4E5N PCSS EM P1 Prelim 2026 (solution for students)

[Turn over PEICAI SECONDARY SCHOOL SECONDARY 4 EXPRESS / 5 NORMAL ACADEMIC PRELIMINARY EXAMINATION 2026 CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS 4052/01 Paper 1 17 August 2026 2 hours 15 minutes Candidates answer on Question Paper READ THESE INSTRUCTIONS FIRST Write your register number, class and name 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 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 𝜋, use either your calculator value or 3.142, unless the question requires the answer in terms of 𝜋. 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 This document consists of 20 printed pages. Setter: Mr Chua JK

2 Mathematical Formulae Compound Interest Total Amount 1 100 n rP=+  Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where θ is in radians Sector area = 21 2 r  , where θ is in radians Trigonometry sin sin sin a b c A B C== Abccba cos2222 −+= Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

[Turn over 3 Answer all questions 1 (a) Write down the first 6 digits of ( ) 3 2 2 2.56.7 −− shown on the calculator. Answer ………………………… [1] (b) Round off your answer in (a), to 3 decimal places. Answer ………………………… [1] 2 Simplify 22 22 10 23 99 29 x xy y x y xy −− − . Answer ………………………… [3] 3 Given that ( ) 0 5 6 7 31xx+= , find the value of x. Answer x = ……………………… [2]

4 4 Jayden deposited some money in a bank that pays a compound interest of 2.2% per annum, compounded half yearly. After 3 years, Jayden withdrew a total of $40 000. Calculate the amount of money deposited by Jayden, correct to the nearest dollar. Answer $ ……………………… [2] 5 1sin 0.1232 x = Find two possible values of x in the range 0 360x . Answer x =…………… or x =…………… [2] 6 The curve below has an equation ny x c=+ . State a possible value of n and the value of c. Answer n = ……………………... [1] c = ……………………… [1] y x 0

[Turn over 5 7 (a) Express 2 4 10xx+− in the form 2()x p q++ . Answer ………………………… [1] (b) Sketch the graph of 2 4 10y x x= + − on the axes below. Indicate clearly the coordinates of the turning point and the value of the y-intercept. [2] 8 A bag contains 10 red pens and 6 black pens. Two pens are chosen from the bag at random without replacement. Fred claims that the probability that one pen is a red pen and one pen is a black pen can be calculated using 10 6 1 16 15 4    =     . Explain why Fred’s claim is not true and find the actual probability. Answer ………………… because …………………………………………..…..…… ……………………………………………………………………………….. [2] x y O

6 9 Written as a product of its primes factors, 3272 2 3= . (a) The number 72 45 p q is a perfect square where p and q are prime numbers. Find the smallest value of p q . Answer p =…………… or q =…………… [2] (b) Given that the highest common factor of 72 and m is 223 , write down the two smallest possible value of m. Answer m =………………………… [1] 10 In the diagram shown below, it is given that AP = 5 cm, BP = 2 cm and AR = 3 cm. ARC, ABP and RQP are straight lines. Identify and prove a pair of congruent triangles. Answer [2] B P R C Q A

[Turn over 7 11 The two containers are geometrically similar in shape. The larger container has a capacity of 3328 ml and a surface area of 1008 cm2. The smaller container has a capacity of 1404 ml. Calculate the surface area of the smaller container. Answer ……………………… cm2 [3] 12 A shopping mall car park has a total of 168 cars and motorcycles. Each car has 4 wheels and each motorcycle has 2 wheels. There were 592 wheels altogether. By forming a pair of simultaneous equations, find the number of cars. Answer ……………………… cars [3]

8 13 52 3 cab a += (a) Find b when c = 18.02 and a = 0.71. Answer b = ………………………… [1] (b) Rearrange the formula to make a the subject. Answer a = ………………………… [3] 14 (a) An AI image generator creates 63.2 10 images on one day and 55.5 10 images on the next day. Calculate the total number of images generated over the two days, leaving your answer in standard form. Answer ………………………… [1] (b) A data centre stores 129.6 10 bytes of data. Each video file has an average of 500 MB, where 1 MB = 106 bytes. Calculate the maximum number of such video files that can be stored, leaving your answer in standard form. Answer ………………………… [1]

[Turn over 9 15 (a)  = {x: x is an integer, 11 < x < 21} A = {x: x is an odd number} B = {x: x is a multiple of 3} (i) List the elements of Set A and of Set B. Answer A = {………………………………………………………} [1] B = {………………………………………………………} [1] (ii) Find ( ' )n A B . Answer ………………………… [1] (b) On the Venn Diagram below, shade the set 'AB . [1] Answer 16 Factorise completely. (a) 22 6 9 16x xy y− + − Answer ………………………… [2] (b) 4 3 6 2pq r qr p+ − − Answer ………………………… [2]  A B

10 17 A map is drawn to a scale of 1 : 80 000. (a) This scale can be expressed as 1 cm represents n km. Find n. Answer n = ………………………… [1] (b) The distance between A and B on the map is 15 cm. Find the actual distance, in kilometres, between A and B. Answer ………………………… km [1] (c) A plot of land has an actual area of 10 km2. Find the area, in square centimetres, of the plot of land on the map. Answer ……………………… cm2 [2]