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 si