2025 Presbyterian HS MA Prelim P1 QP + MS

Name: Index No.: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4052/01 PAPER 1 19 August 2025 Tuesday 2 hours 15 minutes PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2025 SECONDARY FOUR EXPRESS / FIVE NORMAL PRELIMINARY EXAMINATION DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. INSTRUCTIONS TO CANDIDATES: Write your name, index number and class on the spaces provided above. 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. 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 . Note that all the diagrams in this paper are not drawn to scale. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. For Examiner’s Use Category Accuracy Notations Others Marks Deducted Question No. Setter: Mr Tan Chee Wee Vetter: Ms Ong Bi Ru This question paper consists of 23 printed pages (including this cover page) and 1 blank page. Total Marks 90

2 Mathematical Formulae Compound Interest Total amount = nrP      + 1001 Mensuration Curved surface area of a cone = lr Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cab sin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == 2 2 2 2 cosa b c bc A= + − Statistics Mean =   f fx Standard deviation = 22      −     f fx f fx

3 Answer all the questions. 1 Calculate 23 7.927.38 0.021− . Answer …….……………………….. [1] 2 Simplify (a) 6154 yy − , Answer ……………….……………… [1] (b) 5 7 9 3 2x x x− − + − . Answer …………………….………… [1]

4 3 (a) Expand and simplify ( )( ) 22 1 3p p p+ + − . Answer …..….…………………… [2] (b) Write as a single fraction in its simplest form ( ) 2 31 5252 xx − −− . Answer …..….…………………… [2]

5 4 (a) Express 504 as a product of its prime factors. Answer ……….……………………… [1] (b) Find the smallest positive integer value of k such that 3 504k is an integer. Answer k = …….…………………… [1] (c) The highest common factor (HCF) of two numbers is 84. The lowest common multiple (LCM) of the two numbers is 504. Both numbers are more than 100. Find the two numbers. Answer …..….… and …………… [2]

6 5 It is given that x pencils cost y dollars and 4 cents. (a) Find the cost of one pencil in cents. Answer …………………………cents [1] (b) Write down an expression for the number of pencils that could be bought for t dollars. Answer …………………….………… [1] 6 Given that 11:: 65AB = and : 3: 7BC = , find :AC as a ratio of two integers. Answer …….…….. : .…………….. [2]

7 7 Find the smallest integer that satisfies 6 3 17.y− Answer …………….………………… [2] 8 The force F, between two particles is inversely proportional to the square of the distance between them. The force is 64 units when the distance between the particle s is r metres. Find the force when the distance between the particles is reduced by 20%. Answer ………….………….units [2]

8 9 The distance between Earth and Venus is 150.4 million kilometres. (a) Express 150.4 million in standard form. Answer ………….…………………… [1] (b) A space shuttle can travel 7500 metres in 1 second. (i) Find the speed, in kilometres per hour, of the space shuttle. Answer ………….……………km/h [1] (ii) Find the number of days the space shuttle will take to travel from Earth to Venus. Give your answer to the nearest whole number. Answer ………….………………days [2]

9 10 Given that 335 2 cac b −+= , make c the subject of the equation. Answer ……………….…………….. [3] 11 The scale of a map is given as 1: 50000. (a) A road on the map is 16 cm long. Find the actual length of a road in kilometres. Answer ……………….……………..km [1] (b) A lake has an area of 40 km2. Find the area of the lake on the map in square centimetres. Answer ……………….……..… cm2 [2]

10 12 The frequency table shows the masses of 50 students from Class A. Mass (m kg) 20 30m 30 40m 40 50m 50 60m 60 70m Frequency 2 11 20 12 5 (a) Calculate the mean mass of the students from Class A. . Answer …………………………kg [1] (b) Calculate the standard deviation for the mass of students in class A. . Answer …………………………kg [1] (c) Explain why the value of the mean calculated in part (a) is only an estimate. Answer …………………….…………………………………...……………………………………………..… ………………………………………………………………………………………………………..… ………………………………………………………………………………………………………….. [1]