SJI 2025 EMATH PRELIM P2 QP

1 [Turn over] ST JOSEPH’S INSTITUTION PRELIMINARY EXAMINATION 2025 (YEAR 4) CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 2 Candidates answer on the Question Paper. 4052/02 21 August 2025 2 hours 15 minutes (08:05 – 10:20) 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 on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use 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 or 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 marks for this paper is 90. This document consists of 25 printed pages and 3 blank pages.

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = 1 100 n rP    rl 24 r 21 3 r h 34 3 r ABC 1 sin2 ab C r  21 2 r   sin sin sin a b c A B C  2 2 2 2 cosa b c bc A   fx f   22fx fx f f          

3 [Turn over] TURN OVER FOR QUESTION 1

4 1 (a) It is given that 3 2 5 na n k  . (i) Find the value of a when 1 3n and 2 3k  . Answer a = …………………… [1] (ii) Express n in terms of a and k. Answer n = …………………… [3]

5 [Turn over] (b) Solve the inequality 4 5 5 16 4 x x   . Answer …………………………… [2] (c) Solve the equation 2 3 51 1 x x x x     . Give your solutions correct to 2 decimal places. Answer x = ………. or ………. [5]

6 2 (a) The total population of the Philippines was estimated at 114.9 million in June 2023 and 116.79 million in June 2025. (i) Write 114.9 million in standard form correct to 3 significant figures. Answer …………………………… [1] (ii) The land area of the Philippines is about 300 000 square kilometres. The government wants to keep the population density below 350 people per square kilometre. Based on the June 2025 population figure, determine whether the Philippines has exceeded this density limit. Show your calculations. Answer