Yearly Examination, 2008-2009

QUEEN’S COLLEGE

YEARLY EXAMINATION, 2008-2009

MATHEMATICS PAPER II

Secondary: / 3 / Date: / 22THJune, 2009
Time: / 8:30 – 9:30 (1 hour)

INSTRUCTIONS

Answer all questions. You should mark all your answers on the MC Answer Sheet.
You should mark only ONE answer for each question. If you mark more than one answer, you will receive NO MARKS for that question.
Total Score of this paper II is 80 marks.
Calculator is allowed to be used.

DO NOT TURN OVER THIS QUESTION BOOK

UNTIL YOU ARE TOLD TO DO SO

1.Factorizey5 + 27y2.

A.y2( y+ 3)3

B.y2( y+ 3)(y23y +9)

C.y2( y+ 3)(y2+3y +9)

D.( y+ 3)(y23y +9)

2. Which of the following is NOT a factor of ?

A.5

B.m– 7

C.m + 7

D.m– 8

3.Which of the following is / are factor(s) of ?

I.3II.x– 4 III.x + 4

A.I onlyB.I and II onlyC.I and III onlyD. All of them

4.Which of the following is/are a surd (surds)?

I.II.III.

A.I onlyB.II onlyC.I and II onlyD. III only

5.Simplify.

A.B.C.D.

6.Simplify.

A.B.C.2D.–2

7.The total storage capacity of Hong Kong’s reservoirs is 586 000 000 m3. Express the capacity in scientific notation, correct to 2 significant figures.

A.B. C.D.

8.BCDEF5016 =

A.11(166) + 12(165) +13(164) + 14(163) +15(162) + 516

B.11(167) + 12(166) +13(165) + 14(164) +15(163) + 5162

C.10(166) + 11(165) +12(164) + 13(163) +14(162) + 516

D.10(167) + 11(166) +12(165) + 13(164) +14(163) + 5162

9.Mrs. Wu is paid by the hour as a translator. Her hourly wage is increased by 15% but due to pregnancy, she has to reduce her working hours in a week by 20%. What is the percentage change in her weekly income?

A.+108%B.+92%C.–5%D.–8%

10.Mr. Chan deposits a sum of money in a bank at an interest rate of 10% p.a. compounded half yearly. The expected amount after 2 years is $38 896.2. If Mr. Chan takes out all the money afteryears, how much does he get?

A.$32 000B.$33 600C.$35 280D.$37 044

11.If and c is a positive integer, which of the following is true?

B.ac2 bc2

C.a(5 –c)b(5 –c)

12.If and , then

A.B.C.D.

13.Two numbers are randomly drawn at the same time from 3 cards numbered 2, 3 and 4 to form a two-digit number. Find the probability of the two-digit number is a multiple of 3.

A.B.C.D.

14.John tosses three $10 coins. If he is allowed to take away those coins with head showing up, the expected amount of money that he can get is

A.$9

B.$10

C.$12

D.$15

15.The centre of the circumcircle of a triangle is the point of intersection of all the

A.angle bisectors.

B.perpendicular bisectors.

C.altitudes.

D.medians.

16.In the figure, O is the centroid of ABC, BP = 3cm, QC = 4cm and AP = 6cm. Find the perimeter of APC.

A.13cm

B.17cm

C.18cm

D.26cm

17. Joining the mid-points of the four sides of any quadrilateral must form a

A.parallelogram.

B.rhombus.

C.rectangle.

D.square.

18.In the figure, ADB,BEC and CFA are straight lines,ABC and DEF are equilateral triangles. Which of the following must be true?

II.

III.

A.I onlyB.I and II onlyC.I and IIIonly D.I, II and III

19.The figure shows a square. Find the perimeter of the square.

A.180

B.150

C.45

D.15

20.If AB = BC, AF = 5 cm and EB = 3 cm, find DC.

A.5 cm

B.7 cm

C.11 cm

D.13 cm

21.In the figure,ABCD is a trapezium. Find x.

A.50.

B.60.

C.70.

D.80.

22. In the figure, find the length of BD.

A.4

C.6

23.From the 2-D views provided below, find the corresponding solid.

24.In the figure, ABCDEFGH is a cube. Which of the following is not a right angle?

A.ECB

B.FDC

C.GAE

D.HEA

25.The number of faces and the number of edges of a polyhedron are 7 and 15 respectively. Find the number of its vertices.

A.8

B.9

C.10

D.11

26.In the figure, the plane passing through B and C is parallel to the base of the cone. AMN is the height of the cone. If AM:MN = 3:2, what is the ratio of the curve surface area of the cone ABC to thecurve surface area of the frustum BCED?

A.9:25

B.9:16

C.4:9

D.4:5

27.In the figure, the sector is rolled up to form a right circular cone, find the base radius of the cone.

A.3cm

B.4cm

C.5cm

D.6cm

28.Two identical hemispheres of radius 2cm are combined to form a sphere. Find the percentage change in the surface area.

A.0

C.–50%

D.+50%

29.The base of a right pyramid is a square. If the total surface area of the pyramid is 420cm2and the area of one of its lateral faces is 56cm2, find the base area of the pyramid.

A.84cm2

B.105cm2

C.196cm2

D.364cm2

30.In the figure, Q is a point on the y-axis, find AQ : QB.

A.2 : 1

B.2 : 3

C.3 : 2

D.–2 :1

31.Two points A (a1,a2) and B (b1, b2) are given. The slope of AB is

32.Which of the following points lies on the line joining (1, –2) and (–2, 7)?

A.(–1, 4)

B.(0, –1)

C.(3, –9)

D.(2, 5)

33.If M(3, a) is the mid-point of the line segment joining P(7, 3) and Q(b, –9), find the

values a and b.

A.a = –3, b = –1

B.a = –1, b = –3

C.a = –6, b = 5

D.a = –3, b = 2

34.P (–1, 4),Q (3, 2) and R (0, –4) are the vertices of a triangle. Which of the following is true?

A.Slope of PQ is the largest among the sides of PQR.

B.PQR is a right-angled triangle.

C.PQR is a right-angled isosceles triangle.

D.QR is the longest side of PQR.

35.In the figure, the map of a hill with a scale of 1:20 000. If the distance between point AB is 1cm on the map, find the gradient of AB.

36.If the compass bearing of B from A is N32E, then the true bearing of A from B is

A.32.

B.148.

C.212.

D.328

37.Which of the following figures best represents the graph where and ?

38.The angles of depression of boats B and C from Mandy on top of a 160m cliff are 33and 24 respectively. Find the distance between the two boats. ( Correct your answer to the nearest 0.1m.)

A.32.7m

B.112.9m

C.113.0m

D.605.7m

39.The equation of a straight line L is. If y-intercept of L is 4, find the slope of L.

A.–3

B.–

40.In the figure, OABC is a parallelogram. O is the origin. A and C are the points (3 , 6) and (7 , 4) respectively. Find the equation of OB.

A.x 2y = 0

B.xy = 0

C.x + 2y = 0

D.2xy = 0

End of Paper

Answers

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

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