CEDAR 2025 EMATH PRELIM P2 QP

CEDAR GIRLS’ SECONDARY SCHOOL PRELIMINARY EXAMINATION 2025 SECONDARY FOUR CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052/02 Paper 2 22 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. 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. 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  , use either your calculator value or 3.142. For Examiner’s Use 90 This document consists of 19 printed pages and 1 blank page. [Turn over]

2 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 2 4 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 == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 [Turn over Answer all the questions. 1 (a) Solve the inequality 211 4 0 2 yy −+   . Answer ………………………………… [2] (b) Solve ( ) 41 1 3 5xx− − − = . Answer x = ………. and x = ………. [3]

4 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 (c) (i) Given that 56243 2 6p p p −= , find the value of p . Answer p = ……………...…………… [2] (ii) Simplify 3 4 2 5 8 16 p pqq −   and leave your answer in positive index notation. Answer ………………………………… [3]

5 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 [Turn over 2 (a) The diameter of a red blood cell is 68.2 10 − m. Express this value as a decimal, in millimetres. Answer …………………………… mm [1] (b) In 2024, Changi Airport handled 67.7 million passengers. Calculate the mean number of passengers handled by the airport each month. Leave your answer in standard form, correct to 2 significant figures. Answer ………………………………... [2] (c) LBB Bank currently charges 3% per year compound interest on all loans, compounded once every three months. The bank manager proposes to adjust the frequency of interest compounded to once every month instead, so as to increase the earnings of the bank. Do you agree with the bank manager’s proposal? Explain your answer with clear workings. Answer ……………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. [3]

6 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 3 A bakery selling assorted tarts operates for 7 days a week. The matrix, T, shows the number of tarts of different types that are made each day. Apple Banana Cheese T 55 35 70 40 30 30 = The cost of making a small tart is $0.80. The cost of making a large tart is $1.75. (a) Represent these costs in a 12 row matrix N. Answer N = [1] (b) Evaluate the matrix C = 7NT. Answer C = [2] (c) State what each of the elements of C represent. …………………………………………………………………………………………… …………………………………………………………………………………………… [1] Small Large

7 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 [Turn over (d) The tarts are sold at 55% more than the cost to make them. On a particular day, the number of banana tarts to cheese tarts sold is in the ratio 5: 7 while the number of apple tarts to banana tarts sold is in the ratio 5: 4 . A total of 41 unsold tarts were given away. If the number of small cheese tarts sold is twice the number of large cheese tarts sold, calculate the total amount earned by the bakery from selling cheese tarts on that day. Answer $ ……………………………… [3]

8 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 4 (a) The variables x and y are connected by the equation 7 2 11yx x= + − . Some corresponding values are given in the table below. Values are given to 1 decimal place where appropriate. x 0.5 1 1.5 2 3 4 5 6 6.5 y 2− 3.3− 3.5− 2.7− 1.25− 0.4 2.2 3.1 Fill in the missing value in the table. [1] (b) On the grid below, draw the graph of 7 2 11yx x= + − for 0.5 6.5x . [2] y x 1 2 0 3 4 5 6 7 1 2 3 4

9 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 [Turn over (c) By drawing a tangent, find the gradient of the curve at 2x= . Answer Gradient = …………….…….. [2] (d) Using your graph, (i) explain why the equation 72 7 0x x+ − = has no solution. Answer …………………………………………………………………………………………… …………………………………………………………………………………………… [2] (ii) find the x-coordinate of the points where the line 24yx=− intersects the curve. Answer x = ………. and x = ………. [2] (iii) These values of x are the solutions of the equation 2 14 0Ax Bx+ + = . Find the value of A and of B. Answer A = ……… , B = ……… [3]

10 Cedar Girls’ Secondary School 4052/02/S4/Prelim/2025 5 The figure shows a semi-circle AOBD with centre O and OP is perpendicular to BD. BC and CD are tangents to the semi-circle at B and D. (a) Show that triangles ABD and OBP are similar. Give a reason for each statement you make. Answer …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… [2] (b) Find the ratio area of triangle area of triangle OBP AOD . Answer ……………………………………. [2] (c) Show that angle BOD = 2.2689 radians, correct to 5 significant figures. Answer [2] A O B D C P