2024 Sec 4G3 5G2 SPS Prelims P2

NAME CLASS INDEX NO. ST. PATRICK'S SCHOOL PRELIMINARY EXAMINATION 2024 SUBJECT : Mathematics (Revised) 4052/02 DATE : 14 August 2024 LEVEL : Secondary 4G3 & 5G2 DURATION : 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your Name, Class, and Index No. in the spaces at the top of this page. 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 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 𝜋, use either your calculator value of 3.142, unless the question requires the answer in terms of 𝜋. 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. Candidates answer on the Question Paper. For Examiner’s Use Type of Penalties Question Number Accuracy 1− 2− Presentation 1− 2− 90

2 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl 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 = Cabsin2 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 1. (a) Solve the inequality 3 2 1 54 xx−+  . Answer …………...……………… [2] (b) It is given that 2()m V kF r −= . (i) Find the value of F when m = 2023, V = 0.14, k = 1.08− , r = 0.348. . Answer F =… .................................. [1] (ii) Express V in terms of F, m, k and r. Answer V =… .................................. [3] (c) Simplify 2 2 46 49 xx x − − . Answer … ........................................ [2]

4 1 (d) Solve the equation 31 512xx =−+− . Give your solutions correct to 2 decimal places. Answer x = …………...… or ….………… [4] __________________________________________________________________________________

5 2 (a) The selling price of a desktop computer is $2388. The hire purchase price is a deposit of $295 and 18 equal monthly instalments of $125 per month. Calculate the simple interest rate per annum. Answer ……………………...….% [3] (b) Peter took a loan of $5000 at a rate of 0.5% per quarter compound interest. (i) He calculated that he will incur an interest of $100 in the first year. Did he do his calculation correctly? Explain. Answer……………………………..………..…………………………………....... …………………………………………………………………………....... ...............................................................……………………………............[1] (ii) Calculate the interest rate that he will be charged in the first year. Answer ………………………… % [ 2] _______________________________________________________________________________

6 3 Solid VABCD is a right pyramid with a square base ABCD, where AB = BC = 12 cm. The wooden pyramid is cut into two parts, pyramid X and frustum Y, along a plane parallel to its base. The ratio of the volume of X to volume of Y is 1 : 7 while the height of pyramid X is 4 cm. (a) Show that l , the side of the square base of X is 6 cm long. Answer: ….………………………………………………………………………………….……. ….…………………………………………………………………………….…….…… ….…………………………………………………………………………….…….…… ……….…………………………….………………………….……………………….[2] (b) Find the volume of frustum Y. Answer ……………………………. cm3 [2]

7 (c) Frustum Y is to be painted on all its sides, at $0.07 for every square centimetre. Calculate the total cost of painting this frustum. Answer $ ………………………… [3] __________________________________________________________________________________

8 4 The variables x and y are connected by the equation 162 11yx x= + − . Some corresponding values of x and y are given in the table below. x 1 1.5 2 2.5 3 4 5 6 y 7 2.67 1 0.4 p 1 2.2 3.67 (a) Find the value of p, correct to 2 decimal places. Answer p = ………………………… [1] (b) On your axes, plot the points given in the table and join them with a smooth curve. [3]

9 (c) The line 2y x c=− + is a tangent to the curve at T. Use your graph to estimate the x-coordinate of T and the value of c. Answer x = ....……………........ c = ….…………………[2] (d) (i) On the same axes, draw the graph of 4 0.5yx=− for 06 x . [1] (ii) The x-coordinates of the points of intersection of the curve 162 11yx x= + − and the line 4 0.5yx=− are the solutions of the equation 25 32 0x Ax+ + = . Find the value of A. Answer A = ………………………… [2] (iii) Hence, use your graph to solve the equation 25 32 0x Ax+ + = . Answer x = …………...… or ….………… [2] __________________________________________________________________________________

10 5 (a) A, B, C and D are points on the circle. BC produced to E and BFD is a straight line. Angle ABD = 38° and angle CAD = 36°. (i) Justify with reasons why AC is not a diameter of the circle, ABCD. Answer [2] (ii) Given that angle BAC = 59°, find angle DCB. Answer Angle DCB = ……………° [1]