2024 SJI Prelim P1

1 [TURN OVER ST JOSEPH’S INSTITUTION PRELIMINARY EXAMINATION 2024 (YEAR 4) CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Candidates answer on the Question Paper. 4052/01 12 August 2024 2 hours 15 minutes (09:50 – 12:05) 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 consist of 21 printed pages and 3 blank pages.

2 [TURN OVER 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 rh 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 ff  −  

3 [TURN OVER 1 Solve the inequality 23 6 2 36 xx−+  . Answer …………………… [2] 2 (a) Write 0.0001087 in standard form. Answer …………………… [1] (b) The table shows the population in some cities in ASEAN and their land areas. Write down the city in the table that has the smallest population per km2. Answer …………………… [1] City Population Land area, km2 Bangkok 71.07 10 7700.0 Ho Chi Minh City 72.12 10 30 595.0 Manila 71.35 10 24 317.7 Kuala Lumpur 68.46 10 8347.1

4 [TURN OVER 3 Vikas takes a study loan of $12 000 that charges an interest rate of r % per year compound interest for 4 years. The total amount that he would have paid for the loan at the end of 4 years is $12 688. Find the value of r. Answer r = ………………… [3] 4 (a) Simplify 3 20 4 8 81u v −   . Answer …………………… [2] (b) Factorise 2 2 2 244x y x y+ − − completely. Answer …………………… [3]

5 [TURN OVER 5 m