AHS 2025 EMATH PRELIM P1 MS

Name: ( ) Class: 4 ( ) 9o MATHEMATICS 4052/01 Paper 1 21 August 2025 Candidates answer on the Question Paper. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the space at the top of this page. 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. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of marks for this paper is 90. 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 . ------------------------------------------------------------------------------------------------------------------------------ For Examiners’ Use Question 1 2 3 4 5 6 7 Marks Question 8 9 10 11 12 13 14 Marks Question 15 16 17 18 19 20 21 Marks Clarity/ Logic Accuracy/ Precision Units 90 Parent’s Name and Signature: Date: This document consists of 21 printed pages.

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = Anglican High School Preliminary Examination 2025

3 Answer all the questions. 1 Simplify , leaving your answer in positive index form. Answer ………………………………… [2] 2 Expand and simplify . Answer ………………………………… [3] 3 Factorise completely . [Turn Over 1 M1 Open Bracket A1 2 = = = M1 – expand M1 – correct sign when remove bracket A1 3

4 Answer ………………………………… [2] 4 (a) Solve the equation . Answer x = …………………………… [2] (b) Solve the equation . Anglican High School Preliminary Examination 2025 M1 – Factorise x and 2 y A1 4(a) M1 – expand and rearrange A1 4(b) (3s.f.) M1 – to single fraction M1 – apply formula A1

5 Answer x = …………………………… [3] 5 Mr Chan is looking at Deepavali decorations. There are two lights, one green and one red, flashing at different intervals. The green light and the red light flash at intervals of 6 seconds and 8 seconds respectively. If the two lights start flashing at the same time, how long will it take for the two lights to next flash simultaneously? Answer ……………………………… s [2] 6 (a) Express as the product of its prime factors. Answer ………………………………… [1] (b) The number , where and are integers, is a perfect cube. Find the smallest positive integer values of and of . Answer h = …………………………… k = …………………………… [1] (c) Find two smallest possible integers, one is odd and the other is even, such that they have a lowest common multiple of 2250 and a highest common factor of 45. [Turn Over 5 LCM = It will take 24 s for the two lights to next flash simultaneously again. M1 – prime factorisation A1 – LCM 6a B1 6b h = 3 and k = 2 B1 6c B1 each for 90 and 1125

6 Answer …………… and …………… [2] 7 A student makes a pendulum by tying a string to a small solid sphere and hanging it from a retort stand. The time, in seconds, taken by the pendulum to swing from one end to the other and back again is called the period, seconds. The period is directly proportional to the square root of the length of the string, cm. If the value of increases by 25%, what is the corresponding percentage change in the value of ? Answer ……………………………… % [3] 8 The Great Pyramid of Giza, located in Egypt, has a surface area of and a volume of . A vendor is selling geometrically similar replicas of the pyramid. The replica has a volume of . Estimate the surface area of the replica, giving your answer in and in standard form. Anglican High School Preliminary Examination 2025 90 and 1125 7 Let and The length of the string increased by 56.25%. M1 – the equation for direct proportion is given. M1 – value of L A1 – Statement must be written

7 Answer ……………………………… [4] 9 (a) On the Venn diagram, shade the region which represents . B1 [1] (b) Use set notation to describe the shaded region. [Turn Over 7 Let the height of the Great Pyramid be . Let the height of the replica be Let be the surface area of the Great Pyramid and be the surface area of the replica M1 – M1 – value of M1 – A1

8 Answer ………………………………… [1] (c) The Venn diagram shows the universal set and the elements in each of its subsets. (i) Describe the elements of Set A . Answer ………………………………………………….………………………………… [1] (ii) Find the value of . Answer ………………………………… [1] 10 In the diagram above, ABC is part of a polygon. is The remaining interior angles are each equal to Find the number of sides of this polygon. Anglican High School Preliminary Examination 2025 9b B1 9ci Perfect square, square numbers B1 9cii 7 B1 10 Let n be the number of sides of the polygon. M1 – for forming equation A1

9 Answer ………………………………… [2] 11 ABCD is a trapezium where DC is parallel to AB . Diagonals AC and BD intersect at O . DO = CO . (a) Name a pair of similar isosceles triangles. Answer ………………………………… [1] (b) Show that triangle ABC and triangle BAD are congruent. Give a reason for each statement you make. ……………………………………………………………………………………………… [3] 12 The test scores for a group of 24 students were recorded. 0 9 1 [Turn Over 11a B1 11b Hence, by SAS property, triangle ABC and triangle BAD are congruent. B1 – state common length B1 – AC = BD B1 – state test

10 2 1 3 3 1 3 4 7 7 7 8 4 2 5 7 9 5 5 6 7 7 9 9 6 7 0 7 8 8 Key 7 0 means 70 marks The results are shown in the stem-and-leaf diagram. (i) Find the interquartile range. Answer ………………………… marks [2] (ii) Find the median result. Answer ………………………… marks [1] (iii) Find