Queen S College

QUEEN’S COLLEGE

Yearly Examination, 2008-2009

Mathematics II

Date: 26-6-2009

Secondary 4 Time:11:30-12:30

Instructions:

1. Answer ALL questions on the answer sheet.
2. You should mark only ONE answer to each question. Two or more answers will score no marks.
3. Each question carries 2 marks. No marks will be deducted for wrong answers.
4. The diagrams in this paper are not necessarily drawn to scale.

1.If the equationhas two equal real roots, then k

A.3.B.6.

C.3 or 3.D.6 or 6.

2.In the figure, ABC is a right-angled triangle. Find the value of x.

A.2B.3

C.4D.5

3.If, then y

A.6 or 6.B.12 or 12.

C.6.D.12.

4.The graph of andmeet at A and B. Which of thefollowing equations has the x-coordinates of A and B as its roots?

A.B.

C.D.

5.Find the area of AOBin the figure.

A.3B.6

C.9D.15

6.In the figure, . FindBAC.

A.36B.54

C.72D.90

7.In the figure, chords AC and BD intersect at E. Find.

A.90B.180

C.225D.360

8.In the figure, O is the centre of the circle andBOC 50. Findxy.

A.25B.30

C.45D.50

9.In the figure, Ois the centre of the semi-circle. Diameter AE and chord BC are produced to meet at D. If BABC and BAC40, findx.

A.10B.20

C.25D.30

10.In the figure, two circles intersect at B and E.ABC is a straight line. If AFE60, findCDE.

A.100B.120

C.140D.Undetermined

11.In the figure, ABC, AFD, EDC and EFB are straight lines. FAB 40 and FED 30. FindDFB.

A.95B.120

C.125D.140

12.In the figure, DBE 70, BCDx and BAEy. Findxy.

A.110B.220

C.240D.250

13.In the figure, AB, BC and CA are tangents to the circle at D, E and F respectively. If the perimeter of ABC is 40 cm and AB12cm, find the length of CE.

A.6 cmB.7 cm

C.8 cmD.9 cm

14.In the figure, O is the centre of the circle.ED is the tangent to the circle at A. BOCE is a straight line. If BAD 66, findBED.

A.24B.33

C.36D.42

15.

In the figure, PQ is a common tangent to the circles with centres at H and K. If HK = 5, PH = 1 and QK = 2, then PQ =

A. .B. .

C. .D. .

16.

Which of the following pairs of triangles in the figure is NOT similar?

A.PQH,SRHB.PRK,QSK

C.PQK,RSKD.none of the above

17.If and , then

A. .B. .

C. .D. .

18.In the figure

A.B.

C.D.

19.On which of the following intervals is ?

A.B.

C.D.

20.

A.B.

C.D.

21.

A.B.

C.D.

22.Which of the following is a sketch of for ?

A.B.

C.D.

23.The greatest value of is

A.B.

C.D.

24.

In the figure, find correct to the nearest 0.1 degree.

A.B.

C.D.

25.

In the figure, the bearing of B from O is N30E. What is the bearing of B from A?

A.B.

C.D.

26.

A rectangular card, 8 cm 15 cm, is put on a corner of a book as shown. If DF = 12cm, DE = ?

A.3.6 cm .B.4.8 cm .

C.5 cm .D.6.4 cm .

27.In the figure, BCD is a straight line. What is the relation of the lengths of AC, BC and CD?

A.AC > BC > CDB.BCAC > CD

C.BCCDACD.CDACBC

28.

In the figure, BT is a vertical building standing on the level ground ABC, and ABC = 90. If the angles of elevation of T from A and C are 30 and 60 respectively, find tan.

A.B.

C.D.

29.In the figure,ABCDEFGH is a cuboid, M is the mid-point of BC. Find the inclination of HM to the plane ABCD correct to the nearest degree.

A.B.

C.D.

30.The figure shows a right pyramid with a square base ABCD. Let  be the angle between a lateral face and the base. Find cos

A.B.

C.D.

31.

The greatest slope of a hill is  A path is made on its surface and makes an angle  with the line of greatest slope. The angle of inclination  of the path is given by

A. .B. .

C. .D. .

32.If x : y = 4 : 5, then

A. .B. .

C. .D. .

33.If and , then

A. .B. .

C. .D. .

34.Which of the following equations shows that x and y are in direct variation?

A.B.

C.D.

35.

A.B.

C.D.

36.Find the vertex of the graph of .

A.B.

C.D.

37.Find the remainder when is divided by .

A.B.

C.D.

38.If is divisible by , then itis also divisible by

A. .B. .

C. .D. .

39.If , then

A.B.

C.D.

40.Simplify .

A.B.

C.D.

…End of Paper…
Answer

1