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 …………………………………………………………………………….. …………………………………………………………………………….. [2] (b) The cost of making a bicycle was made up of three components: materials, wages, and factory rent. These costs were split in the ratio 2 : 3 : 5, respectively. In the following year, the cost of materials increased by 40%, the cost of wages was halved, and the cost of factory rent remained unchanged. Based on these changes, calculate the percentage change in the total cost of making the bicycle. Answer …………………………% [2]

7 [Turn over] (c) Jia Min and 11 friends went for dinner. The set meal cost $x per person excluding service charge and Goods and Services Tax (GST). The restaurant applied a 10% service charge to the total meal cost, followed by a 9% GST on the amount including the service charge. She collected $30 from each of her 11 friends, then topped up the remaining $29.70 herself to cover the full bill. Find the value of x. Answer x = …………………… [4]

8 3 The diagram shows a solid made up of a cuboid with dimensions (4 ) x cm by (4 ) x cm by x cm and a triangular prism stacked on top of it. The height of the triangular prism is 2x cm. (a) Show that the volume of the solid, y cm 3 , is given by 3 22 16 32y x x x   . Answer [3] (b) Explain why 0 4 x  . ………………………………………………………………………………….. [1] (c) Complete the table of values for 3 22 16 32y x x x   . [1] x 0.5 1 1.5 2 2.5 3 3.5 y 12.25 18 18.75 16 11.25 6 4 x x 2x 4 x

9 [Turn over] (d) On the grid, draw the graph of 3 22 16 32y x x x   for 0.5 3.5x  . [3] (e) Use your graph to find the smallest value of x when the volume of the solid is equal to 15 cm 3 . Answer x = …………………… [1] (f) Explain how the graph shows that the volume of the solid cannot be equal to 20 cm 3 . ………………………………………………………………………………….. ………………………………………………………………………………….. [1]

10 4 (a) Figure 1 shows a container in the shape of a frustum of a cone. The container has an open circular top with a diameter of 24 cm and a circular base with a diameter of 18 cm. It is completely filled with water to a height of 10 cm. Calculate the volume of water in the container, in litres, leaving your answer in terms of π. Answer ……………………... litres [4] 24 cm 10 cm 18 cm Figure 1 Figure 2 20 cm