2024 SJI Prelim P2

ST JOSEPH’S INSTITUTION PRELIMINARY EXAMINATION 2024 (YEAR 4) CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 2 Candidates answer on the Question Paper. 4052/02 15 August 2024 2 hours 15 minutes (08:30 – 10:45) 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 mark for this paper is 90. This document consists of 20 printed 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 1 (a) In 2024, apples cost $x per kilogram and oranges cost $y per kilogram. The total cost of 5kg of apples and 10kg of oranges is $40. (i) Show that 8 2 y x  . Answer [2] (ii) In 2023, the cost, per kilogram, of apples were 9% lower than in 2024 while the cost of oranges, per kilogram were 9% higher than in 2024. Find an expression, in terms of x and y, for the total cost of 3kg of apples and 2kg of oranges in 2023. Give your answer in its simplest form. Answer ………………………...... [3]

4 (b) Write as a single fraction in its simplest form 2 3 12 4 x x x x x    . Answer …………………….......... [4]

5 [TURN OVER 2 The diagram shows a sequence made by using grey and white squares. (a) Draw Pattern 2 in the space above. [1] (b) Complete the table for the next three pattern in the sequence. Pattern Number 4 5 6 Number of grey squares 18 Number of white squares 32 [2] (c) Find an expression, in terms of k, for the num