NASS 2026 MA-O S4&5 Prelim P1 (QP)

Name: .............................................................. Register no: ........... Class: ........... NGEE ANN SECONDARY SCHOOL O PRELIMINARY EXAMINATION MATHEMATICS 4052/01 Paper 1 25 August 2026 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 , 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/2026/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 r h Volume of a sphere = 34 π3 r Area of a triangle ABC = Cab sin2 1 Arc length = r , where  is in radians Sector area = 21 2 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 = 22fx fx f f        

3 NAS/2026/Prelim/MA-O/P1 Answer all the questions. 1 Expand and simplify 2(3 2)(8 5 1)x x x   . Answer …………………………… [2] _____________________________________________________________________________________ 2 The box-and-whisker plot shows the waiting times, in minutes, for 60 patients at a clinic. (a) Use the box-and-whisker plot to find the median waiting time. Answer ……………………………mins [1] (b) Renee says, “There were almost twice as many patients who had waiting time less than 43 minutes as there were patients who had waiting time more than 66 minutes”. Is she correct? Give a reason for your answer. .…………………………………………………………………………………………. ………………………… …. ……………………………………………………………. …………………………………………………………………………………………. [1] _____________________________________________________________________________________

4 NAS/2026/Prelim/MA-O/P1 3 A number has exactly fifteen factors. Two of the factors are 81 and 108. Find this number. Answer …………………………… [2] _____________________________________________________________________________________ 4 The solution for the equation 3 6 5 4 5 x x k   is twice the value of k and k is a constant. Find the value of k. Answer k = …………………………… [2] _____________________________________________________________________________________

5 NAS/2026/Prelim/MA-O/P1 5 The Venn diagram shows the universal set and the number of elements in each of its subsets. Find the value of (a)   n A B A   Answer ……………………………… [1] (b)     n A B A B    Answer ……………………………… [1] _____________________________________________________________________________________ 6 Factorise completely. (a) 15π – 24πb + 3π2 Answer …………………………… [1] (b) 4x2 + 9y2 – 12xy – 64 Answer …………………………… [2] _____________________________________________________________________________________ A B 7 2 4 10 

6 NAS/2026/Prelim/MA-O/P1 7 Express as a single fraction in its simplest form 5 3( 1) 2 7 6 4 12 x x x    . Answer …………………………… [2] _____________________________________________________________________________________ 8 Six students took a Mathematics quiz and the marks were recorded. 9 11 10 14 11 10 (a) Calculate the standard deviation. Answer …………………………… [1] (b) Two other students also took the quiz and their marks were recorded. Both the mean mark and modal mark obtained by the eight students were 11. Find the marks of these two students. Answer ……………… and …………… [2] _____________________________________________________________________________________

7 NAS/2026/Prelim/MA-O/P1 9 According to World Bank data, Singapore's population was 6.037 million in 2024. In the same year, its Gross Domestic Product (GDP) was US$547.39 billion. (a) Express 547.39 billion in standard form. Answer ……………………………… [1] (b) What is the GDP per person in Singapore? Answer US$……………………………… [2] _____________________________________________________________________________________ 10 Solve these simultaneous equations. 3 5 4 7 4 22 x y x y     You must show your working. Answer x =……………………………… y =……………………………… [3] _____________________________________________________________________________________

8 NAS/2026/Prelim/MA-O/P1 11 OABC is a quadrilateral where AB and BC are tangents to a circle with centre O and radius of 6 cm. (a) Explain why angle OAB is 90°. Answer [1] (b) Calculate the shaded area. Answer ……………………………cm 2 [2] _____________________________________________________________________________________

9 NAS/2026/Prelim/MA-O/P1 12 A map has a scale of 1: 6 000 000. The distance between Malaysia and Indonesia shown on the map is 24 cm. (a) Calculate the actual distance, in kilometres, between Malaysia and Indonesia. Answer ……………………………… km [1] (b) The difference in actual area between the two countries is 1 574 722 km2. Calculate the difference in area on the map. Answer ………………………………cm 2 [2] _____________________________________________________________________________________

10 NAS/2026/Prelim/MA-O/P1 13 In triangle BCD, BC = 12 cm, CD = 16 cm and DB = 20 cm. ADC is a straight line. (a) Is BC perpendicular to CD? Show your working clearly. Answer [1] (b) Angle ADB = x° Find the exact value of cos sinx x  . Answer ……………………………… [2] ____________________________________________________________________________________ 16 cm 20 cm 12 cm A D C B