[Presbyterian High] [2023] 4E EM 4052 Prelims P1 QP

4052/01/4E Preliminary Examination/2023 Name: Index No.: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4052/01 PAPER 1 14 August 2023 Monday 2 hours 15 minutes PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2023 SECONDARY FOUR EXPRESS PRELIMINARY EXAMINATION DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. INSTRUCTIONS TO CANDIDATES: Write your name, index number and class on the spaces provided above. 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 the questions. If working is needed for any question, it must be shown 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of . 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 90. For Examiner’s Use Category Accuracy Notations Others Marks Deducted Question No. This question paper consists of 23 printed pages (including this cover page) and 1 blank page. Total Marks 90 Note that all the diagrams in this paper are not drawn to scale.

2 Presbyterian High School 4052/01/4E Prelim/2023 Mathematical Formulae Compound Interest Total amount = nrP       1001 Mensuration Curved surface area of a cone = lr Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1  Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin  2 2 2 2 cosa b c bc A   Statistics Mean =   f fx Standard deviation = 22           f fx f fx

3 Presbyterian High School 4052/01/4E Prelim/2023 Answer all the questions. 1 Solve 7 18 3 .x x  Answer x …………… … ……….. [1] 2 (a) Calculate 3 2 26.18 4.52 0.4 . Write your answer correct to 5 significant figures. Answer …………… …. ……………… [1] (b) Write your answer to part (a) in standard form. Answer ……………… ……. … …… … [1]

4 Presbyterian High School 4052/01/4E Prelim/2023 3 (a) Express 784 as the product of prime factors. Answer …… …. ……………………… [1] (b) It is given that a and b are prime numbers. Find the smallest values of a and b such that 784 a b is a perfect cube. Answer a … …. …………………… [1] b ………… …. …………… [1] 4 Expand and simplify   5 1w w  . Answer …………… …. ……………… [2]

5 Presbyterian High School 4052/01/4E Prelim/2023 5 The bar graph below shows the results of a survey conducted on the service quality of a hotel. Service quality of a hotel (a) Find the percentage of respondents who answered ‘Strongly Satisfied’ and ‘Satisfied’. Answer …………… … ……….…… % [1] (b) Suggest the use of another statistical diagram to represent the results of the survey conducted, that can show the relative size of a part in relation to the whole. Answer …………… …. ……………… [1] Number of respondents 0 10 20 30 Satisfied Strongly Satisfied Somewhat Satisfied Unsatisfied Strongly Unsatisfied Responses

6 Presbyterian High School 4052/01/4E Prelim/2023 6 Find the largest integer that satisfies 2 3 4.y  Answer ………… …. ………………… [2] 7 P is directly proportional to 3.Q When 2, 64Q P  . When the value of Q is halved, the value of P changes by a factor of m. Find the value of m. Answer m ……… …. ……………… [2]

7 Presbyterian High School 4052/01/4E Prelim/2023 8 The diagram shows a quadrilateral playground ABCD. A circular fence is constructed around the playground such that the vertices, A, B, C and D of the playground touch the circumference of the fence. (a) Construct the perpendicular bisector of AB. [1] (b) Construct the bisector of angle ADC. [1] (c) A sand pit is to be constructed inside the circular fence but outside the quadrilateral playground. The sand pit is nearer to AD than CD and nearer to B than A. Shade the region for the sand pit to be constructed. [1] A B C D

8 Presbyterian High School 4052/01/4E Prelim/2023 9 The diagram below shows the graph of   2 3 4y x h   . (a) Find the value of h. Answer h  …… ...…. ……….…… .. [2] (b) Explain why the graph of   23 1y x h   does not cut the x-axis. Answer …………………….…………………………………...……………………………………………..… ………………………………………………………………………………………………………..… ………………………………………………………………………………………………………….. [1] 10 A group of six students took a Mathematics quiz and the marks were recorded below. 8 10 9 13 10 9 (a) Calculate the standard deviation. Answer ……………… …. ……....…… [1] (b) Two other students also took the quiz, and their marks were recorded. Given that the mean mark obtained by the eight students was 10 and the mode was also 10, find the marks of these two students. Answer …… … …… and …… … .…… [2] x y 

9 Presbyterian High School 4052/01/4E Prelim/2023 11 The distance-time graph shows the journey Tan took to run from town A to B. (a) Find the distance Tan ran in the first two hours. Answer ………………… …. …..… km [1] (b) Calculate the average speed, in m/s, for the whole journey Tan ran. Answer …………… …. ………..… m/s [2] Time 10 am 11 am 12 noon 1 pm 2 pm 3 pm 4 8 12 16 0 B A Distance from A (km)

10 Presbyterian High School 4052/01/4E Prelim/2023 12 Simplify 2 2 2 3 4 9 y y y    . Answer …………………… …. ....…… [3] 13 In the diagram, ABC is a straight line and triangles ABE and BCD are equilateral triangles. Show that triangle ABD and triangle EBC are congruent. Give a reason for each statement you make. Answer …………………….…………………………………...……………………………..………………..……… …………………………………………………….…………………………………….…………..………… ………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………… [3] A B C D E