NASS 2025 EMATH PRELIM P1 QP

Name: .............................................................. Register no: ........... Class: ........... NGEE ANN SECONDARY SCHOOL O PRELIMINARY EXAMINATION MATHEMATICS 4052/01 Paper 1 27 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class 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 the 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 π, use either your calculator value or 3.142. For Examiner’s Use Total /90 Checked by student: ………………………………. Date: ………………… This document consists of 25 printed pages and 1 blank page.

2 NAS/2025/Prelim/MA-O/P1 Mathematical Formulae Compound interest Total amount = 1 100 n rP+ Geometry and Measurement Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of a triangle ABC = C absin2 1 Arc length = θr , where θ is in radians Sector area = 21 2 r θ , where θ is in radians Trigonometry C c B b A a sin sin sin= = 2 22 2 cosa b c bc A=+− Statistics Mean = f fx ∑ ∑ Standard deviation = 22fx fx ff ∑∑ −∑∑ 

3 NAS/2025/Prelim/MA-O/P1 Answer all the questions. 1 Represent the inequality 2.5 6 x− ≤< on the number line below. [1] 2 Solve 8 96x− −= . Answer x = …………………………… [1] 3 The number of pandas in the world increased from 2410 in 2018 to 2660 in 2024. The number increased by r% each year. Find the value of r. Answer r = …………………………… [2] 6 5 4 3 2 1 0 1− 2− 3− 4− x

4 NAS/2025/Prelim/MA-O/P1 4 (a) Calculate 3 18.73 9.85 12.07 − . Write your answer correct to 5 significant figures. Answer ……………………………… [1] (b) Write your answer to part (a) in standard form. Answer ……………………………… [1] 5 James has 600 one-centimetre cubes. He arranges all the cubes into a cuboid such that the base area of the cuboid is a square. Find the smallest possible height of the cuboid. Answer ……………………………… [2]

5 NAS/2025/Prelim/MA-O/P1 6 The accurate pie charts show how a family spent their annual income in 2023 and 2024. (a) The family’s annual income in 2023 was $160 000. Find the amount of money the family spent on food in 2023. Answer $…………………………… [2] (b) ‘The family spent more money on food in 2024 than in 2023.’ Explain why this statement might be false. …………………………………………………………………………………….. …………………………………………………………………………………….. ……………………………………………………………………………….......... [1] Food Food Education Education Leisure Leisure Others Transport Transport Others 2023 2024

6 NAS/2025/Prelim/MA-O/P1 7 (a) Expand and simplify ( )( )52 34xy xy− − −+ . Answer ……………………………… [2] (b) Factorise completely 29 12 28 21ab ac bc b−+− . Answer ……………………………… [2] 8 (a) The equation of a straight line is 2 36yx= − . Find the gradient of the line. Answer ……………………………… [1] (b) Another line has gradient 3− and passes through the point ( )0, 1 . Explain why this line will not intersect the line in part (a). …………………………………………………………………………………….. …………………………………………………………………………………….. ……………………………………………………………………………….......... [2]

7 NAS/2025/Prelim/MA-O/P1 9 The quadrilateral ABCD is made up of two triangles, triangle ABC and triangle BCD. AB = 3 cm, AC = 4 cm, BD = 2 cm, CD = 3 cm and angle ABC = 90°. (a) Find the length of BC. Answer ……………………………cm [2] (b) Is triangle BCD right-angled? Show your working clearly. Answer [1] A B C D 4 3 2 3

8 NAS/2025/Prelim/MA-O/P1 10 Simplify 2 3 4 19 30 32 50 xx xx +− − . Answer ……………………………… [3] 11 Solve 231 13 23 xx x −− −= − . Answer ……………………………… [3]

9 NAS/2025/Prelim/MA-O/P1 12 The diagram shows a shape made from a regular pentagon and a regular octagon. Find the sum of the angles a, b and c. Answer ……………………………… [3] a b c

10 NAS/2025/Prelim/MA-O/P1 13 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. A ball falls 320 metres in the first 8 seconds. How long does it take for the ball to fall 80 metres? Answer ……………………………s [2]