Yearly Examination, 2005-2006

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QUEEN’S COLLEGE

Yearly Examination, 2005-2006

MATHEMATICS PAPER II

Secondary 4 Date: 23/6/2006

Time: 10:30am - 11:30am

1.Write down the information required in the spaces provided in the Answer Sheet.

2.When told to open this question paper, check that all the questions are there. Look for the words ‘END OF PAPER’ after the last question.

3.ANSWER ALL QUESTIONS. All the answers should be marked on the Answer Sheet.

4.Note that you may mark only ONE answer to each question. Two or more answers will score NO MARKS.

5.All questions carry 2 marks. No marks will be deducted for wrong answers.

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

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There are 40 questions in this paper.

1.Which of the following numbers is rational?

D.+ 1

2.If the curve is shifted two units to the left, then the new curve is

3.The equation of the line of symmetry of the graph of y = 5(x + 3)2 4 is

A..

B..

C..

D..

4.The length of a rectangle is 4 cm longer than twice its width. If its area is 48.cm2, find the length.

A.4 cm

B.6 cm

C.12 cm

D.48 cm

5.If ,

what is the value of ?

A.0

B.4

D.any positive numbers

7.The greatest value of (2sin3x – 1)2 + 4 is

A.4

B.5

C.8

D.13

8.What is the remainder if is divided by ?

A.a + 5

B.a + 7

C.5 – a

D.7 – a

9.In the figure, PA is the diameter of a circle. O is the center. OA = r and
arc AB = then x =

A.38.2o

B.43.0o

C.47.0o

D.85.9o

10.In the figure, AB = p and . Find AD.

11.In the figure, ACB is a semi-circle with AB as diameter. If AB = 2 and ABC = 30, then the area enclosed by the arc AC and the lines AB and BC =

A..

12.If is an
identity in x, then b =

A.1– a.

B.a– 1.

C.a.

D..

13.If and sin, then tan

A..

B..

C..

D..

14.If , the number of intersection points of the graphs of

y =sin2 and y=cos is

A.1

B.2

C.3

D.4

15.cos10+cos20+cos30+…+ cos180=

C.– 1

D.0

16.A large circlular coin of radius 2 cm is placed on the table. Small circular coins of radius 1 cm are placed around the large coin and touch it. At most how many small coins can be placed.

A.6

B.7

C.8

D.9

17.The least value of 7 + 4sinx – cosx is

A.2

B.3

C.4

D.5

18.If , which of the following is/are true

Isinxsiny

IIcosxcosy

IIItanxtany

A.I only

B.II only

C.III only

D.II and III only

19.If sin and x lies in quadrant III, find the value of .

C.–4

D.1

20.The extreme values of are

A.maximum = 1, minimum = –1

B.maximum = 1, minimum = –3

C.maximum = 2, minimum = –1

D.maximum = 2, minimum = –3

21.If , where , and are positive numbers, which of the following must be true?

(1)

(2)

(3)

A.(1) only

B.(2) only

C.(3) only

D.(2) and (3) only

22.

23.The greatest value of is

C.1

D.2

24.If sin is increasing and cos is decreasing, then must lie in

A.quadrant I only

B.quadrant II only

C.quadrant IV only

D.quadrant I and III only

25.The figure shows the graphs of
y =sin x andy = cos x. Find the range
of values of x for which sin x cos x 
for 0 < x < 360.

A.0 < x < 45 or 225 < x < 360

B.0 < x < 135 or 225 < x < 360

C.45 < x < 135

D.45 < x < 225

26.If sin– cos =1, then sin– cos =

A.–1

B.0

C.1

D.2

27.In the figure, TP and TQ are tangents to the circle at P and Q respectively. If M is a point on the minor arc PQ and
PTQ = , then PMQ =

A.2.

B. 90.

C.180.

D..

28.In the figure, TA is tangent to the circle at A. BCT is a straight line. CAT = 40and : = 4.:.3. Find x.

A.20

B.30

C.40

D.50

29.In the figure, DC is the diameter of the circle BDC. ABC and EDC are straight lines. EBA + DAE =

A.45.

B.90.

C.120.

D.150.

30.In the figure, a quadrilateral ABCD is inscribed in a circle with AB as diameter. If AD = DC and CBA = 70, find DAB.

A.55

B.70

C.75

D.85

31.In ABC, 1 – sinAsin(B+C) =

A.1

32.For , how many roots does the equation 3cos2– 1 = 0 have?

A.2

B.3

C.4

D.5

33.If sinAtanA0, then A may lie in quadrants(s)

A.I and III only

B.II and III only

C.II and IV only

D.I and IV only

34.Let and a : c = 4 : 1,
then a : b : c =

A.12 : 8 : 3

B.8 : 3 : 2

C.4 : 6 : 1

D.2 : 3 : 4

35.A quantity y is partly constant and partly varies directly as x. When x = 10, y = 63. When x = 15, y = 83. Find the value of y when x = 18.

A.93

B.95

C.100

D.none of the above.

36.In the figure, ABCD is a cyclic quadrilateral. If DAB = 110o and BC = BD , find DAC.

A.20o

B.40o

C.45o

D.70o

37.A boat goes upstream from A to B at
20 km/h and then returns downstream from B to A at 30 km/h. What is the average speed of the boat for the whole trip ?

A.24 km/h

B. km/h

C.25 km/h

D.cannot be determined

38.If then

A.x  z

B.x z2

39.In the figure, if  is the angle between the diagonals AF and BE of the cuboid, then

40.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

 END OF PAPER 

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QUEEN’S COLLEGE

Yearly Examination, 2005-2006

MATHEMATICS PAPER II

Secondary 4 Date: 23/6/2006

Time: 10:30am - 11:30am

Solution

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

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