2026 GMS P1 QP

[Turn Over Candidate Name 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 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  −  Answer all the questions.

GMS(S)/Math/P1/Prelim2026/4E5N 3 [Turn Over 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] 4 (a) Written as a product of its prime factors, 4725 = 3x × 52 × 7y. –5 – 4 –3 –2 –1 x

GMS(S)/Math/P1/Prelim2026/4E5N 4 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] 6 A map of Singapore has a scale of 1 : 4 000 000 .

GMS(S)/Math/P1/Prelim2026/4E5N 5 [Turn Over (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]

GMS(S)/Math/P1/Prelim2026/4E5N 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] × × Dhoby Ghaut North N Paya Lebar Promenade

GMS(S)/Math/P1/Prelim2026/4E5N 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 of the price at the end of 2023. Answer …………………………………… % [3]

GMS(S)/Math/P1/Prelim2026/4E5N 8 11 The box-and-whisker plot gives information about the times, in minutes, that 160 adults spent on walking after dinner. (a) Use the box-and-whisker plot to find the interquartile range. Answer …………………………… minutes [2] (b) An article published in a health journal suggested that adults should spend at least 30 minutes walking after dinner to help in digestion. Based on the box-and-whisker plot, more than half of the adults took up the suggestion in the article. Is this statement true? Give a reason for your answer. ………………………………………………………………………………………… ………………………………………………………………………………………… [2] 12 The area of triangle XYZ is 10.3 cm2. XY is 4.2 cm and YZ is 5.7 cm. Find the two possible sizes of the angle XYZ. Answer Angle XYZ = ……………° or ……………° [3]

GMS(S)/Math/P1/Prelim2026/4E5N 9 [Turn Over 13 ABC is a triangle with A (–1, 4), 1 2OB −=−  and 8 6AC =−  . (a) Show that triangle ABC is a right-angled triangle. Answer [2] (b) Explain why it is possible to draw a circle touching points A, B and C. ………………………………………………………………………………………… ………………………………………………………………………………………… [1] (c) State the length of the radius of this circle. Answer ………………………………… units [1]

GMS(S)/Math/P1/Prelim2026/4E5N 10 14 Simplify 3 2 49 8 12 xx xx − + . Answer ……………………………………… [2] 15 (a) Write 43 as a power of 2. Answer ……………………………………… [1] (b) 0.0483 ×105 × 10–6 = m × 10–n written in standard form. Find the values of m and n. Answer m = ………………………………… [1] n = ………………………………… [1] (c) 82 = 2a + 2a + 2a + 2a. Find the value of a. Answer a = ……………………