , then

A.

B.

C.

D.

  1. If the graph of y = (x + 1)2 + 1 is translated to the right by 1 unit and then translated downwards by 1 unit, we get

A.y = x2 + 2

B. y = x2

C.y = (x + 2)2 + 2

D.y = (x + 2)2

  1. In the figure, AD BC .

Find .

A.

B.

C.

D.

  1. In the figure, TC is a tangent to the circle at C and AB // DC .

If BCT = 68 , then  =

A.68 .

B.92 .

C.136 .

D.160 .

  1. Given that y . If x is increased by 25%, find the percentage change in y .

A.Decreased by 20%

B.Decreased by 25%

C.Decreased by 80%

D.Increased by 25%

  1. The cost of two kinds of tea A and B are $12/kg and $20/kg respectively. In what ratio by weight should A and B be mixed so that the mixture will cost $15/kg?

A.4 : 3

B.5 : 3

C.5 : 2

D.3 : 2

  1. The figure shows the graph of a quadratic function y = f(x) .

Given that the graph has vertex (2, 18) and it cuts the x-axis at (5, 0) , find the quadratic function.

A.

B.

C.

D.

  1. Which of the following figures correctly shows the graphs of and for?

A.

B.

C.

D.

  1. In the figure, if , find the value of x .

A.2

B.3

C.4

D.5

  1. In the figure, O is the centre of the smaller circle. OAB and PQR are straight lines. Find  .

A.108

B.112

C.118

D.124

  1. What is the co-ordinates of the vertex of the graph y = (2x + 1)2– 3 ?

A.(1 , – 3)

B.(– 1, – 3)

C.

D.

  1. In the figure, TP and TQ are tangents to the circle PQR at P and Q respectively. If RQP = 50 and PTQ = 40, then

RPQ =

A. 20.

B. 45.

C. 60.

D. 70.

  1. In figure, ABC is a straight line. AB is a diameter and CD is a tangent to circle. If CAD = 30, then ACD =

A. 28

B. 30

C. 32

D. 34

  1. In the figure, the area of ABC is 15 cm2 and A = 30 . AC is longer than AB by 4 cm . Then AC =

A.6 cm .

B.8.8 cm .

C.10 cm .

D.11.5 cm .

  1. Given that , which of the following is/ are true?

(1)0 < 90

(2)90 < 180

(3)180 < 270

A.(1) only

B.(3) only

C.(1) and (2) only

D.(1) and (3) only

  1. In the figure, O is the center of the circle of radius 5 . AB is a tangent and AO = 12 . AC =

A.13 .

B.17 .

C. .

D. .

  1. In the figure, O is the center of the circle of diameter 13. AC = 12 . =

A. .

B. .

C. .

D. .

  1. In the figure, a circle, centre , of radius 1 cm,isinscribed in a sector of radius 3 cm. Thelength of the arc in cm is

A.

B.

C.

D.

  1. In the figure, is a diameter of the circle. . If and , the length ofthe diameter is

A.2.5

B.3

C.3.5

D.5

  1. Which of the following cannot be factorized?

A.

B.

C.

D.

  1. The weight of a gold coin of a given thickness varies as the square of its diameter. If the weights of two such coins are in the ratio 1 : 4 , then their radii are in the ratio

A.1 : 2 .

B.2 : 1 .

C.1 : 4 .

D.4 : 1 .

  1. If , then

A. 1

B. x

C. 2x

D. 

  1. If , then =

A. .

B. .

C. .

D. .

  1. The figure shows a wedge. P and Q are mid-points of AD and EF respectively. Which of the following angles is the greatest ?

A.PBQ .

B.DCF .

C.ACE .

D.DBF.

  1. Rationalize .

A.

B.

C.

D.

  1. If , then

A. or

B.x + y =1

C.xy =1

D.x = y = 1

  1. The figure shows a right prism with a right-angled triangle as the cross-section. Find the angle between the line BF and the plane ABCD correct to the nearest degree.

A. 20

B. 30

C.35

D.40

  1. Suppose the graph of is given. Find the equation of a straight line which should be added to the graph in order to solve .

A.y = 3x + 2

B.y = x– 2

C.y = 3x– 3

D.y = –4x + 2

  1. In ABC , AB = 12 , AC = 15 and

B = 56 . Find A correct to 0.1

A.82.5

B.87.6

C.91.7

D.94.6

  1. Find the minimum value of .

A.0

B.1

C.2

D.5

  1. If x : y = 4 : 3 and ,

find x : y : z .

A.28 : 21 : 36

B.36 : 21 : 28

C.12 : 5 : 13

D.7 : 9 : 12

  1. If z varies directly as and z = 27 when x = 4 , find the value of x when z = 75 .

A.3

B.

C.5

D.7

  1. In the figure, is a right-angled triangle with O, A, B on the samehorizontal plane and. OC is avertical line. If , then

A.

B.

C.

D.

END OF PAPER

- 1 -

QUEEN’S COLLEGE

Yearly Examination, 2007-2008

Mathematics II

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

1