2025 CCHY E.Math Prelim P2 QP + MS

* 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over 2025 Preliminary Examination Secondary Four Express / Five Normal Academic CANDIDATE NAME FORM CLASS / SUBJECT GROUP / INDEX NUMBER MATHEMATICS 4052/02 Paper 2 19 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on 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 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. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. 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 signifi cant figures. Give answers in degrees to one decimal place. For π , use either your calculator value or 3.142. This document consists of 20 printed pages. Question Number Marks Possible Marks Obtained 1 11 2 9 3 11 4 9 5 8 6 9 7 12 8 12 9 9 Presentation Deduction – 1 / – 2 TOTAL 90 CHUNG CHENG HIGH SCHOOL (YISHUN)

2 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over Mathematical Formulae Compound Interest Total amount 1 100 n rP= + Measurement Curved surface area of a cone πrl= 2Surface area of a sphere 4 πr= 21Volume of a cone 3 πr h= 34Volume of a sphere 3 πr= 1Area of triangle sin 2ABC ab C= , where is in radiansArc length rθθ= 2 , where is in radians1Sector area 2 r θθ= Trigonometry sin sin sin abc ABC= = 2 22 2 cos Aa c bcb += − Statistics Mean fx f= ∑ ∑ 22 Standard deviation fx fx ff  = −  ∑∑ ∑∑

3 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over 1 (a) Solve the equation 2 05 32x x+ =− by completing the square. Give your solutions correct to 2 decimal places. Answer x = ……………… or ……………… [3] (b) Write as a single fraction in its simplest form 2 25 42 x xx +−− . Answer ………………………………… [3]

4 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over (c) Solve the inequalities 5 3 2 21x xx+≤+ < − . Answer ………………………………… [3] (d) Simplify 3 12 4 8 256x y −   . Answer ………………………………… [2]

5 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over 2 (a) Which of the graphs shown above could be the graph of (i) 2xy= , Answer Figure……………………… [1] (ii) 2 3 xy = , Answer Figure……………………… [1] (iii) 1=+ yx ? Answer Figure……………………… [1] Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6

6 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over (b) (i) Complete the table of values for 2 49 4 xyx = − . x 0 2 4 6 8 10 12 y 0 96 180 264 240 156 [1] (ii) On the grid, draw the graph of 2 49 4 xyx = − for 0 12x≤≤ . [3] (iii) The line 120,y kx= + where k is a constant, is a tangent to the curve. By drawing a suitable straight line on the graph, find the value of k. Answer k = ......................................... [2] 280 200 160 120 80 40 0 240 2 4 6 8 10 12 x y

7 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over 3 (a) A packet contains a large number of flower seeds that produce white, yellow or red flowers. Half of the seeds produce white flowers and one third produce yellow flowers. The remainder of the seeds produce red flowers. (i) Two seeds are chosen at random. Find the probability that (a) one will produce a yellow flower and one will produce a white flower, Answer ………………………………… [2] (b) neither will produce a red flower. Answer ………………………………… [2] (ii) Three seeds are chosen at random. F ind the probability that at most two seeds will produce white flowers. Answer ………………………………… [2] (iii) Given that n seeds are chosen at random, find the probability that all the seeds will produce red flowers. Answer ………………………………… [1]

8 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over (b) The stem and leaf diagram below shows the marks attained by 23 students in Class X for a Science quiz. 1 5 6 8 9 9 9 2 0 0 1 1 2 3 4 7 3 3 4 4 5 6 8 4 0 1 2 Key : 1 | 5 means 15 marks (i) Using the data given, find the median mark. Answer ............................. marks [1] (ii) The box-and-whisker plot shows the distribution of the results of students in Class Y for the same Science quiz. Marks Find the interquartile range. Answer ............................. marks [1] (iii) Make two comparisons of the performance of the two classes X and Y for the Science quiz. 1. ………..………………………………………………………………………. [1] …………..………………………………………………………………………. [1] …………..………………………………………………………………………. [1] 2. ………..………………………………………………………………………. [1] …………..………………………………………………………………………. [1] …………..………………………………………………………………………. [2]

9 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over 4 In the diagram, O is the centre of a circular picture ACBQ of radius 20 m. APB is an arc of a circle centre C and radii AC and BC. COQ is a diameter of the circular picture ACBQ. COQ bisects AB at M. If angle ACB = 1.4 radians, (a) show that AC is approximately 30.594 m, Answer [3] (b) calculate the perimeter of the shaded region, Answer ………………………………… m [3] (c) calculate the total cost of painting the sector OAQB if the painting cost is $0.50 per square metre. Answer $ ................................................ [3]

10 2025 Prelim Mathematics / 4052/02 / Sec 4E5N [Turn_over 5 Salim owns three cafes A, B and C which sell burgers and salad. The cafes operate 7 days a week. The sales on a weekend are on average half of that on a weekday. (a) Suggest a reason why sales on a weekend are lower than sales on a weekday. ………………..……………………………………………………………………….. [1] ………………..……………………………………………………………………….. [1] The matrix, F, show the average number of food items that are sold on a weekday. Burger Salad 120 11 Cafe A 12 135 Cafe B 80 92 Cafe C  = F (b) Evaluate the matrix 6=WF . Answer =W ......................................... [1] (c) In all of his three cafes, each burger costs $12 and each plate of salad costs $8. Represent the costs of the food items in a 21× column matrix C. Answer =C ......................................... [1] (d) Evaluate the matrix R = WC. Answer =R ......................................... [2]