AISS Prelim EMath Paper 1 QP

This document consists of 20 printed pages. AISS PRELIM/4052/01/2025 [Turn over p AHMAD IBRAHIM SECONDARY SCHOOL GCE O-LEVEL PRELIMINARY EXAMINATION 2025 SECONDARY 4 EXPRESS /5 NORMAL ACADEMIC Name: Class: Register No.: MATHEMATICS Paper 1 Candidates answer on the Question Paper. 4052/01 05 Aug 2025 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. 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 questions 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 . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. For Examiner’s Use /90

2 AISS PRELIM/4052/01/2025 Mathematical Formulae Compound Interest Total amount = n rP    + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry C c B b A a sinsinsin == a2 = b2 + c2 − 2bc cos A Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 AISS PRELIM/4052/01/2025 [Turn over Answer all the questions. 1 Expand ( )( ) 22 5 3 5p q p q r+ − + . Answer ...…………….……………. [2] 2 Lee has two pieces of string. Their lengths are in the ratio 5 : 3 and the total length of the two pieces of string is 8x cm. Lee cuts 6 cm from each piece of string. The ratio of their lengths is now 9 : 5. Find the value of x. Answer x =…………….………… [3] 3 A salesperson earns a fixed weekly salary of $1000 plus 8% commission on the total value of items he sells. (a) In one week, he sold items worth $1750. Calculate the total amount the salesperson earned that week. Answer $...…………….…………… [1] (b) The following week, the salesperson earned a total of $1450. Calculate the total value of items he sold that week. Answer $...…………….…………… [2]

4 AISS PRELIM/4052/01/2025 4 The box-and-whisker-plot gives information about the time, in hours, that 120 adults spent on social media in one week. (a) State the median time. Answer ………………………hours [1] (b) State the range. Answer ………………………hours [1] (c) There was an error in the collection of data. Every adult spent 2 hours less on social media in one week. Describe the effect this change would have on the box-and-whisker plot. ………………………………………………………………………………….. ………………………………………………………………………………. [1] 2

5 AISS PRELIM/4052/01/2025 [Turn over 5 6 Sketch the graph of ( )( )83y x x=− − + on the axes below. Indicate clearly the values where the graph crosses the x- and y- axes and its turning point. [3] Express as a single fraction in its simplest form 45 3 2 3yy−−+ . Answer ...…………….…………….. [2]

6 AISS PRELIM/4052/01/2025 7 (a) A map has a scale of 1 : 2 500 000. The distance between Singapore and Phuket is 1314 km. Calculate the distance, in centimetres, between Singapore and Phuket on the map. Answer .....…………….………...cm [2] (b) When a ball is dropped, the distance, d metres, it falls is directly proportional to the square of the time, t seconds, from when the ball is released. The distance from which the ball is dropped is increased by 44%. Calculate the percentage change in the time taken for the ball to reach the ground. Answer ………………………… % [2] 8 Simplify 2 2 9 39 x xx − − . Answer ...…………….……………. [3]

7 AISS PRELIM/4052/01/2025 [Turn over 9 Factorise 2 2 2 26 3 2x y xy x y xy+ − − . Answer ….….……………………… [3] 10 Five positive integers have a mean of 6, a median of 7 and a mode of 10. Find the five numbers. Answer ………., ………., ………., ………., ………. [2] 1 1 1 1 2 4

8 AISS PRELIM/4052/01/2025 11 Calculate the perimeter of the shaded area. All lengths are in centimetres. Answer ….….…………………... cm [2]

9 AISS PRELIM/4052/01/2025 [Turn over 12 X, Y and Z are three points on horizontal ground. Angle ZXY = 35  , angle XYZ = 90  and XZ = 20 cm. (a) Calculate the distance YZ. Answer YZ = …………… cm [2] (b) Calculate the area of triangle XYZ. Answer ………………………... 2cm [2]

10 AISS PRELIM/4052/01/2025 13 A group of 200 people estimated the time, t minutes, they spent at an exhibition. The cumulative frequency diagram represents their estimates. (a) Use the diagram to find the estimated interquartile range of the estimated times. Answer …...….….…………minutes [2] (b) One of these people is chosen at random. The probability that the person’s estimate is greater than t minutes is 4 5 . Find the value of t. Answer t = ….….…………………... [2] Cumulative Frequency Time (t minutes)