YCKSS EM PRELIM QP 2025 P2

Name: Index Number: Class: YIO CHU KANG SECONDARY SCHOOL O-LEVEL PRELIMINARY EXAMINATION 2025 SECONDARY FOUR EXPRESS SECONDARY FIVE NORMAL (ACADEMIC) MATHEMATICS 4052/02 Paper 2 2 hours 15 minutes Additional Materials: Nil 1 September 2025 (Monday) READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Candidates answer on Question Paper. Write your name, class and index number on the cover sheet. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 the calculator value or 3.142, unless the question requires the answer in terms of  . 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 90 Setter: Mdm Annie Mathews This document consists of 19 printed pages and 1 blank page.

2 O-LEVEL PRELIMINARY EXAM 2025 4052/02 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of sphere = 4r2 Volume of cone = hr 2 3 1 Volume of sphere 3 3 4 r Area of AcbABC sin2 1= Arc length = r  , where  is in radian Sector area = 2 2 1 r , where  is in radian Trigonometry sin sin sin a b c A B C== Abccba cos2222 −+= Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 O-LEVEL PRELIMINARY EXAM 2025 4052/02 1 (a) Find all the prime numbers that satisfy the inequality 5 2 3 7.x−  −  Answer ............................................. [3] (b) Simplify 3 3 5 2 3 18 3 .5 10 c d c d ff  Answer ............................................. [2] (c) Simplify 3 8 4 12 16 .81 y x −   Answer ............................................. [2] (d) Write as a single fraction in its simplest form ( ) 2 32 .2121 x xx − −− Answer ............................................. [2]

4 O-LEVEL PRELIMINARY EXAM 2025 4052/02 2 (a) On average, fruit seller A is able to sell 20 mangoes, 32 apples and 15 oranges in a day. On average, fruit seller B is able to sell 15 mangoes, 35 apples and 18 oranges in a day. The information can be represented by the matrix 20 32 15 .15 35 18 = F (i) Evaluate the matrix T = 5F 1 1. 1    Answer T = [2] (ii) State what each of the elements of T represents. ………………………………………………………………………………… ………………………………………………………………………….… [1] (b) Seller A sells a mango for 80 cents, an apple for 50 cents and an orange for 60 cents. Seller B sells a mango for 70 cents, an apple for 40 cents and an orange for 50 cents. (i) Represent this information in a 32 matrix C. Answer C = [1]

5 O-LEVEL PRELIMINARY EXAM 2025 4052/02 (ii) Evaluate the matrix P = FC. Answer P = [2] (iii) The cost price of all the fruits sold is $10 for each seller. Explain which seller made a higher profit. ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………..…………... [1] (c) In a promotion, both seller A and B decide to give a discount of 20% for each mango and 10% for each apple. With the use of matrix multiplication, find a 32 matrix N where each element represents the new selling price of a mango, an apple and an orange by seller A and B respectively. Answer N = [2]

6 O-LEVEL PRELIMINARY EXAM 2025 4052/02 3 (a) The diagram shows the points P(−2, −1), R(7, 17) and S(20, 3). Q is a point on PR such that SQ is perpendicular to PR. The product (gradient of ) (gradient of ) 1.SQ PR =− Use this information to find the equation of SQ. Answer ............................................ [4] y x R (7, 17) S (20, 3) P (−2, −1) Q O

7 O-LEVEL PRELIMINARY EXAM 2025 4052/02 (b) G is the point (5, 3). H is the point ( −4, h), where h > 0. The length of line GH is 15 units. Find the value of h. Answer h = ...................................... [3] (c) The y-intercept of the line 2 6 0x ky+ − = is −2. Find the value of k. Answer k = ........................................ [2]

8 O-LEVEL PRELIMINARY EXAM 2025 4052/02 4 (a) Complete the table of values for y = x 4 8 - 6x + x2 ( ) . Give your answer correct to 2 decimal places. x –1 0 0.5 1 1.5 2 2.5 3 4 5 y –3.75 0 0.75 0.47 0 –0.47 –0.75 0 3.75 [1] (b) On the grid opposite, draw the graph of y = x 4 8 - 6x + x2 ( ) for 1 5.x−   [3] (c) Use your graph to find the solution to the equation 32 6 8 12x x x− + = for 1 5.x−   Answer x = ....................................... [2] (d) (i) Line L has gradient – 0.5 and passes through the point (3, 1). Draw line L on the same axes for -1£ x £ 5 . [2] (ii) Write down the x-coordinate of the point where line L intersects the curve. Answer x = ....................................... [1] (iii) This value of x is the solution of the equation 32 0.x Ax Bx C+ + + = Find the value of A, B and C. Answer A = ........................................... B = ........................................... C = ..................................... [3]

9 O-LEVEL PRELIMINARY EXAM 2025 4052/02 1 y