2026 GMS P1 MS

[Turn Over Candidate Name WORKED SOLUTIONS & SUGGESTED ANSWER SCHEME Class Index Number MATHEMATICS Paper 1 4052/01 4 Express 5 Normal (Academic) Candidates answer on the Question Paper. 2 hours 15 minutes Setter: Ms Nainee Ismail Thursday, 13 August 2026 READ THESE INSTRUCTIONS FIRST Write your class, index number 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 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 90 This document consists of 20 printed pages including the cover page. Geylang Methodist School (Secondary) Preliminary Examination 2026

GMS(S)/Math/P1/Prelim2026/4E5N/Answer Scheme 2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r 2 Volume of a cone = 1 3 r 2h Volume of a sphere = 4 3 r 3 Area of triangle ABC = 1 2 ab sin C Arc length = r, where  is in radians Sector area = 1 2 r 2, where  is in radians Trigonometry sin sin sin a b c A B C== a 2 = b 2 + c 2 – 2bc cos A Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

GMS(S)/Math/P1/Prelim2026/4E5N/Answer Scheme 3 [Turn Over Answer all the questions. 1 Simplify 14 3 2 123 xxx− + − + − . Answer ……………………………………… [2] 2 A range of values for x is represented on the number line below. Write down the smallest integer value of x. Answer ……………………………………… [1] 3 Ann’s monthly salary is $5000. She spends 60% of her salary and saves the rest. Bob’s monthly salary is $7500. He spends $4125 and saves the rest. (a) Find the amount that Ann spends every month. Answer $ …………………………………… [1] (b) Who saves a higher percentage of their monthly salary? Justify your answer with workings. Answer [2] 14 3 2 123 xxx− + − + − 1 9 4 3212 3 3 3 x x x= + − − − + 3 10 23 x=− 3 10 23 x− Amount Ann spent = 60% × $5000 = $3000 3000 % saved (Ann) = 100% – 60% = 40% % saved (Bob) 7500 4125 100%7500−= 45%= % saved (Bob) 45% > % saved (Ann) 40% Bob saves a higher percentage. – 2 –5 – 4 –3 –2 –1 x

GMS(S)/Math/P1/Prelim2026/4E5N/Answer Scheme 4 4 (a) Written as a product of its prime factors, 4725 = 3x × 52 × 7y. Find the values of x and y. Answer x = …………… , y = …………… [2] (b) Written as a product of its prime factors, 3 4 2178200 2 3 5 11=    . Find the smallest positive integer k such that 178200 k is a square number. Answer k = ………………………………… [1] (c) 17 11 72 3 5S =   . 13 11 92 3 5T =   . Find the highest common factor (HCF) of S and T as a product of its prime factors. Answer ……………………………………… [1] 5 Factorise completely. (a) 10ac – 6bc – 5ad + 3bd Answer ……………………………………… [2] (b) 6x2 – 9xy – 6y2 Answer ……………………………………… [2] 24725 3 5 7xy=   4725 3 25 7 4725 3725 3 7 189 xy xy xy =   =   = 313 7 189= 22 10ac – 6bc – 5ad + 3bd = 2c (5a – 3b) – d (5a – 3b) = (5a – 3b) (2c – d ) (5a – 3b) (2c – d ) 6x2 – 9xy – 6y2 = 3 (2x2 – 3xy – 2y2) = 3 (2x + y) (x – 2y) 3 (2x + y) (x – 2y) By Prime Factorisation, 3 189 3 63 3 21 7 7 1 3 1 3 4 2 2 4 2 2 4 2 178200 2 3 5 11 178200 2 2 3 5 11 178200 2 3 52 11 =    =     =   2 4 2178200 2 3 522 =   (square number) 22k = 172S = 113  75 T = 132  113  95 13 11 72 3 5HCF =   13 11 72 3 5

GMS(S)/Math/P1/Prelim2026/4E5N/Answer Scheme 5 [Turn Over 6 A map of Singapore has a scale of 1 : 4 000 000 . (a) The scale can be written in the form 1 cm : n km. Find the value of n. Answer n = ………………………………… [1] (b) The area of Changi Airport is approximately 24 km2. Calculate the area, in square centimetres, of Changi Airport on the map. Answer ………………………………… cm2 [2] 7 Expand ( )( ) 235 16 3 4 8x x x+ − − . Answer ……………………………………… [2] 1 : 4 000 000 1 cm : 4 000 000 cm 40 1 cm : 40 km 1 cm2 : 402 km2 1 cm2 : 1600 km2 1 1600 cm2 : 1 km2 3 200 or 0.015 1 241600  cm2 : ( )1 24 km2 3 200   cm2 : 24 km2 OR 0.015 cm2 : 24 km2 1 cm : (4 000 000  100) m 1 cm : (40 000  1000) km 1 cm : 40 km 1 cm : n km  4 8x− 35 140 –280x 16x 64x –128x2 23x− –12x2 24x3 ( )( ) 235 16 3 4 8x x x+ − − 2 2 3140 280 64 128 12 24x x x x x= − + − − + 23140 216 140 24x x x= − − + 23140 216 140 24x x x− − +

GMS(S)/Math/P1/Prelim2026/4E5N/Answer Scheme 6 8 A printout of the Circle Line MRT map includes all the stations inside the circle and on its boundary, as shown in the diagram. (a) Based on the printout above, measure the bearing of Paya Lebar station from Dhoby Ghaut station. Answer ……………………………………… [1] The total length of the Circle Line railway track is approximately 36 km, excluding the section from Dhoby Ghaut station to Promenade station. A student sketched a simplified map of the Circle Line, showing only the stations on the circle, and made the following assumptions. (b) Assumption 1: In the sketch, an angle of 10° at the centre of the circle represents an arc length of 1 km on the Circle Line. Explain with mathematical justifications, why this assumption will result in an accurate sketch of the map. ………………………………………………………………………………………… ………………………………………………………………………………………… [1] (c) Assumption 2: The arc length between any 2 consecutive stations on the map is equal. Explain why this assumption may result in a misleading representation of the Circle Line. ………………………………………………………………………………………… ………………………………………………………………………………………… [1] Based on the concept of arc length, subtended angle of 360° at the centre represents 36 km, hence 360 1036 km = at the centre of the circle measures an arc of 1 km. If arc length between 2 stations is all equal, this suggests on the scale that the stations are all equidistant from each other but in reality, this may not be true. Actual Measurement (with protractor) 070° ± 1° × × Dhoby Ghaut North N 070° (±1°) Paya Lebar Promenade

GMS(S)/Math/P1/Prelim2026/4E5N/Answer Scheme 7 [Turn Over 9 Cyn and Don shared an amount of money. The ratio of Cyn’s share to Don’s share is 5 : 7 before Don gave $36 to Cyn. The ratio of Cyn’s share to Don’s share is now 7 : 8. What is the total amount of money Cyn has now? Answer $ …………………………………… [2] 10 The price of a bicycle increased by 7% from 2023 to 2024, then decreased by 5% from 2024 to 2025. Calculate the price of the bicycle at the end of 2025 as a percentage