1

QUEEN’S COLLEGEYearly Examination, 2010-2011Mathematics Paper II

Secondary 5 Date: 23 June, 2011. Time: 8:30-9:30

Full Marks: 80

1. Write down the information required in the spaces provided on 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 provided.

4. You should mark only ONE answer for each question. Two or more answers will score no

marks.

5. There are 40 questions in this paper. All questions carry equal marks.

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

1. Which of the following graphs shows that y is

partly constant and partly varies directly as x?

A. B.

C. D.

2. Suppose (2x – y) (x + y). Which of the following

is true?

A. y x

B. y

C. y x2

D. y

3. The following table shows several pairs of

x and y.

x 1 2 4 6

y 3 12 48 108

Which of the following is true?

A. y x

B. y

C. y xD. y (x + 1)

4. Find the minimum value of k

such that the simultaneous

equations

have real solutions.

A. –10

B. 10

C. –5D. 5

5. Which of the following points

lie(s) inside the circle C : x2 + y2

+ 4x + 16y + 28 = 0?

I. P(0, 14)

II. Q(4,2)

III. R(3, 4)

IV. S(4, 2)

A. II only

B. III only

C. II and III only

D. I and IV only

6. In the figure, the graph of y =

g(x) is obtained by translating

the graph of y = x2 – 2x in the

direction of the x-axis. If A(0, 3)

lies on the graph of y = g(x),

find the symbolic representation

2

of g(x).

A. g(x) = x2 – 1

B. g(x) = x2 + 4x + 3

C. g(x) = x2 – 8x + 15

D. g(x) = x2 – 4x + 3

7. Solve .

A. x = 2

B. x = 3C. x =

D. x =

8.

In the figure, the circle touches the y-axis,

the equation of the circle is

A. x2 + y2 + 14x + 12y – 36 = 0.

B. x2 + y2 – 14x – 12y + 36 = 0.

C. x2 + y2 + 7x – 6y + 18 = 0.

D. x2 + y2 – 7x + 6y – 18 = 0.

9. An insect crawls on the inner surface of a

cylindrical plastic bottle from point A to point B with the shortest path.

The plastic bottle is cut and unfolded

as a flat surface. Which of the

following figures shows the locus of

the insect?

A. B.

C. D.

10. A shopkeeper has 10 keys,

only one of which can open

the shop. If the keys are

chosen at random one by one

without repetition, find the

probability that he can open

the door in less than 3 trials.

A.

3

B.

C.

D.

11.

The equations of lines L1 and L2 are y =

–1 and x = 1 respectively. A moving

point P(x , y) maintains an equal

distance from L1 and L2. Which of the

following is the equation of the locus of

P?

I. x – y = 0

II. x + y = 0

III. x – y = 2

A. II only

B. III only

C. I and III only

D. II and III only

12. Which of the following box-and-whisker

diagrams may represent the data 17, 13, 19, 21,

17, 23?

A.

B.

C.

D.

13. In the figure, ,

, BD bisects .

A. .

B. .

C. .

D. .

14.

4

Find ∠PSR.

A. 79.6, cor. to 3 sig. fig.

B. 82.3, cor. to 3 sig. fig.

C. 84.8, cor. to 3 sig. fig.

D. 90

15.

In the figure, AB is a flagpole with

height 10 m vertically erected on an

inclined plane with an inclination of 15.

Given that the angle between sun rays

and the horizontal plane is 65, find the

length of the shadow BF, correct to 3

significant figures.

A. 4.29 m

B. 4.66 m

C. 5.52 m

D. 7.09 m

16.

In the figure, the bearings of B and C

from A are 140 and 200

respectively, and the bearing of C

from B is 245. Given that B and C

are 10 km apart, find the distance

between A and C, correct to 3

significant figures.

A. 9.43 km

B. 9.73 km

C. 11.2 km

D. 12.0 km

17.

In the figure, VABCD is a pyramid

whose base is a rectangle. M is the

mid-point of AB and VM is

perpendicular to the plane ABCD.

Given that AB = 10 cm, BC = 6 cm and

VM = 8 cm, find the angle between VC

and the plane ABCD, correct to the

nearest degree.

A. 44

5

B. 46

C. 58

D. 61

18.

B

35 cm

A

DC

F

15 cm

15 cm

E

The dimension of a card is 15 cm 35 cm. When two identical cards stand on a table as shown in the diagram, the angle between them is

. Calculate the angle between plane FAD and the table. A. 63.6B. 66.6 C. 69.6D. 72.6

19.

The figure shows the cumulative

frequency curve of two data sets, A and B.

Which of the following must be correct?

I. Median of A > median of B.

II. Range of A > range of B.

III. Inter-quartile range of A = inter-

quartile

range of B.

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

20. The mean and the standard deviation of

the lengths of the rolls of toilet paper

of a brand are 2 400 cm and 17.2 cm

respectively. If the lengths of the rolls

of toilet paper of this brand are

normally distributed, find the

percentage of the rolls of toilet paper

with lengths less than 2 365.6 cm.

(Assume that in a normal distribution,

68%, 95% and 99.7% of the data lie

within one, two and three standard

deviations respectively from the mean.)

A. 2.35%

B. 2.5%

C. 97.5%

D. 100%

21. Given two groups of numbers:

Group A: a + 1, a + 2, a + 3

Group B: b + 1, b + 2, b + 3

where m1 and m2 are the means of the

group A and B respectively, s1 and s2

are the standard deviations of group A

and B respectively. If a > b, which of

the following is true ?

A. and

B. and C. and

D. and

22. Suppose z varies jointly as x and

the square root of y. If x increases by

6

8% and y decreases by 19%, find the percentage

change of z.

A. Decreased by 2.8%

B. Decreased by 7.2%

C. Decreased by 11%

D. Decreased by 10.2%

23. Suppose y varies directly as x. Which of

the following must be true?

I. y will be increased by 10 when x is

increased by 10.

II. y will be decreased by 10% if x is

decreased by 10%. III. y varies directly as x .

A. II only

B. I and II only

C. II and III only

D. I, II and III

24. In the figure, the circle C : x2 + y2 8x 6y

+ 12 = 0 and the straight line L intersect at

A and B. If the straight line L divides the

circle C into two equal parts, find the

equation of L.

A.

B.

C.

D.

25. If the straight line y = mx + 6 is a

tangent to the circle x2 + y2 = 12,

find the possible values of m. A. or B. or

C. or

D. or

26. In the figure, C is a moving point.

OACB is a quadrilateral. Which of the

following dotted lines shows the locus

of C such that the area of OACB is

fixed?

A. B.

C. D.

27.

7

G(0 , 3) and H(5 , 0) are two points in a

rectangular coordinate plane. Point P(x , y) moves

such that PG PH. Find the equation of the locus

of P.

A. 3x + 5y – 15 = 0

B. 5x – 3y – 8 = 0

C. x2 + y2 – 5x – 3y = 0

D. x2 + y2 – 10x – 6y = 028.

Find ∠CDA.

A. 77.4, cor. to 3 sig. fig.

B. 77.6, cor. to 3 sig. fig.

C. 78

D. 78.2, cor. to 3 sig. fig.

29.

In the figure, ABD is a triangle. Find ,

correct to 3 significant figures.

A. 50.6

B. 52.0

C. 54.9

D. 58.1

30.

In the figure, ABCDEFGH is a cube

and the diagonals BE and CF

intersect at X. If ∠BXC = , find

.

A.

B.

C.

D.

31. The box-and whisker diagram shows

the marks distribution of students in

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Chinese and English examination.

From the diagram above, which of the following

are correct?

I. The ranges of marks of the students in

both examinations are the same.

II. The inter-quartile range of marks of the

students in Chinese examination is less

than that of English examination.

III. The median mark of the students in

Chinese examination is higher than that in

English examination

A. I and II only

B. II and III only

C. I and III only

D. I, II and III

32. Wai Ming scores p in a singing contest.

Given that the mean mark of the contest

is 65, the standard deviation is 6.2 while

his standard score is –1.4. Find the value

of p, correct to the nearest integer.

A. 52

B. 56

C. 66

D. 74

33. It is given that the data 50, 69, a, 101, 129,

b, and 133 are arranged in ascending

order. Their mean is 98 and their standard

deviation is c, where a, b and c are

constants. If the datum 101 is deleted,

which of the following must be correct?

I. New mean < 98

II. New standard deviation < c

III. New range = 83

A. I only

B. III only

C. I and II only

D. I and III only

34. The figure shows the histograms of three frequency distributions. Arrange their standard deviations in ascending order of magnitude.

(1) (2) (3)

(3)

A. (1), (2), (3) B. (1), (3),

(2)

C. (2), (1), (3) D. (3), (2),

(1)

9

x

Frequency

x

Frequency

x

Frequency

35.

In the figure, the circle passes through O(0 , 0),

P(0 , 3) and Q(–4 , 0) with the centre R. Which

of the following must be correct?

I. The coordinates of the centre are (–2 , 1.5).

II. R lies on the straight line .

III. OR is perpendicular to PQ.

A. I only

B. I and II only

C. I and III only

D. II and III only

36.

100

D

5 cm

A

B

C

12 cm 30

A tetrahedron ABCD with A, B and C on the horizontal plane and D vertically above A has volume of

Given that AB = 12 cm, AD

= 5 cm, and

calculate BDC.

A.

B.

C.

D.

37. The mean, the range and the

inter-quartile range of a set of

data are x, y and z respectively.

If each datum is first multiplied

by 4 and 3 is then added to

each, find the new mean, range

and inter-quartile range.

Mean Range Inter-

quartile range

A. 4x + 3 4y 4z

B. 3y – 4 4z + 3

C. 4x + 3 4z

+ 3

D. 3x + 4 y z

38. F(k , 0) is a point on the x-axis.

When the point P(x , y) moves, it

maintains an equal distance from

point F and the y-axis. If the

equation of the locus of P is y2 =

4x – 4, find k.

A. 0

B. 1

C. 2

D. 4

39.

10

In the figure, a triangular board ABC

stands vertically on the horizontal ground

along the east-west direction. F is a point on BC such that AF BC, where BC = 3

m, AF = 1 m. When the sun shines from

N40W with an angle of elevation 25, the

shadow of the board on the horizontal

ground is △BDC. Find the area of the

shadow △BDC, correct to 3 significant

figures.

A. 2.07 m2

B. 2.46 m2

C. 2.72 m2

D. 3.22 m2

40.

LA

C By

x

N

M

In right-angled ,

.

A moving line L cuts AB and BC at M and N

respectively. It is given that

area of (area of

).

Find the minimum value of MN.

A. 2

B. 3

C. 4

D. 5

END OF PAPER

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QUEEN’S COLLEGEYearly Examination, 2010-2011

Form 5 Mathematics Paper IIAnswer Sheet

QuestionNumber A B C D

QuestionNumber A B C D

1 √ 21 √

2 √ 22 √

3 √ 23 √

4 √ 24 √

5 √ 25 √

6 √ 26 √

7 √ 27 √

8 √ 28 √

9 √ 29 √

10 √ 30 √

11 √ 31 √

12 √ 32 √

13 √ 33 √

14 √ 34 √ √

15 √ 35 √

16 √ 36 √

17 √ 37 √

18 √ 38 √

19 √ 39 √

20 √ 40 √