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Canotta2023Set1P2

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Northeastern University**We aren't endorsed by this school
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MATH 10
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Mathematics
Date
Dec 18, 2024
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15
Uploaded by HighnessGorilla8375
2023-HKDSE Math CP Paper 2 CANOTTA PUBLISHING CO., LTD. HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION MATHEMATICS Compulsory Part Practice Paper Set 1 Paper 2 (1 1/4 hours) o 1. Read carefully the instructions on the Answer Sheet. Stick a barcode label and insert the information required in the spaces provided. 2. 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. 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 deducted for wrong answers. N © Canotta Publishing Co., Ltd. PP1-DSE-MATH-CP-2-1 1
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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 6300 9150 = 25 A £ (3) 2150 B =z (3) C. 2 D. 2300 2 If ——c=— ,then b= A c+cd ’ ad B ad " c+ed C c—cd ’ ad D ad " c—cd 3. 9x? —(3+4y)* = A, (Bx+4y+3)(3x+4y-3). B. (3x+4y+3)(3x-4y-3). C. (Bx—-4y+3)(3x+4y-3). D. (Bx-4y+3)(3x-4y-3). PP1-DSE-MATH-CP-2-2 2
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4. 0.0045982 = A. 0.0046 (correct to 2 decimal places). B. 0.0046 (correct to 4 significant figures). C. 0.00460 (correct to 3 significant figures). D. 0.0045 (correct to 2 significant figures). 5. If 2y -3x=x+4y=-7,then y= 6. Find the solutionof 7—2x<3x-8 or 2x+42>0. A x2>2-2 B. x>3 C. -2<x<3 D. all real numbers 7. Let fix)=(x-h)(x+2)—k ,where h and k are constants. If f(1)=-5 and f(7)=37 , find the y-intercept of the graph y = f{(x) . A 37 B 1 cC. -5 D. -7 PP1-DSE-MATH-CP-2-3 3 @on to the next pag@:>
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8. If the graph of y =-9x? + 6x — k+ 1 touches the x-axis, then k= 9. If 0<h<1,which of the following may represent the graph of y = %(x +h)?-h? A. B. ¥y N >\ \>‘< 10. If a and b are non-zero numbers such that @ — 5ab + 6b%=0 ,then a: b= 2:1 or 3:1. :2 or 1:3. 1:1 or6:1. 1:1 or 1:6. S 0w » PP1-DSE-MATH-CP-2-4 4
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11. z varies directly as x* and inversely as \/}7 .If x isincreased by 20% and y is decreased by 19%, then zis SN wp increased by 29.6% . increased by 60% . decreased by 37.5% . decreased by 40% . 12. The marked price of a watch is 55% above its cost. The watch is then sold at a discount of 20% on its marked price. Find the percentage profit. oo w e 69% 35% 24% 16% 13. The ratio of the cost per litre of wine X to that of wine Yis 4 : 3 . The two types of wine are then mixed in the ratio 1:2 by volume so that the mixture costs $50 per litre. Find the cost per litre of wine X. 14. According to the figure, which of the following must be true? L II. ML A. B. v o w $15 $45 $55 $60 x+y=360° x+y+z=720° X=2Zz I only II only I and HI only I and III only PP1-DSE-MATH-CP-2-5 Go on to the next page
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15. Inthe figure, the 1st pattern consists of 13 dots. For any positive integer #, the (n+ 1)th pattern is formed by adding (n + 5) dots to the nth pattern. Find the number of dots in the 6th pattern. 34 43 53 64 O aw p» o0 XX XYy’ XXX X —» XXX XX YX XYY 16. In the figure, AD { BC, AC1 AB and BDC is a straight line. If AD =44 cm and CD =33 cm, find 4B. A. 4125cm B. 55cm 176 C. 3 cm 5 220 . 3 cm A 44 cm 33¢cm 17. Inthe figure, ABCD is a parallelogram and DCEFG is a regular pentagon. If ZBCE = 115°, then ZADG = A, 115°. B. 137°. C. 151°. D. 173°. PP1-DSE-MATH-CP-2-6
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18. The radius of a solid sphere and the base radius of a solid right circular cone are equal. If the height of the circular cone is equal to 0.75 times its base radius, then the ratio of the surface area of the sphere to the total surface area of the circular cone is A, 4:3. B. 16:7. C. 16:9. D. 16:27. 19. Inthe figure, ABCD is a rectangle. F is the mid-point of BC. A4C and BD intersect at E ,and AC and DF intersect at G . If the areas of ADEG , ADGC , AGFC and the quadrilateral EBFG are a,b,c and d respectively, which of the following must be true? 1. a=c A D II. b=d . d=3a E A. 1 and II only g B. 1 and III only B F C C. II andIII only D. I,II and HI 20. Inthe figure, OAXB and OCYD are major sectors with centre O, where 04 =12 cm and OC=9 cm JIf the perimeter of the shaded region is (28 7+ 6) cm, which of the following must be true? L. The angle of the major sector O4AXB is 210°. II. The area of the shaded region is 427 cm?. III. The perimeter of the minor sector O4B is (8z+ 24) cm. I only I and III only A B. 1I only C D. 1I and I only PP1-DSE-MATH-CP-2-7 7 Go on to the next page
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21. Inthe figure, AD = A acos . . ———-—asina. tan S asin a B. ——-acosa. tan B C. acosatan f-asina . D. asinatan f—acos a . 22. Afrustum is formed by cutting the upper part of a right pyramid with a square base along a plane parallel to the base. What is the number of planes of reflectional symmetry of the frustum? S 0w > 2 4 6 8 23. Inthe figure, O is the centre of the circle ABC . Which of the following must be true? A a+tc=b B. a+tc=2b C. a+c=180° D. a+2b+¢=360° 24, If an exterior angle of a regular n-sided polygon is 30°, which of the following about the polygon is NOT true? A. The polygon has rotational symmetry. B. The number of diagonals is 12. C. The sum of all interior angles is 1 800°. D. The value of nis 12. PP1-DSE-MATH-CP-2-8 8
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25. Ifthestraightlines Ly :4x—3y—15=0 and L;:ax+by+10=0 do not intersect and L, passes through the point (2, 1), then b= 26. Let O be the origin. A straight line L :x+ 2y -4 =0 cuts the x-axisat 4 .Ifa point P in the first quadrant lies on the straight line L such that AAOP is isosceles, then the coordinates of P are A (L 1). B. (2,1). C. (0,2). D. (4,0). 27. The equation of the circle C is (2x—1)? +(2y+1)? =1 . Which of the following is/are true? L. The radius of C is 1. 1 1 II. Thecentre of C is (27 2) . III. The point (1, 0) lies outside C. A. 1I only B. I only C. 1II and III only D. I,II and III PP1-DSE-MATH-CP-2-9 9 [Go on to the next page>
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28. Thereare 2 red ballsand 1 blue ball in a bag. A man randomly draws 2 balls from the bag at the same time. If the 2 balls are of the same colour, he will gain $12 ; otherwise, he will lose $9 . What is the expected gain or loss for the man? Expected loss of $2 Expected loss of $5 Expected gain of $2 O 0w > Expected gain of $5 29. Mr. Wong has one $2 coin and two $5 coins in his left pocket. He has one $1 coin, one $5 coin and one $10 coin in his right pocket. If he takes out randomly one coin from each pocket, find the probability that he gets at least $10 . A L 3 B 2 3 c. 4 9 D. 2 9 30. If the median of the integers 8,4 ,x—-3,x+3,17 and 6 is 7 and the mode is 8, then x= o w 2 5 7. 8 PP1-DSE-MATH-CP-2-10 10
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Section B 31. Which of the following is the greatest? A (867 i B. 78686 2 —-876 1 \678 D. (_) 876 32. Itis given that logsy is a linear function of x » where 0 <k <1. The intercepts on the vertical axis and on the horizontal axis of the graph of the linear function are 5 and 3 respectively. If y = ab*, which of the following is/are true? I a<l] II. b<1 1. ab’=1 I only 1T only I and III only 11 and TII only O o w » 33. If logsy=2x+1 and (logs y)>=24x - 15, then logyyy = A. 1lor3. B. 1lor4. C. 9or27. D. 27 or 81. PP1-DSE-MATH-CP-2-11 11 (G0 on 1o the next page
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34. 17A0000DEOOOOOF ¢ = 378 x 2% 4+ 222 x 224+ 15 . 379 x 248 +239 x 224 + 16, 378 x 252+ 222 x 28 + 15, 379 x 252+ 239 x 28+ 16. O 0w > k+2i . T 35. Let z= 3Tkz , where & is a positive number. If the real part and the imaginary part of z are equal, then the real part of z is A -2 3 B. -1 2 c. 1. 2 p. %. 3 36. Consider the system of linear inequalities: x<9 y=0 2x-y20 x+3y<21 Let D be the region which represents the solution of the above system of inequalities. If (x, y) is a point in D, then at which point will —x — 2y attain its least value? A (9,0 B. (9,4) C. (9,10) D. (3,6) PP1-DSE-MATH-CP-2-12 12
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37. Let a, be the nthterm of a geometric sequence. If @, =30 and the sum to infinity of the sequence is 20, which of the following is/are true? L The common ratio of the sequence is % . 1. The sum of all the negative terms of the sequence is ~20 . III. The sum of the first 9 terms of the sequence is greater than 20 . A. Tonly B. I only C. TandIII only D. IIandUIonly 38. Inthe figure, ABC isacircle. P4 and QB are tangents to the circle at 4 and B respectively and ACQ is a straight line. If ZPAC=92° and ZAQB =28°,then LBAC= A 26°. o o B. 28°. P C. 30°. < D. 32°. 4 B 39. For 0° < 6#<360°, how many roots does the equation 3 sin? @+ cos 8+ 1 =0 have? A1 B. 2 C. 3 D. 4 PP1-DSE-MATH-CP-2-13 13 LGo on to the next page
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40. Inthe figure, ABCDEFGH is a cuboid, AB=20cm,BC=10cm and BG=6cm . Let a be the angle between A4BH and AABG while § be the angle between AdBH and ABGH . Which of the following is true? A, p<50°<a B. a<50°<g C. 50°<fB<a D. 5S0°<a<p 41. Let O be the origin. The coordinates of the points 4 and B are (a, 0) and (0, b) respectively, where a and b are positive numbers. If the in-centre of AOA4B lies on the straight line 5x+ 7y =3a,then a: b= S0 w ~J 42. Mr. Chan has 13 male friends and 6 female friends. Among them, there is a couple. Mr. Chan now wants to invite 4 male and 4 female friends to a party. If the couple will either both attend the party or both not attend the party, in how many different ways can Mr. Chan choose to invite his friends? A 10725 B. 4675 C. 2475 D. 2200 PP1-DSE-MATH-CP-2-14 14 CH _— v
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43. If 8 girlsand 4 boys randomly form a queue, find the probability that no boys are next to each other in the queue. 44. Inan IQ test, the difference of the test scores and the difference of the standard scores of two students are 48 and 3 respectively. In the IQ test, the variance of the test scores is A 4. B. 16. C. 32. D. 256. 45. Itis given that m is a real number. Let Si be a group of numbers {m-9. m-1,m,m+5 m+ 7} and S2 be another group of numbers m-T,m-5, m,m+1,m+ 9} . Which of the following is/are true? L The means of S; and S, are equal. II. The inter-quartile ranges of Sy and S, are equal. IIl. The standard deviations of §, and Sy are equal.. A. Tonly B. IIonly C. Tand Il only D. IIand I only END OF PAPER Scan the QR code to download the Solution of this paper. ' PP1-DSE-MATH-CP-2-15 15 Practice Paper Set 1 Paper 2
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