QUEEN S COLLEGE. Yearly Examination, Mathematics Paper II. Secondary 5 Date: 23 June, Time: 8:30-9:30 Full Marks: 80

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1 QUEEN S COLLEGE Yearly Examination, 00-0 Mathematics Paper II Secondary 5 Date: June, 0. Time: 8:0-9:0 Full Marks: 80. Write down the information required in the spaces provided on the Answer Sheet.. 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.. 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.

2 . Which of the following graphs shows that y is partly constant and partly varies directly as x? A. 4. Find the minimum value of k such that the simultaneous equations real solutions. A. 0 0 C. 5 D. 5 y 5x k y x have C. D. 5. Which of the following points lie(s) inside the circle C : x + y + 4x + 6y + 8 = 0? I. P(0, 4) II. Q( 4,) III. R(, 4) IV. S( 4, ). Suppose (x y) (x + y). Which of the following is true? A. y x y x C. y x D. y x. The following table shows several pairs of x and y. A. II only 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 = x x in the direction of the x-axis. If A(0, ) lies on the graph of y = g(x), find the symbolic representation of g(x). x 4 6 y Which of the following is true? A. y x y x C. y x D. y (x + ) A. g(x) = x g(x) = x + 4x + C. g(x) = x 8x + 5 D. g(x) = x 4x +

3 7. Solve log ( x ) log ( x ). A. x = x = C. x = or D. x = or C. D. 8. In the figure, the circle touches the y-axis, the equation of the circle is A. x + y + 4x + y 6 = 0. x + y 4x y + 6 = 0. C. x + y + 7x 6y + 8 = 0. D. x + y 7x + 6y 8 = A shopkeeper has 0 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 trials. A. C. D 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. The equations of lines L and L are y = and x = respectively. A moving point P(x, y) maintains an equal distance from L and L. Which of the following is the equation of the locus of P? I. x y = 0 II. x + y = 0 III. x y = A. II only III only C. I and III only D. II and III only

4 . Which of the following box-and-whisker diagrams may represent the data 7,, 9,, 7,? A. 4. C. Find PSR. A. 79.6, cor. to sig. fig. 8., cor. to sig. fig. C. 84.8, cor. to sig. fig. D. 90 D. 5.. In the figure, BAD 45, BCD 0, BD bisects ABC. AD : CD In the figure, AB is a flagpole with height 0 m vertically erected on an inclined plane with an inclination of 5. Given that the angle between sun rays and the horizontal plane is 65, find the length of the shadow BF, correct to significant figures. A. :. :. C. :. D. :. A. 4.9 m 4.66 m C. 5.5 m D m 4

5 6. 8. A B E 5 cm C 5 cm D 5 cm F In the figure, the bearings of B and C from A are 40 and 00 respectively, and the bearing of C from B is 45. Given that B and C are 0 km apart, find the distance between A and C, correct to significant figures. The dimension of a card is 5 cm 5 cm. When two identical cards stand on a table as shown in the diagram, the angle between them is 60. Calculate the angle between plane FAD and the table. A. 9.4 km 9.7 km C.. km D..0 km A C D 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 = 0 cm, BC = 6 cm and VM = 8 cm, find the angle between VC and the plane ABCD, correct to the nearest degree. The figure shows the cumulative frequency curve of two data sets, A and Which of the following must be correct? I. Median of A > median of II. Range of A > range of III. Inter-quartile range of A = inter-quartile A C. 58 D. 6 range of A. I and II only I and III only C. II and III only D. I, II and III 5

6 0. The mean and the standard deviation of the lengths of the rolls of toilet paper of a brand are 400 cm and 7. 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 65.6 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..5%.5% C. 97.5% D. 00%. Given two groups of numbers: Group A: a +, a +, a + Group B: b +, b +, b + where m and m are the means of the group A and B respectively, s and s are the standard deviations of group A and B respectively. If a > b, which of the following is true? A. m m and s s m m and s s C. m m and s s D. m m and s s. Suppose z varies jointly as x and the square root of y. If x increases by 8% and y decreases by 9%, find the percentage change of z. A. Decreased by.8% Decreased by 7.% C. Decreased by % D. Decreased by 0.%. Suppose y varies directly as x. Which of the following must be true? I. y will be increased by 0 when x is II. increased by 0. y will be decreased by 0% if x is decreased by 0%. III. y varies directly as x. A. II only I and II only C. II and III only D. I, II and III 4. In the figure, the circle C : x + y 8x 6y + = 0 and the straight line L intersect at A and If the straight line L divides the circle C into two equal parts, find the equation of L. A. y x y x C. y x D. y x 5. If the straight line y = mx + 6 is a tangent to the circle x + y =, find the possible values of m. A. or or C. D. or or 6

7 6. 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? 8. Find CDA. A. A. 77.4, cor. to sig. fig. 77.6, cor. to sig. fig. C. 78 D. 78., cor. to sig. fig. 9. C. D. 7. In the figure, ABD is a triangle. Find, correct to significant figures. A C D. 58. G(0, ) 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. x + 5y 5 = 0 5x y 8 = 0 C. x + y 5x y = 0 D. x + y 0x 6y = 0 7

8 0. A. I and II only II and III only C. I and III only D. I, II and III In the figure, ABCDEFGH is a cube and the diagonals BE and CF intersect at X. If BXC =, find A. C. D. sin.. The box-and whisker diagram shows the marks distribution of students in Chinese and English examination.. Wai Ming scores p in a singing contest. Given that the mean mark of the contest is 65, the standard deviation is 6. while his standard score is.4. Find the value of p, correct to the nearest integer. A C. 66 D. 74. It is given that the data 50, 69, a, 0, 9, b, and 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 0 is deleted, which of the following must be correct? I. New mean < 98 II. New standard deviation < c III. New range = 8 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 only III only C. I and II only D. I and III only 8

9 4. The figure shows the histograms of three 6. frequency distributions. Arrange their standard deviations in ascending order of magnitude. () Frequency () Frequency () cm 0 D 5 cm A B 00 () Frequency x x C A tetrahedron ABCD with A, B and C on the horizontal plane and D vertically above A has volume of V cm. Given that AB = cm, AD = 5 cm, ABC 00 and BAC 0, x calculate BDC. 5. A. (), (), () (), (), () C. (), (), () D. (), (), () A. 8 8 C. 48 D. 58 In the figure, the circle passes through O(0, 0), P(0, ) and Q( 4, 0) with the centre R. Which of the following must be correct? I. The coordinates of the centre are (,.5). x y II. R lies on the straight line. 4 III. OR is perpendicular to PQ. 7. 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 is then added to each, find the new mean, range and inter-quartile range. Mean Range Inter-quartile range A. 4x + 4y 4z x 4 C. 4x + y 4 4z + y 4 4z + D. x + 4 y z A. I only I and II only C. I and III only D. II and III only 9

10 8. 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 y = 4x 4, find k. A. 0 C. D A C In right-angled N ABC, ACB 90, AC and BC 4. A moving line L cuts AB and BC at M and N respectively. It is given that area of BMN (area of ABC ). Find the minimum value of MN. M L y x B A. C. 4 D. 5 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 = m, AF = m. When the sun shines from N40 W with an angle of elevation 5, the shadow of the board on the horizontal ground is BDC. Find the area of the shadow BDC, correct to significant figures. END OF PAPER A..07 m.46 m C..7 m D.. m 0

11 QUEEN S COLLEGE Yearly Examination, 00-0 Form 5 Mathematics Paper II Answer Sheet Question Number A B C D Question Number A B C D