Paper 2 QP

Name: Index Number: Class: HUA YI SECONDARY SCHOOL Preliminary Examination 2022 MATHEMATICS Paper 2 30 August 2022 2 hours 30 minutes Candidates answer on the Answer Space provided. READ THESE INSTRUCTIONS FIRST Write your Name, Class and Index Number in the spaces provided at the top of this page. Write your answers in the spaces provided on the question paper. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown in the space below with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. For Examiner’s Use This document consists of 19 printed pages including the cover page. © HYSS 2022 No part of this document may be reproduced in any form or transmitted in any form or by any means without the prior permission of Hua Yi Secondary School. [Turn Over 4E/5N 4E/5N 4048/2 100

2 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = l rπ Surface area of a sphere = 24 rπ Volume of a cone = h r2 3 1π Volume of a sphere = 3 3 4 rπ Area of triangle ABC C absin2 1 Arc length = θr , where θ is in radians Sector area = θ2 2 1 r , where θ is in radians Trigonometry C c B b A a sin sin sin= = A bc c b acos22 2 2− + = Statistics Mean = f fx ∑ ∑ Standard deviation = 22       ∑ ∑−∑ ∑ f fx f fx

3 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 Answer all the questions. 1. John and Peter took part in a marathon race. They each ran 42 km. (a) John ran at a constant speed of x kilometres per hour. Write down an expression, in terms of x, for the number of hours he took. Ans: ____________ h [1] (b) Peter ran at a constant speed which was 1 2 km/h more than John’s speed. Write down an expression, in terms of x, for the number of hours he took. Ans: ____________ h [1] (c) The difference between their times was 15 minutes. (i) Write down an equation in x to represent this information, and show that it reduces to 22 168 0xx+− = . Answer: [3] (ii) Solve the equation 22 168 0xx+− = , giving your answers correct to 3 decimal places. Ans: x = _________or__________ [3] (iii) Calculate the time that Peter took to complete the race, giving your answer in hours and minutes. Ans: _______h_____ min [2]

4 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 2. (a) In the diagram, OAB is a sector of a circle with centre O. Given that OA = 12 cm, AOB θ∠= radians, OC = 8 cm and the length of the arc AB = 15 cm. (i) Calculate the value of 𝜃𝜃. Ans: ____________ [1] (ii) Find the area of the shaded region. Ans: __________cm2 [3] (iii) Calculate the perimeter of the shaded region. Ans: __________cm [2] 15 cm θ

5 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 (b) In the diagram, A, B , C and D are four points on a circle, centre O. DO and CB are parallel. Find, giving reasons for each answer, (i) angle DAB, Ans: ____________ ° [1] (ii) angle DOB, Ans: ____________ ° [1] (iii) angle ODC. Ans: ____________ ° [2] A B C D O

6 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 3. The diagram shows a solid trapezoidal prism with four rectangular faces. AB = 10cm, BC = 12cm, DC = 6cm and CT = 16cm. (a) Show that AD = 12.649 cm , correct to 5 significant figures. Answer [2] (b) Calculate the surface area of the prism. Ans: __________cm2 [3] (c) Calculate the volume of the prism. Ans: __________cm3 [2] A B C D T

7 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 4. The figure shows a triangle ABC. E is the mid-point of AC. 3AB= a   and 3AC = c   . K lies on EB such that EB = 3EK. (a) Express 𝐵𝐵𝐵𝐵�����⃗ in terms of a and c, as simply as possible. Ans: BC   =_______________ [1] (b) Express 𝐸𝐸𝐵𝐵�����⃗ in terms of a and c, as simply as possible. Ans:= _______________ [1] (c) Given that 1 2KP=   a 1 2+ c , explain why A, K and P lies on a straight line. Answer [3] (d) Find the value of area of area of AEK AKB ∆ ∆ . Ans: ____________ [1] (e) Find the value of area of area of AEK ABC ∆ ∆ . Ans: ____________ [1] A E C B K

8 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 5. The diagram shows the speed-time graph of a motorcyclist. The shaded area represents the distance travelled. The distance travelled is 450m. (a) Show that v = 12. [2] Answer (b) Find the speed of the motorcyclist after 8 seconds. Ans: ____________m/s [2] (c) Describe the motion of the motorcyclist between 10 and 30 seconds. Answer ……………………………………………………………………………………….. ……………………………………………………………………………………….. [1] Time (s) Speed (m/s)

9 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 (d) Find the deceleration of the motorcyclist for the last 25 seconds. Ans: ____________m/s2 [1] (e) Sketch the distance time graph for the journey on the grid. Answer [3] Distance (m) Time (s)

10 Sec 4E/5N Preliminary Examination 2022 Mathematics Paper 2 6. The variables x and y are connected by the equation 3 215 xyx=−+ . Some corresponding values of x and y are given in the table below. x −4 −3 −2 −1 0 1 2 3 4 y −3.8 1.6 p 2.8 1 −0.8 −1.4 0.4 5.8 (a) Find the value of p. Ans: p = ____________ [1] (b) On the graph paper on page 11, draw the graph of 3 215 xyx=−+ for 44 x−≤≤ . [3] (c) Using your graph, find the value of m such that the graph of 2y mx= − intersect the curve at exactly 2 points. Ans: m = ____________ [2] (d) Using your graph, explain why 3 2 305 x x− −= has only one solution. Answer …………………………………..…………………………………..……………… …………………..…………………………………..……………………………… [2] (e) On the same axes, draw the graph of 24yx+= . [1] (f) Show that the x coordinates of the points of intersection of the line and the curve give the solutions to the equation 32 15 10 0xx− −= . Answer [3]