Northbrooks 4E5N E Math 2026 Prelim P1 QP

O NORTHBROOKS SECONDARY SCHOOL Preliminary Examination 2026 Secondary 4 and 5 CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS 4052/01 Paper 1 Select a time zone. 17 August 2026 2 hours 15 minutes Candidates answer on the Question Paper. 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 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 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO. This document consists of 22 printed pages. [Turn Over  90

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 a2 = b2 + c2 – 2bc cos A Statistics Mean = Standard deviation = n rP      + 1001 lr 24 r hr 2 3 1 3 3 4 r Cba sin2 1 r  2 2 1r  C c B b A a sinsinsin ==   f fx 22       −     f fx f fx

3 Answer all the questions. 1 There are 1000 people in an auditorium, correct to the nearest hundred. State the minimum number of people that could be in the auditorium at this time. Answer ……………………………… [1] 2 Miss Wong invests $55000 at rate of 1.8% per annum compounded half yearly. She leaves the money in the account for 2 years. Calculate the value of her investment at the end of 2 years. Answer $ …………………………… [2] 3 A cuboid has a volume of 1008 cm3. The area of the largest face is 144 cm2. The dimensions of the cuboid have integer values. Find a possible set of dimensions of the cuboid. Answer ………… cm by ………… cm by ………… cm [2] [Turn Over

4 4 The diagram shows a quadrilateral CDEF. (a) Construct the perpendicular bisector of EF. (b) Construct the bisector of angle CDE. (c) A point P is inside the quadrilateral. It is nearer to F than E and is nearer to CD than DE. Shade the region where P could be. [1] [1] [1] C D E F

5 5 Six workers take two days to complete building a structure. Assuming all the workers work at the same efficiency, find (a) the number of workers needed to complete building the structure in 3 days, Answer ……………………………… (b) the number of structures that can be completed by 36 men in 5 days. Answer ……………………………… [1] [2] 6 From 2022 to 2025, the mean Singapore’s Certificate of Entitlement (COE) price for small cars (1600 cc) increased by 35.2%. From 2022 to 2023, the mean COE price increased by 25.4%. From 2023 to 2024, the mean COE prices decreased by 5.05%. Calculate the percentage increase in the mean COE price from 2024 to 2025. Answer …………………………… % [3] [Turn Over

6 7 The accurate pie charts show the sales of shirt design by colours in Outlet A and Outlet B in a particular month. (a) “The number of blue shirts sold in Outlet A is less than the number of blue shirts sold in Outlet B.” Explain why this statement might be false. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. (b) Find the percentage of the black shirts sold in Outlet A. Answer …………………………… % [1] [2] Outlet B White Blue Black Others Outlet A Black White Blue Others

7 8 The diagram shows a card which consists of a square PQRS of sides 10 cm and four identical isosceles triangles. In triangle BQR, BX is perpendicular to QR and BX = 13 cm. The card is folded to form a right pyramid with PQRS as base and A, B, C and D meeting at the vertex. Calculate (a) the height of the pyramid, Answer ………………………..… cm (b) the volume of the pyramid. Answer ……………………….… cm3 [2] [2] P S Q R A C B D 10 13 X [Turn Over

8 9 (a) Simplify 43 5 28 21 p q q x px . Answer ……………………………… (b) Factorise completely 15ab – 3ac – 5b + c. Answer ……………………………… [2] [2] 10 The diagram shows a sketch of a quadratic curve. The line of symmetry is x = 1. Find the value of p and the value of q. Answer p = ….…… , q = …..…… [2] y x –3 p q

9 11 351 12 ca c=+− (a) Find a when c = – 7 . Answer a = ……….……………..… (b) Rearrange the formula to make c the subject. Answer c = ……….……………..… [1] [3] [Turn Over

10 12 Triangle PQR is a right-angled triangle. S is a point on PR such that QS = QR. T is a point on PQ such that PT = ST. Angle PST = x. Show that angle RQS = 2x. Give a reason for each step of your working. Answer [3] P R C Q T S x C