MATHEMATICS Compulsory Part PAPER 2

Transcription

1 015-DSE MATH CP PAPER LONGMAN MATHEMATICS SERIES HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 015 MOCK PAPER MATHEMATICS Compulsory Part PAPER Time allowed: 1 hour 15 minutes INSTRUCTIONS 1 Read carefully the instructions on the Answer Sheet After the announcement of the start of the examination, you should first write the information required in the spaces provided When told to open this book, you should check that all the questions are there Look for the words END OF PAPER after the last question 3 All questions carry equal marks 4 ANSWER ALL QUESTIONS You are advised to use an HB pencil to mark all the answers on the Answer Sheet, so that wrong marks can be completely erased with a clean rubber You must mark the answers clearly; otherwise you will lose marks if the answers cannot be captured 5 You should mark only ONE answer for each question If you mark more than one answer, you will receive NO MARKS for that question 6 No marks will be deduced for wrong answers 015-DSE-MATH-CP -1 Pearson Education Asia Limited 014

2 There are 30 questions in Section A and 15 questions in Section B The diagrams in this paper are not necessarily drawn to scale Choose the best answer for each question Section A n 1 (3 9 1 ) = A B C D 4 3 n n 9 n + 9 n x 4xy + 4y 4 = A ( x + y + )( x + y ) B ( x y + )( x y ) C ( x + y + )( x + y ) D ( x y + )( x y ) 3 If p and q are constants such that px( x ) + x qx( x + ) 6x, then p = A 1 B 1 C D 5 4 Let k be a constant If the quadratic equation 3x 4kx + 6k = 0 has equal roots, then k = A B 9 9 C 0 or D 0 or DSE-MATH-CP - Pearson Education Asia Limited 014

3 5 The figure shows the graph of the following is true? A a > 0 and b > 0 B a > 0 and b < 0 C a < 0 and b > 0 D a < 0 and b < 0 y 1 a x + b = ( ), where a and b are constants Which of 6 If c < 0 < b < a, which of the following must be true? I a c > b c II b > c III ac < bc A I only B II only C I and III only D II and III only 7 The solution of 5 x < < 4x is 3 A 1 x > 6 B x > 15 C 1 < x < 15 6 D 1 x < or x > Let f(x) = 8x 3 4x + k, where k is a constant If f(x) is divisible by x 1, find the remainder when f(x) is divided by x + 1 A B 1 C D DSE-MATH-CP -3 Pearson Education Asia Limited 014

4 9 A sum of $0 000 is deposited at an interest rate of 4% per annum for 5 years, compounded monthly Find the total amount received after 5 years correct to the nearest dollar A $4 000 B $4 333 C $4 403 D $ In the figure, the 1st pattern consists of 4 dots For any positive integer n, the (n + 1)th pattern is formed by adding (n + 4) dots to the nth pattern Find the number of dots in the 7th pattern A 40 B 54 C 64 D The scale of a map is 1 : 4000 If the area of a pond on the map is 5 cm, then the actual area of the pond is A 10 m B 1000 m C m D km 015-DSE-MATH-CP -4 Pearson Education Asia Limited 014

5 = A (correct to 3 decimal places) B (correct to 3 significant figures) C (correct to 5 decimal places) D (correct to 5 significant figures) 13 A bottle of soft drink is poured into 10 small cups such that the volume of each cup is measured 50 ml correct to the nearest ml Find the least possible volume of the bottle of soft drink A 490 ml B 495 ml C 499 ml D 500 ml 14 It is given that y varies jointly as the square of x and the square root of z If x is decreased by 0% and y is decreased by 0%, then z A is increased by 0% B is increased by 565% C is decreased by 36% D is decreased by 43% 15 In the figure, ABCD is a trapezium with AB = AD, ABC = 90 and BCD = 45 If CD = 10 cm, then the area of trapezium ABCD = A 75 cm B 100 cm C 15 cm D 150 cm 015-DSE-MATH-CP -5 Pearson Education Asia Limited 014

6 16 In the figure, OA = OB and the bearing of B from O is S5 W A is due west of O Find the bearing of B from A A S1 E B S19 E C N19 W D N1 W 17 In the figure, the solid consists of a right circular cone and a hemisphere with a common base If the volume of the cone is twice the volume of the hemisphere, find the ratio of the height to the base radius of the cone A 4 : 1 B : 1 C 1 : D 1 : 4 18 In the figure, ABCD is a parallelogram E is a point lying on AD BE and AC intersect at F It is given that AE : ED = : 1 and area of AEF = 8 cm Find the area of CDE A 8 cm B 10 cm C 13 cm D 15 cm 015-DSE-MATH-CP -6 Pearson Education Asia Limited 014

7 CD 19 In the figure, D is a point lying on AB If BDC = ACB = 90, then = AB A sin α sin β B sin α cos β C D sinα sin β cosα cos β sin (180 + θ ) 0 = sin(70 + θ ) + 1 A 1 cosθ B 1 cosθ C 1+ cosθ D 1+ cosθ 1 In the figure, BC is the diameter of the semicircle BAC If ABC = 30 and AB =1 cm, then the area of the shaded region is A B C D ( 8 π 1 3)cm ( 8 + π 1 3) cm ( 16 π 1 3)cm ( 16 + π 1 3)cm 015-DSE-MATH-CP -7 Pearson Education Asia Limited 014

8 In the figure, AE is a diameter of the circle ABCDE If ACB = 30, then EAB = A 50 B 55 C 60 D 70 3 If an interior angle of a regular n-sided polygon is 5 times an exterior angle of the polygon, which of the following statements about the polygon is/are true? I It is a 10-sided polygon II Each interior angle is 150 III It s order of rotational symmetry is 1 A I only B II only C I and III only D II and III only 4 The polar coordinates of the point P are (, 40 ) If P is rotated clockwise about the pole through 90, then the rectangular coordinates of its image are A ( 1, 3) B ( 1, 3) C ( 3, 1) D ( 3, 1) 015-DSE-MATH-CP -8 Pearson Education Asia Limited 014

9 5 The coordinates of the points A and B are (4, 9) and (, 1) respectively Let P be a moving point on the rectangular coordinate plane such that AP = PB Find the equation of the locus of P A x + y + x + 10y + 1 = 0 B x + y x 10y + 1 = 0 C 3 x + 4y 3 = 0 D 3 x 4y + 17 = 0 6 In the figure, the equations of the straight lines L1 and L are x + Ay = B and x + Cy = D respectively They are perpendicular to each other and intersect at a point on the positive y-axis Which of the following are true? I A > 0 II AC = 1 III B > D A I and II only B I and III only C II and III only D I, II and III 7 Let k be a real constant Which of the following may represent the graph of the circle x + y + 6x + ky 11 = 0? A B C D 015-DSE-MATH-CP -9 Pearson Education Asia Limited 014

10 8 Two fair dice are thrown Find the probability that the sum of these two numbers is not greater than 4 A B C D The following table shows the distribution of the number of children in the families living in a building Number of children Number of families Find the median of the number of children in the families A 1 B 16 C 15 D 30 The stem-and-leaf diagram below shows the distribution of the waiting times (in minutes) of some customers in a bank Stem (tens) Leaf (units) 0 a b If the mean and the range of the above distribution are 1 and r respectively, which of the following statement(s) is/are true? I a 4 II 1 b 3 III 19 r 3 A I only B II only C I and III only D II and III only 015-DSE-MATH-CP -10 Pearson Education Asia Limited 014

11 Section B 31 The HCF and the LCM of three expressions are If the first and the second expressions are third expression is A B C D x y 3 z 8 3 xy 3 z x y 9 z 8 3 xy 9 z 3 x and 3 y 3 xy and x y respectively 9 z 5 5 x y z respectively, then the 3 The graph in the figure shows the linear relation between log x and log y 7 7 b y = ax, then If A 1 1 a = and b = 7 B 1 1 a = and b = 7 C 1 1 a = and b = 7 D a = 7 and b = = A B C D DSE-MATH-CP -11 Pearson Education Asia Limited 014

12 34 If α β and A 18 B 0 C 6 D 7 α 3α + 1 = 0, then α 3 + β 3 = β 3β + 1 = 0 35 If k is a positive real number, then the imaginary part of A k + 4 B k 4 C k + D k 5k + 10i 1 i is 36 The figure shows the graph of y = f(x) If f(x) = g(x), which of the following may represent the graph of y = g(x)? A B C D 015-DSE-MATH-CP -1 Pearson Education Asia Limited 014

13 37 Consider the following system of inequalities: x 4 y 1 3x y 3 x 5y Let E be the region which represents the solution of the above system of inequalities If (x, y) is a point lying in E, then the greatest value of y 4x + 0 is A 5 B 7 C 0 D 4 38 The sum of the first n terms of an arithmetic sequence is n(n 1) Which of the following is/are true? I 1 is a term of the sequence II The common difference of the sequence is III The general term of the sequence is n 4 A I only B II only C I and III only D II and III only 39 For 0 x 360, how many roots does the equation cos x = 3tan x have? A 1 B C 3 D DSE-MATH-CP -13 Pearson Education Asia Limited 014

14 40 The figure shows a right pyramid with a square base If VA = VB = VC = VD = AB, find the angle between the plane VAB and the plane VBC correct to the nearest degree A 71 B 90 C 109 D In the figure, ABC is a circle BCD is a straight line DE and BE are the tangents to the circle at A and B respectively If DAC = 30 and AEB = 48, then CDA = A 18 B 30 C 36 D 4 4 Find the range of values of m such that the circle x + y + 6x + 5 = 0 and the straight line y = mx intersect at two distinct points A 1 0 < m < 5 1 B < m < C m > or m < D m < or m > If the coordinates of the points A, B and C are (, ), (, 8) and (10, 14) respectively, then the x-coordinate of the circumcentre of ABC is A 3 B 6 C 9 D DSE-MATH-CP -14 Pearson Education Asia Limited 014

15 44 There are 15 students, including John and Mary, in the art club of a school A committee of 3 members consists of chairman, secretary and treasurer is selected from the club If John and Mary cannot be both selected, how many different committees can be formed? A 468 B 754 C 936 D If the mean and the standard deviation of the five numbers a, b, c, d and e are 9 and 4 respectively, find the mean and the standard deviation of the five numbers 9 a, 9 b, 9 c, 9 d and 9 e mean standard deviation A 0 5 B 0 4 C 9 5 D 9 4 END OF PAPER 015-DSE-MATH-CP -15 Pearson Education Asia Limited 014