2025 GDLSS P1 QP

Name:____________________________ ( ) Class:________ TG : _______ This document consists of 23 printed pages, including this cover page. Greendale Secondary School 2025 GREENDALE SECONDARY SCHOOL Preliminary Examination 2025 MATHEMATICS 4052/01 Paper 1 13 August 2025 Secondary 4 EXP / 5 N(A) 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name in the spaces 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 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  , 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. Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Strand Marks Question Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Strand Marks 90

Greendale Secondary School 2 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curve surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry C c B b A a sinsinsin == a2 = b2 + c2 – 2bc cos A Statistics Mean =   f fx Standard deviation = 22 −  ffxffx

Greendale Secondary School 3 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 Answer all questions. 1 A piece of cloth 1.95 m is cut into three pieces in the ratio 8 : 1 : 4. Find the difference in length between the longest and the shortest piece. Answer ………………………… m [2] 2 (a) The area of a triangle ABC is 124.7 cm2. 25.6 cmAB= and 17.2 cmBC= . Find the two possible sizes of the angle ABC. Answer …………………… or …………………… [2] (b) Convert 127 into radians. Answer ………………………… radians [1]

Greendale Secondary School 4 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 3 (a) Simplify ( ) 253xy . Answer …………………………… [1] (b) 504 3 4 243 3 m −  = Use the laws of indices to find the value of m. Show your working. Answer m =………………………… [2] 4 (a) 3rM p q=   where p and q are prime numbers, r is a positive integer and r >1. Find the smallest possible value of r if 66 M is a perfect cube. Answer r =………………………… [1] (b) 522 3 5X =   and Y a b= where a and b are integers between 20 and 30. The highest common factor (HCF) of X and Y is 235m . The lowest common multiple (LCM) of X and Y is 522 3 5 7   . Express Y as a product of prime factors and find the value of m. Answer Y =…………………………….. m =………………………… [2]

Greendale Secondary School 5 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 5 Alvin intends to borrow $8000 from a finance company at a rate of 0.375% per month compound interest for 2 years. He claims that the interest will be lower than that of a bank which charges 4.5% per annum compound interest for 2 years. Determine if Alvin’s claim is correct. Show your working clearly. Answer [3]

Greendale Secondary School 6 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 6 The expression 2 5x px−− is equivalent to ( ) 2 6xq−− . (a) Find the value of p and the value of q. Answer p = …………………………… q = ………………………… [2] (b) The graph of 2 5y x px= − − is drawn. Write down the equation of the line of symmetry of the curve. Answer …………………………… [1]

Greendale Secondary School 7 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 7 The diagram shows speed-time graphs for two vehicles, A and B, travelling along the same road in the same direction and starting at the same point. A decelerates from a speed of v km/h for 6 minutes, then travels at a constant speed of 50 km/h for 4 minutes and decelerates to 5 km/h. B accelerates for t minutes from rest. (a) Given that the deceleration of A in the first 6 minutes is 250 km/h 2, show that v = 75. Answer [2] (b) Given that the distance travelled is given by the area under the speed -time graph, find the value of t if B overtakes A after t minutes. Answer t =………………………… [3] Speed (km/h) Time (minutes) v 80 50 0 t 6 10 A B 5

Greendale Secondary School 8 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 8 The cumulative frequency curve shows the time taken by 120 students to complete a Mathematics quiz. (a) 1 6 of the students took more than n minutes to complete the quiz. Find n. Answer n =………………………… [1] (b) Complete the cumulative frequency table. [1] Time (t minutes) Frequency 5 10t 4 10 15t 15 20t 20 25t 62 25 30t 14 0 5 10 15 20 25 30 20 40 60 80 100 120 Cumulative frequency Time (t minutes)

Greendale Secondary School 9 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 (c) Find the estimated (i) mean timing of the students, Answer ………………………… minutes [1] (ii) standard deviation of the timing. Answer ………………………… minutes [1] (d) Use the diagram to estimate the median timing of the students. Answer ………………………… minutes [1] (e) Another group of 120 students took the same Mathematics quiz. The median timing is the same but has a larger standard deviation. Describe how the cumulative frequency curve for this group of students will differ from the first group of students. Answer ……………………………………………………………………………... …………………………………………………………………………... [1]

Greendale Secondary School 10 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 1 9 Ally travels from Singapore to Australia. She wants to change 800 Singapore dollars ($) into Australian dollars (A$). She would receive A$5 more if she changes the money in Singapore. The exchange rate in Australia is A$1 = $0.8323. Calculate the exchange rate in Singapore. Give your answer in Australian dollars per Singapore dollar. Answer $1 = A$…………………… [2] 10 The coordinates of the point P are ( 7,7)− . Line q passes through point P and has a gradient of 3 7− . Show that the equation of line q is 7 3 28yx+= . Answer [2]