Canotta2023Set2P1
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School
Northeastern University**We aren't endorsed by this school
Course
MATH 10
Subject
Mathematics
Date
Dec 18, 2024
Pages
24
Uploaded by HighnessGorilla8375
2023-HKDSE Math CP PAPER 1 CANOTTA PUBLISHING CO., LTD. HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION MATHEMATICS Compulsory Part Practice Paper Set 2 Paper 1 Question-Answer Book (2%a hours) This paper must be answered in English INSTRUCTIONS 1. This paper consists of THREE sections, A(1), A(2) and B. 2. Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question-Answer Book. Do not write in the margins. Answers written in the margins will not be marked. 3. Unless otherwise specified, all working must be clearly shown. 4. Unless otherwise specified, numerical answers should be St either exact or correct to 3 significant figures. 5. The diagrams in this paper are not necessarily drawn to scale. © Canotta Publishing Co., Ltd. PP2-DSE-MATH-CP-1-1 1 Please stick the barcode label here Candidate Number
Answers written in the margins will not be marked. SECTION A (1) (35 marks) 2 p-3:4 1. Simplify % and express your answer with positive indices. (3 marks) a . 8a+3b 2. Make a the subject of the formula =3a+5 . (3 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-2 2 Page total Answers written in the margins will not be marked.
Answers written in the margins will not be marked. 3. Factorize (a) b*+2b-15, (by &b +22°b-154%. (3 marks) 4. The price of 3 sandwiches is equal to the price of 4 cakes. The price of 4 sandwiches and 5 cakes is $186 . Find the price of a sandwich. (3 marks) Answers written in the margins will not be marked. Answers written in the margins will not be marked. to th t PP2-DSE-MATH-CP-1-3 3 Go on to the next page > Page total
Answers written in the margins will not be marked. 5. Consider the compound inequality 5x-3 3x-5> and 3 +x < 14......(*) (a) Solve (*). (b) Write down the smallest integer satisfying (*). (4 marks) 6. Ina shop, the marked price of a shirt is higher than its cost by $100 . The shirt is sold at a discount of 20% on its marked price. After selling the shirt, the percentage profit is 20% . Find the marked price of the shirt. (4 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-4 4 Page total Answers written in the margins will not be marked.
Answers written in the margins will not be marked. (a) (b) 7. Let G(x)=9x—30x + ¢, where c is a constant. The equation G(x) =0 has equal roots. Find the value of ¢, the x-intercept(s) of the graph of y = G(x) — 484 . (5 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-5 5 Answers written in the margins will not be marked. Go on to the next page > Page total
Answers written in the margins will not be marked. 8. InFigure 1, O is the centre of the circle BCDE . ABC and AED are straight lines. A Figure 1 (a) Prove that AABE ~ AADC . (b) If ZCOE=130° and ACOE is a cyclic quadrilateral, find ZAEB . (5 marks) Answers written in the margins will not be marked. Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-6 6 Page total
Answers written in the margins will not be marked. students during a particular vacation. 9. The table below shows the distribution of the number of hours spent on online games per day by a group of Number of hours 1 2 3 4 5 Number of students 13 12 11 9 5 (a) Write down the mean, the median and the standard deviation of the above distribution. (b) A new student now joins the group. The number of hours spent by him on online games per day during that vacation is 3 . Find the change in the median of the distribution as a result of this. (5 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-7 @) on to the next page> Answers written in the margins will not be marked. Page total
Answers written in the margins will not be marked. SECTION A (2) (35 marks) 10. The stem-and-leaf diagram below shows the distribution of the average daily expenses (in dollars) of a group of students last month. Stem ($10) | Leaf ($1) 4 |5 6 7 514 4 5 6 9 6 (0 0 2 5 8 8 711 2 3 3 (a) Find the median and the inter-quartile range of the distribution. (3 marks) (b) The box-and-whisker diagram below shows the distribution of the average daily expenses (in dollars) of the same group of students this month. Average daily 48 62 67 74 78 expenses (dollars) A student Chris claims that at least 25% of the students’ average daily expenses have increased this month. Do you agree? Explain your answer. (3 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-8 8 Page total Answers written in the margins will not be marked.
Answers written in the margins will not be marked. 11. The cost $C of making a metal ball is partly constant and partly varies as the cube of the radius » cm of the ball. It is known that when »=2, C=224 and when r=5,C=575. (2) Find the cost of the metal ball when r=10. (4 marks) (b) Someone claims that the cost of a metal ball of radius 6 cm is higher than the total cost of two metal balls each of radius 2 cm? Is the claim correct? Explain your answer. (2 marks) Answers written in the margins will not be marked. Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-9 9 [ Go on to the next page > Page total
Answers written in the margins will not be marked. 12. A vessel X in the form of a frustum is made by cutting off the lower part of an inverted right circular cone. The vessel X has a height of 8 cm with the radii of the top and the base equal to 15 cm and 9 cm respectively. (a) Find the capacity of the vessel X in terms of 7. (3 marks) (b) Abigger vessel Y is similar to vessel X. The slant edge of vessel Y is of length 12 em. Edwin claims that the capacity of vessel Y is less than 6 000 cm®. Do you agree? Explain your answer. (3 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-10 10 Page total Answers written in the margins will not be marked. v, e
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Answers written in the margins will not be marked. 13, The cubic polynomial G(x) is divisible by x — 1. When G(x) is divided by x*>— 1, the remainder is kx — 32 , where k is a constant. (a) Find %. (3 marks) (b) Itis given that x — 3 is a factor of G(x). When G(x) is divided by x, the remainder is —30. Find all the rational roots of the equation G(x) = 0. (5 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-12 12 Page total Answers written in the margins will not be marked.
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Answers written in the margins will not be marked. 14. The equation of the circle Cisx?+»* — 8x— 6y — 75 =0 . Denote the centre of C by G and the origin by O. (@) Find OG. (3 marks) (b) Does O lie inside circle C ? Explain your answer. (2 marks) (c) Let Q beamoving point in the same rectangular coordinate plane such that OQ = GQ . Suppose that the locus of O cuts C at the points 4 and B . Find the perimeter of the quadrilateral OAGB . (4 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-14 14 Page total Answers written in the margins will not be marked.
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Answers written in the margins will not be marked. SECTION B (35 marks) 15. Abagcontains 1 red pen, 5 blue pens and 6 green pens. 4 pens are randomly selected. (a) Find the probability that 2 blue pens and 2 green pens are selected. (2 marks) (b) Find the probability that the number of blue pens and the number of green pens selected are different. (2 marks) Answers written in the margins will not be marked. Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-16 16 Page total
Answers written in the margins will not be marked. 16. Let f(x)=5x*~20kx +22k*+ 4, where k is a non-zero constant. (@) Using the method of completing the square, express, in terms of % , the coordinates of the vertex of the graph of y=f(x). (2 marks) (b) On the same rectangular coordinate system, denote the vertex of the graph of y = f(x) and the vertex of the graph y =5 f(x +4) by U and V respectively. Let S be a point lying on UV such that the area of AOUV is four times the area of AOQUS, where O is the origin. Express in terms of &, the coordinates of S. (3 marks) Answers written in the margins will not be marked. Answers written in the margins will not be marked. t PP2-DSE-MATH-CP-1-17 17 Go on (o the nex pa&> Page total
Answers written in the margins will not be marked. 17. Let k be areal constant. The roots of the equation x> +kx—18=0 are « and B, where a > f . (a) Find ¢ — f interms of k. ' (3 marks) (b) The 1st term, the 2nd term and the 3rd term of an arithmetic sequence are k,a — f and k+ 8 respectively. Find the least value of » such that the sum of the fist » terms of the sequence is greater than 3 x 10°. (4 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-18 18 Page total Answers written in the margins will not be marked.
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Answers written in the margins will not be marked. 18. Figure 2(a) shows two similar triangles 4BE and ACD with AB=AE=34cm, BC=ED=17 cm and CD =48 cm. When AACD is folded along BE, AABE and BCDE form two of the faces of the pyramid ABCDE shown in Figure 2(b), where 4D =AC=40cm. 17cm_~ € B / 34 cm A 48 cm 34 e 4 40 cm D E\ 17 cm Figure 2(a) D Figure 2(b) (a) Find the angle between the faces ABE and BCDE in the pyramid. (4 marks) (b) Find the angle between AE and the face BCDE in the pyramid. (3 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-20 20 Page total Answers written in the margins will not be marked.
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Answers written in the margins will not be marked. 19. The centre of the circle C is the point G (45, 60) . It is found that the point P (145, 135) lies outside C. PQ and PR aretangents to C atthe points O and R respectively. It is given that C passes through the origin O . (a) (b) © @ Find the equation of the straight line passing through P and G. (2 marks) Find the coordinates of the point of intersection of PG and QR . (3 marks) Find the equation of the inscribed circle of APQR . (4 marks) Let S be a moving point on the inscribed circle of APQR . Someone claims that when S is farthest from O, its y-coordinate is greater than 125 . Is the claim correct. Explain your answer? (3 marks) Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-22 22 Page total Answers written in the margins will not be marked.
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Answers written in the margins will not be marked. END OF PAPER Answers written in the margins will not be marked. PP2-DSE-MATH-CP-1-24 Scan the QR code to download the Solutiol 24 of this paper. n EIEERR Practice Paper Set 2 Paper 1 Page total Answers written in the margins will not be marked.