HKDSE Math Comp PP 20120116 Eng

PP-DSE MATH CPPAPER 1 HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION Please stick the barcode label here. Candidate Number PRACTICE PAPER MATHEMATICS Compulsory Part PAPER 1 Question-Answer Book (2¼ hours) This paper must be answered in English INSTRUCTIONS 1. After the announcement of the start of the examination, you should first write your Candidate Number in the space provided on Page 1 and stick barcode labels in the spaces provided on Pages 1, 3, 5, 7, 9 and 11. This paper consists of THREE sections, A(1), A(2) and B. Attempt ALL questions in this paper. Write your answers in the spaces provided in this QuestionAnswer Book. Do not write in the margins. Answers written in the margins will not be marked. Graph paper and supplementary answer sheets will be supplied on request. Write your Candidate Number, mark the question number box and stick a barcode label on each sheet, and fasten them with string INSIDE this book. Unless otherwise specified, all working must be clearly shown. Unless otherwise specified, numerical answers should be either exact or correct to 3 significant figures. The diagrams in this paper are not necessarily drawn to scale. No extra time will be given to candidates for sticking on the barcode labels or filling in the question number boxes after the ‘Time is up’ announcement. 2. 3. 4. 5. 6. 7. 8. © Hong Kong Examinations and Assessment Authority All Rights Reserved 2012 PP-DSE-MATH-CP 1−1 權版留保 局核評及試考港香 1 *A030e001* SECTION A(1) (35 marks) 1. Simplify (m 5 n −2 ) 6 m 4 n −3 and express your answer with positive indices. (3 marks) Answers written in the margins will not be marked. 2. Make a the subject of the formula 5+b = 3b . 1− a (3 marks) Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−2 2 Page total Answers written in the margins will not be marked. Please stick the barcode label here. 3. Factorize (a) (b) 9 x 2 − 42 xy + 49 y 2 , 9 x 2 − 42 xy + 49 y 2 − 6 x + 14 y . (3 marks) Answers written in the margins will not be marked. 4. The cost of a chair is $ 360 . If the chair is sold at a discount of 20 % on its marked price, then the percentage profit is 30 % . Find the marked price of the chair. (4 marks) Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−3 3 Go on to the next page Page total Answers written in the margins will not be marked. O and C collinear? Explain your answer. The ratio of the capacity of a bottle to that of a cup is 4 : 3 . 337°) respectively. 157°) . 247°) and (15 . (4 marks) Answers written in the margins will not be marked. the polar coordinates of the points A . 6. (4 marks) Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−4 4 Page total Answers written in the margins will not be marked. Are A . Find the area of ∆ ABC .5. In a polar coordinate system. B and C are (13 . Find the capacity of a bottle. (14 . (a) (b) Let O be the pole. . The total capacity of 7 bottles and 9 cups is 11 litres. In Figure 1.Please stick the barcode label here. If AB = AC and ∠BDC = 36° . . find ∠ABD . PP-DSE-MATH-CP 1−5 5 Go on to the next page Page total Answers written in the margins will not be marked. Figure 1 Answers written in the margins will not be marked. (4 marks) A D 36° C B Answers written in the margins will not be marked. 7. BD is a diameter of the circle ABCD . PP-DSE-MATH-CP 1−6 6 Page total Answers written in the margins will not be marked. B is rotated anticlockwise about the origin O through 90° to B ′ . A′ is the reflection image of A with respect to the y-axis. (a) (b) Write down the coordinates of A′ and B ′ . − 5) respectively. The coordinates of the points A and B are (−3 .8. . Answers written in the margins will not be marked. Let P be a moving point in the rectangular coordinate plane such that P is equidistant from A′ and B′ . 4) and (−2 . Find the equation of the locus of P . (5 marks) Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−7 7 Go on to the next page Page total Answers written in the margins will not be marked. If r = 9 and the median of the distribution is 3 . (5 marks) (b) Answers written in the margins will not be marked. The following table shows the distribution of the numbers of online hours spent by a group of children on a certain day. (a) Find the least possible value and the greatest possible value of the inter-quartile range of the distribution. Answers written in the margins will not be marked. how many possible values of s are there? Explain your answer.Please stick the barcode label here. Number of online hours Number of children 2 r 3 8 4 12 5 s It is given that r and s are positive numbers. 9. . SECTION A(2) (35 marks) 10. Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−8 8 Page total Answers written in the margins will not be marked. (3 marks) (3 marks) Answers written in the margins will not be marked. . Factorize f ( x) . (a) (b) Find f (−3) . the quotient is 6 x 2 + 17 x − 2 . Let f ( x) be a polynomial. When f ( x) is divided by x − 1 . It is given that f (1) = 4 . C = 112 . C = 42 . (a) Find the cost of manufacturing a cubical carton of side 50 cm . find the length of a side of the carton. Answers written in the margins will not be marked. Let $ C be the cost of manufacturing a cubical carton of side x cm .Please stick the barcode label here. (4 marks) (b) If the cost of manufacturing a cubical carton is $ 58 . PP-DSE-MATH-CP 1−9 9 Go on to the next page Page total Answers written in the margins will not be marked. (2 marks) Answers written in the margins will not be marked. 11. when x = 120 . It is given that C is partly constant and partly varies as the square of x . . When x = 20 . It is given that town P and town Q are 16 km apart. Figure 2 shows the graphs for Ada and Billy running on the same straight road between town P and town Q during the period 1:00 to 3:00 in an afternoon. (a) (b) (c) How long does Billy rest during the period? How far from town P do Ada and Billy meet during the period? Use average speed during the period to determine who runs faster. Q 16 Distance from town P (km) 12 Ada Billy 2 P 0 1:00 1:32 2:03 Time Figure 2 2:18 3:00 Answers written in the margins will not be marked. (2 marks) (3 marks) (2 marks) Answers written in the margins will not be marked. . Explain your answer. Ada runs at a constant speed.12. PP-DSE-MATH-CP 1−10 10 Page total Answers written in the margins will not be marked. Answers written in the margins will not be marked. Answers written in the margins will not be marked.Please stick the barcode label here. PP-DSE-MATH-CP 1−11 11 Go on to the next page Page total Answers written in the margins will not be marked. . It is given that each student has only one most favourite fruit. Suppose that the above distribution is represented by a pie chart. (4 marks) Answers written in the margins will not be marked.13. (3 marks) Some new students now join the group and the most favourite fruit of each of these students is orange. Answers written in the margins will not be marked. then the probability that the most favourite fruit is apple 3 . Distribution of the most favourite fruits of the students in the group students in class Number of students 11 k 10 6 5 Apple Banana Orange Fruit Papaya Pear (a) (b) Find k . is 20 . If a student is randomly selected from the group. PP-DSE-MATH-CP 1−12 12 Page total Answers written in the margins will not be marked. The bar chart below shows the distribution of the most favourite fruits of the students in a group. (i) (ii) Find the angle of the sector representing that the most favourite fruit is orange. Will the angle of the sector representing that the most favourite fruit is orange be doubled? Explain your answer. PP-DSE-MATH-CP 1−13 13 Go on to the next page Page total Answers written in the margins will not be marked. . Answers written in the margins will not be marked.Answers written in the margins will not be marked. It is given that AB produced and OC produced meet at D . the equation of the circle OABC . A rectangular coordinate system. is introduced in Figure 3 so that the coordinates of A and D are (6 . If the ratio of the area of ∆ BCD to the area of ∆OAD is 16 : 45 . PP-DSE-MATH-CP 1−14 14 Page total Answers written in the margins will not be marked. Answers written in the margins will not be marked.14. D B C O A Figure 3 (a) (b) Write down a pair of similar triangles in Figure 3. (7 marks) Answers written in the margins will not be marked. In Figure 3. Suppose that ∠ AOD = 90° . 12) respectively. OABC is a circle. 0) and (0 . . with O (2 marks) as the origin. find (i) (ii) the coordinates of C . Answers written in the margins will not be marked. . Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−15 15 Go on to the next page Page total Answers written in the margins will not be marked. withdraws from the class and his test score is then deleted. The scores of Mary and John in the test are 36 marks and 66 marks respectively. . (2 marks) A student. Will there be any change in the standard score of John due to the deletion of the test score of David? Explain your answer. PP-DSE-MATH-CP 1−16 16 Page total Answers written in the margins will not be marked. It is given that his test score is 48 marks.SECTION B (35 marks) 15. Answers written in the margins will not be marked. The mean score of a class of students in a test is 48 marks. David. The standard score of Mary in the test is −2 . (a) (b) Find the standard score of John in the test. (2 marks) Answers written in the margins will not be marked. (a) (b) Find the probability that the class committee consists of boys only. From the class. (2 marks) (2 marks) Answers written in the margins will not be marked. . There are 18 boys and 12 girls in a class. 4 students are randomly selected to form the class committee.16. PP-DSE-MATH-CP 1−17 17 Go on to the next page Page total Answers written in the margins will not be marked. Answers written in the margins will not be marked. Find the probability that the class committee consists of at least 1 boy and 1 girl. PP-DSE-MATH-CP 1−18 18 Page total Answers written in the margins will not be marked. (a) Express 1 in the form of a + bi . the range of values of r such that the quadratic equation x 2 + px + q = r has real roots.17. (5 marks) Answers written in the margins will not be marked. where a and b are real numbers. 1 + 2i 10 10 and . Answers written in the margins will not be marked. . Find 1 + 2i 1 − 2i (2 marks) (b) The roots of the quadratic equation x 2 + px + q = 0 are (i) (ii) p and q . .Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−19 19 Go on to the next page Page total Answers written in the margins will not be marked. Answers written in the margins will not be marked. B C A D Figure 4 (a) (b) (c) Find the length of AB . (2 marks) Answers written in the margins will not be marked. Find the angle between the plane ABC and the plane ABD . Explain your answer. AC = AD = 20 cm . It is found that ∠ACB = 60° . . BC = BD = 12 cm and CD = 14 cm .18. Figure 4 shows a geometric model ABCD in the form of tetrahedron. PP-DSE-MATH-CP 1−20 20 Page total Answers written in the margins will not be marked. Answers written in the margins will not be marked. Describe how ∠CPD varies as P moves from A to B . (2 marks) (4 marks) Let P be a movable point on the slant edge AB . . Answers written in the margins will not be marked.Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−21 21 Go on to the next page Page total Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−22 22 Page total Answers written in the margins will not be marked. (a) (b) Find r .19. . The amount of investment in each successive year is r % less than the previous year. (10 marks) (ii) (iii) Answers written in the margins will not be marked. The manager of the firm claims that the total revenue made by the firm will exceed the total amount of investment. (i) Find the least number of years needed for the total revenue made by the firm to exceed $ 9 000 000 . Answers written in the margins will not be marked. The amount of investment of a commercial firm in the 1st year is $ 4 000 000 . Do you agree? Explain your answer. The amount of investment in the 4th year is $ 1 048 576 . (2 marks) The revenue made by the firm in the 1st year is $ 2 000 000 . The revenue made in each successive year is 20 % less than the previous year. Will the total revenue made by the firm exceed $ 10 000 000 ? Explain your answer. Answers written in the margins will not be marked. .Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−23 23 Go on to the next page Page total Answers written in the margins will not be marked. END OF PAPER 24 Answers written in the margins will not be marked. Page total .Answers written in the margins will not be marked. PP-DSE-MATH-CP 1−24 Answers written in the margins will not be marked. PP-DSE MATH CP PAPER 2 HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION PRACTICE PAPER MATHEMATICS Compulsory Part PAPER 2 (1¼ hours) INSTRUCTIONS 1. All questions carry equal marks. You are advised to use an HB pencil to mark all the answers on the Answer Sheet. No extra time will be given for sticking on the barcode label after the ‘Time is up’ announcement. If you mark more than one answer. Read carefully the instructions on the Answer Sheet. ANSWER ALL QUESTIONS. You must mark the answers clearly. 6. so that wrong marks can be completely erased with a clean rubber. You should mark only ONE answer for each question. you should first stick a barcode label and insert the information required in the spaces provided. No marks will be deducted for wrong answers. 4. 3. you should check that all the questions are there. Hong Kong Examinations and Assessment Authority All Rights Reserved 2012 PP-DSE-MATH-CP 2−1 權版留保 局核評及試考港香 © Not to be taken away before the end of the examination session 1 . After the announcement of the start of the examination. otherwise you will lose marks if the answers cannot be captured. When told to open this book. you will receive NO MARKS for that question. Look for the words ‘END OF PAPER’ after the last question. 2. 5. a+3 . a− 3. B. p2 − q2 − p − q = A. B. C. 2x 5 . The diagrams in this paper are not necessarily drawn to scale. If 3a + 1 = 3(b − 2) . B. a +1 .There are 30 questions in Section A and 15 questions in Section B. 2. 3x 4 . D. ( p − q)( p + q − 1) . Section A 1. x 3 (2 x + x) = A. 3 D. ( p − q)( p − q + 1) . Choose the best answer for each question. 3 5 . PP-DSE-MATH-CP 2−2 2 . D. ( p + q )( p + q − 1) . then b = A. a+ 7 . 2x 6 . C. 3x 5 . ( p + q)( p − q − 1) . C. −2 . −4 . If the quadratic equation 3x 2 + 2k x − k = 0 has equal roots. The slope of L2 is A. C. y 3 . the x-intercepts of the straight lines L1 and L 2 are 5 while the y-intercepts of the straight lines L2 and L3 are 3 . B. 3. Let m and n be constants. D. 11 . Let k be a constant. In the figure. C. 6. D. If m( x − 3) 2 + n( x + 1) 2 ≡ x 2 − 38 x + 41 . the remainder is A. B. 3. 31 . Let f ( x) = x 4 − x 3 + x 2 − x + 1 . I and II only I and III only II and III only I . 5. 5. The equation of L1 is x = 5 . 0 or 3 .4. −3 . 3) lies on L3 . 0. D. When f ( x) is divided by x + 2 . then k = A. C. The point (2 . Which of the following are true? I. C. B. then m = A. B. D. 7. II. 5 III. II and III 3 L3 O 5 x L1 L2 PP-DSE-MATH-CP 2−3 3 Go on to the next page . −1 . −3 or 0 . At what price should Susan sell the vase in order to have a profit of 20% ? A. 18% . x < −2 or x > −1 . a>0 II. John buys a vase for $ 1 600 . 10. x > −1 . B. C. D. Which of the following is/are true? y I. B. D. C. PP-DSE-MATH-CP 2−4 4 . He then sells the vase to Susan at a profit of 20% . 96% . The figure shows the graph of y = a x 2 − 2 x + b . B. The solution of 4 x > x − 3 or 3 − x < x + 7 is A. ab < 1 O x 2 y = a x − 2x + b A.8. x > −2 . then the area of the circle is increased by A. D. II only I and III only II and III only 9. If the circumference of a circle is increased by 40% . where a and b are constants. 20% . x < −2 . I only B. 40% . b < 0 III. C. D. C. $ 2 240 $ 2 304 $ 2 400 $ 2 500 11. 14. C.00905 (correct to 6 decimal places). B.12. which of the following must be constant? A. 0. find the area of the segment ABC . 0.00905 (correct to 3 significant figures). 0. 0. 3(π − 2) cm 2 3(π − 1) cm 2 6(π − 2) cm 2 6(π − 1) cm 2 C B O A PP-DSE-MATH-CP 2−5 5 Go on to the next page . 13. B. D. In the figure.00905 (correct to 6 significant figures). Let α and β be non-zero constants. 19 : 29 .00905 (correct to 3 decimal places). A. then α : β = A. C. C. If the area of ∆OAC is 12 cm 2 . If (α + β ) : (3α − β ) = 7 : 3 . 0. 5:9 .009049999 = A. O is the centre of the sector OABC . D. 15. 29 : 19 . C. B. D. x y2z z xy 2 yz x2 xz y2 B. 9:5 . D. If z varies directly as x and inversely as y 2 . Find the volume of the circular cone. E is the mid-point of BC . C. 2 cm 2 . D. 255π cm3 8 cm 345π cm 3 480π cm 3 600π cm3 17 cm 17. ABCD is a rectangle. F is a point lying on CD such that DF = 2CF . C. BC = CD = DE = 8 cm and FG = 9 cm .16. 60 cm 74 cm 150 cm B 164 cm A H C F G D E PP-DSE-MATH-CP 2−6 6 . C. B. D F C E A B 18. The figure shows a right circular cone of height 8 cm and slant height 17 cm . then the area of ∆ AEF is A. A. D. 6 cm 2 . In the figure. A. In the figure. 3 cm 2 . D. If the area of ∆CEF is 1 cm 2 . Find the perimeter of ∆ AEH . 4 cm 2 . B. AB = 4 cm . B. If AB // CE . B O 70° A C D PP-DSE-MATH-CP 2−7 7 Go on to the next page . then ∠BCD = A. 48° . C. In the figure. find ∠CDE . C. If AD // OC . A. In the figure. O is the centre of the circle ABCD . 55° . 64° . 57° . then ∠ AED = A. AC and BD intersect at E . B. AB = BC and D is a point lying on BC such that CD = DE . B. O is the centre of the semi-circle ABCD . 52° 58° 64° 76° 64° A C E D B 20. C. A D E C 24° O B 21. B. If AB = BC = 2 CD .19. D. D. 116° . 66° . 87° . 93° . D. In the figure. 22. 6 6 III. B. 30 3 sin θ + 2 sin 2 (90° − θ ) 2 is 24. 6 8 A. If AB = AE . 17° 18° 22° 26° D F A 112° C B 23. 15 . C. D. B. F is a point lying on AD such that CF // BE . D. E A. ABCD is a square. 5. D. 10 . I and II only I and III only II and III only I . C. 6 6 PP-DSE-MATH-CP 2−8 8 . In the figure. II and III II. C. Which of the following parallelograms have rotational symmetry and reflectional symmetry? I. 6. find ∠ ABF correct to the nearest degree. For 0° ≤ θ ≤ 90° . B. the least value of A. 3) lies outside the circle. 26. − 9) . Which of the following are true? I. C. D. (3 . then the coordinates of its image are A. 2) . C. B. 27. D. II. 7) respectively. 3) . − 1) . (−8 . B. The coordinates of the points A and B are (1. ( 0 . The coordinates of the centre of the circle are (− 2 . II and III PP-DSE-MATH-CP 2−9 9 Go on to the next page . (12 . If P is a point lying on the straight line y = x + 2 such that AP = PB . then the coordinates of P are A. − 3) and (−5 .25. 11) . If the point (− 2 . (− 2 . A. D. − 1) . C. B. III. The point (2 . (− 2 . (− 2 . The radius of the circle is 7 . 0) . I and II only I and III only II and III only I . 5) . 2) . − 1) is reflected with respect to the straight line y = −5 . (− 2 . The equation of a circle is 2 x 2 + 2 y 2 + 8 x − 12 y + 3 = 0 . The figure below shows the cumulative frequency polygons of the test score distributions X and Y . s1 > s 2 I. Which of the following are true? A. 1 3 1 4 1 6 5 16 B. Find the probability that the sum of the numbers drawn is a multiple of 4 . C. r1 and s1 be the median. I only II only I and III only II and III only 30. 3 . The inter-quartile range of the distribution is 15 cm . Let m1 . 5 and 7 respectively. Two numbers are randomly drawn at the same time from four cards numbered 2 . D.28. C. Which of the following is/are true? 155 160 165 170 175 180 185 Height (cm) I. 29. The box-and-whisker diagram below shows the distribution of the heights (in cm) of some students. A. the range and the standard deviation of Y respectively. Less than half of the students are taller than 170 cm . r1 > r2 III. B. II and III Cumulative frequency m1 > m 2 II. The height of the tallest student is 180 cm . D. A. C. r2 and s 2 be the median. II. X Y 0 PP-DSE-MATH-CP 2−10 10 Test score . I and II only I and III only II and III only I . D. the range and the standard deviation of X respectively while m 2 . III. B. If 2 f ( x) = g( x) . y O x O 1 3 x 2 6 −1 −1 y = g ( x) y = g ( x) C. 11×1610 + 23 . y B. 11×1610 + 35 . y O x 2 6 −2 y = f ( x) The figure above shows the graph of y = f ( x) . B. D. PP-DSE-MATH-CP 2−11 11 Go on to the next page . y O −4 x D. 12 × 1611 + 23 . 12 × 1611 + 35 . C. which of the following may represent the graph of y = g( x) ? A.Section B 31. B000000002316 = A. y O −4 x 1 3 2 6 y = g ( x) y = g ( x) 32. 12 log b 12 . 3x . 3x + 3 . B. Let b > 1 . then the real part of ( x + 3i )( 3 + i ) is A. then 1 = a A. log b 12 PP-DSE-MATH-CP 2−12 12 . k 3 − 9k . 34. 53 . If a = log 12 b . D. 52 . 56 . 3x − 3 . k 3 − 3k . then the greatest value of m is A. D. B. B.33. 36. The nth term of a sequence is 2n + 3 . D. C. x+3 . 1 . If the roots of the quadratic equation x 2 − k x + 3 = 0 are α and β . C. k 3 − 12k . If the sum of the first m terms of the sequence is less than 3 000 . C. 35. B. C. 57 . k3 . b D. If x is a real number. then α 3 + β 3 = A. log b 1 . log12 1 . a = 2 and θ = − 45° . The figure shows a right prism ABCDEF with a right-angled triangle as the cross-section. then k = A. a>c>d a>d >c c>b>d c>d >b A D C E a d G c B b F PP-DSE-MATH-CP 2−13 13 Go on to the next page . If ∠DAE = a . B. B . a = −2 and θ = 45° . C. 81 81 . B. D. −4 . D.37. E and F lie on the horizontal ground. C. 135 x 39. A . ∠CBF = b . If the figure shows the graph of y = a sin( x° + θ ) . 1 . a = −2 and θ = − 45° . 4 −5 log 3 x O −4 log 3 t D. 38. ∠CGF = c and ∠ DGE = d . y 2 −2 O a = 2 and θ = 45° . B. C. The graph in the figure shows the linear relation between log 3 t and log 3 x . 5 −5 . which of the following is true? A. then A. If x = k t a . Let a be a constant and −90° < θ < 90° . G is a point lying on AB such that AG : GB = 5 : 3 . −14 . find the range of values of k . 10 . 24) respectively. C. D. If BC = 24 cm and DE = 8 cm . BC is a chord of the larger circle and touches the smaller circle at D . D. then the x-coordinate of the orthocentre of ∆ OA B is A. B. PP-DSE-MATH-CP 2−14 14 . A and F are collinear. 25 .40. 2 < k < 18 −18 < k < −2 k < 2 or k > 18 k < −18 or k > −2 42. 18 cm . If the straight line x − y = 0 and the circle x 2 + y 2 + 6 x + ky − k = 0 do not intersect with each other. 12 . D . In the figure. 13 cm . 16 cm . AD produced meets the larger circle at E . If the coordinates of the points A and B are (18 . C. F is a point lying on the smaller circle such that E . C. 20 cm . then EF = A. A is the common centre of the two circles. B. A C D B E F 41. A. D. Let O be the origin. B. − 24) and (18 . C. µ + 2 . II and III END OF PAPER PP-DSE-MATH-CP 2−15 15 . δ + 2 } . C. B. γ + 2 . B. the variance and the inter-quartile range of a set of numbers are 40 . D. The mean.43. find the probability that Mary performs just after Tom. If 5 is added to each number of the set and each resulting number is then tripled to form a new set of numbers. where α < β < µ < γ < δ . find the mean. The range of A and the range of B are the same. 44. the variance and the inter-quartile range of the new set of numbers. A. β + 2 . Which of the following must be true? A be a group of numbers I. δ } and B be another group of numbers {α + 2 . Tom and 8 other students participate in a solo singing contest. II. 9 and 18 respectively. If each participant performs once only and the order of performance is randomly arranged. The standard deviation of A is greater than that of B . Let {α . Mary. 1 2 1 10 1 45 1 90 B. β . A. D. Mean A. 120 120 135 135 Variance Inter-quartile range 27 81 27 81 69 69 54 54 45. C. I and II only I and III only II and III only I . III. The median of A is smaller than that of B . D. γ .