YCKSS EM PRELIM QP 2025 P1

Name: Index Number: Class: YIO CHU KANG SECONDARY SCHOOL O-LEVEL PRELIMINARY EXAMINATION 2025 SECONDARY FOUR EXPRESS SECONDARY FIVE NORMAL (ACADEMIC) MATHEMATICS 4052/01 Paper 1 2 hours 15 minutes 1 September 2025 (Monday) 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. DO NOT WRITE ON ANY BARCODES. 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. Gives answers in degrees to one decimal place. For π, use either your calculator value or 3.142. For Examiner’s Use 90 Setter: Mr Tan Thiam Boon This document consists of 19 printed pages and 1 blank page.

2 4E PRELIMINARY EXAM 2025 4052/01 Mathematical Formulae Compound interest Total Amount = P( Mensuration Curved surface area of a cone = rl Surface area of sphere = 4r2 Volume of cone = Volume of sphere Area of Arc length = r , where is in radian Sector area = , where is in radian Trigonometry Statistics Mean = Standard deviation = nr )1001+ hr 2 3 1 3 3 4 r AcbABC sin2 1=   2 2 1 r  sin sin sin a b c A B C== Abccba cos2222 −+=   f fx 2 2 ][     − f fx f fx

3 4E PRELIMINARY EXAM 2025 4052/01 Answer all the questions. 1 Simplify ( )5 4 3 2 6p p p− − + + − . Answer …….......……...……......…….... [2] 2 (a) Write down the inequalities that represent the numbers indicated on the number line. Answer …….......……...……......…….... [1] (b) State the smallest prime number that satisfies the number line shown. Answer …….......……...……......…….... [1] 3 Express as a single fraction in its simplest form ( )713 2 5 3 12 8 6 xxx +−− −− . Answer …….......……...……......…….... [3] 3 4 5 x 2 1 0 –1 –2

4 4E PRELIMINARY EXAM 2025 4052/01 4 The box-and-whisker plot gives information about the marks of 40 students in a class who sat for a Mathematics examination. (a) Use the box-and-whisker plot to find the median mark. Answer …….......……...……......…….... [1] (b) Layla says, “There are twice as many students who scored more than 35 marks as those who scored less than 35 marks”. Is Layla correct? Give a reason for your answer. ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………… [1] 5 Factorise. (a) 2224 15 9pq pq p q+− Answer …….......……...……......…….... [1] (b) 25 2 5 2a bc ac ab+ − − Answer …….......……...……......…….... [2] Marks 30 40 50 60 20 70

5 4E PRELIMINARY EXAM 2025 4052/01 6 A map of Singapore has a scale of 1 : 125000. (a) The length of the longest river in Singapore, Kallang River, is 10 km. Calculate the length of Kallang River on the map. Answer …….......……...…………… cm [2] (b) The area of Pulau Ubin island on the map is 6.56 cm2. Calculate the area, in square kilometres, of Pulau Ubin island. Answer …….......……...…………… km2 [2] 7 In this sequence, the difference between any two consecutive terms is the same number. w x y 23 z … The sum of the first five terms is 80. Find the values of w, x, y and z. Answer w = ………… x = ………… y = ………… z = ………… [2]

6 4E PRELIMINARY EXAM 2025 4052/01 8 The diagram shows the coverage of a car windscreen wiper ABCD. AB and DC are arcs of circles centre O with radii 28 cm and 44 cm respectively. The perimeter of ABCD is 72π – 76 cm. (a) Calculate angle AOB in radians, leaving your answer in terms of π. Answer …….......……...……......…….... [2] (b) Calculate the area of the windscreen that the car wiper wipes through. Answer …….......……...…………… cm2 [2] O A B D C 28 44

7 4E PRELIMINARY EXAM 2025 4052/01 9 A, B, C and D are four points on horizontal ground. AC = 12 km and BC = 5 km. (a) Calculate angle ACD. Answer angle ACD = …….......……...  [2] (b) Find the bearing of A from C. Answer …………………….......…….  [1] A 12 B C D 5 North

8 4E PRELIMINARY EXAM 2025 4052/01 10 The cumulative frequency curve shows the marks of 400 pupils who sat for a Mathematics Paper 1 examination. (a) Use the diagram to find (i) the interquartile range of the marks, Answer …….......……...……......…….... [2] (ii) the 35th percentile. Answer …….......……...……......…….... [1] (b) One of the students is chosen at random. Find the probability that this student’s estimated mark is between 42 and 78. Answer ..…………...…………….....…. [2]

9 4E PRELIMINARY EXAM 2025 4052/01 11 2 2 xyPw w=− (a) Find P when w = 86.3, x = 21.41 and y = 0.872. Give your answer correct to 4 significant figures. Answer P = ....……...……......…….... [1] (b) Rearrange the formula to make x the subject. Answer x = ....……...……......…….... [3] 12 The diagram shows a triangle ABC such that AB = 26 cm, BC = 10 cm and AC = 24 cm. When a circle is drawn, it passes through A, B and C. Explain, with reasons, why AB is the diameter of the circle. …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… ……………………………………………………………………………………………… [3] 10 cm 26 24 B C A

10 4E PRELIMINARY EXAM 2025 4052/01 13 Solve the simultaneous equations. 8 3 25 12 5 9 xy xy −= += You must show your working. Answer x = ………… y = ………… [3] ___________________________________________________________________________________ 14 Sketch the graph of ( ) 2 2 16yx=− − + on the axes below. Indicate clearly the coordinates of the points where the graph crosses the axes and the maximum point on the curve. [3] ___________________________________________________________________________________ y x