QUEEN’S COLLEGE
Yearly Examination, 2008-2009
Mathematics II
Date: 26-6-2009
Secondary 4 Time:11:30-12:30
Instructions:
- Answer ALL questions on the answer sheet.
- You should mark only ONE answer to each question. Two or more answers will score no marks.
- Each question carries 2 marks. No marks will be deducted for wrong answers.
- 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, . FindBAC.
A.36B.54
C.72D.90
7.In the figure, chords AC and BD intersect at E. Find.
A.90B.180
C.225D.360
8.In the figure, O is the centre of the circle andBOC 50. Findxy.
A.25B.30
C.45D.50
9.In the figure, Ois the centre of the semi-circle. Diameter AE and chord BC are produced to meet at D. If BABC and BAC40, findx.
A.10B.20
C.25D.30
10.In the figure, two circles intersect at B and E.ABC is a straight line. If AFE60, findCDE.
A.100B.120
C.140D.Undetermined
11.In the figure, ABC, AFD, EDC and EFB are straight lines. FAB 40 and FED 30. FindDFB.
A.95B.120
C.125D.140
12.In the figure, DBE 70, BCDx and BAEy. Findxy.
A.110B.220
C.240D.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 AB12cm, 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, findBED.
A.24B.33
C.36D.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 N30E. 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
2 / C / 22 / C
3 / D / 23 / B
4 / D / 24 / B
5 / A / 25 / D
6 / B / 26 / B
7 / B / 27 / B
8 / A / 28 / A
9 / D / 29 / C
10 / B / 30 / A
11 / C / 31 / A
12 / D / 32 / A
13 / C / 33 / D
14 / D / 34 / B
15 / D / 35 / D
16 / D / 36 / B
17 / A / 37 / A
18 / A / 38 / B
19 / D / 39 / C
20 / A / 40 / A
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