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 and n are positive integers, where mn . Explain why ( ) ( ) 22 m n m n+ − − is not a prime number for all positive integer values of m and n . ……………………………………………………………………………………… ……………………………………………………………………………………… [2] 6 The marked price of a smart watch at a shop is 25% above the cost price. The shop gives a p % discount during a sale. Calculate the value of p such that the shop makes neither a loss nor a profit from the sale of the smart watch. Answer p = ……………… [2]

6 [TURN OVER 7 The graph shows the average cost for a dozen of Grade A eggs in the year 2022. Source: News Daily Mail UK (https://www.dailymail.co.uk/news/article-11671431/Egg-prices-soar-60-2022-group-blaming-collusive- scheme-producers.html) State one misleading feature of the graph and explain how this feature affects the reader’s interpretation of the cost for a dozen of Grade A eggs. ………………………………………………………………………………………… ………………………………………………………………………………………… ……………………………………………………………………………………… [2]

7 [TURN OVER 8 In triangle XYZ, YZ = 13 cm, XY = 20 cm and angle YXZ = 35 . Find the two possible values of angle XZY. Answer ……….. or ……….. [3] 9 The Mandai Wildlife Reserve conserves and promotes South-East Asian biodiversity. (a) The Mandai Wildlife Bridge is 140 m long. It is represented by a length of 3.5 cm on a map. Express the scale of the map in the form 1 : r. Answer …………………… [1] (b) The Bird Paradise covers a land area of 17 hectares. Find, in cm2, the area representing the Bird Paradise on the same map. (1 hectare = 10000 m2) Answer …………………cm2 [2]

8 [TURN OVER 10 The sketch shows the graph of xy ka −= . The points P (−2, 96) and Q (0, 3 2 ) lie on the graph. Find the value of k and of a. Answer k = ……………… Answer a = ……………… [2] 11 13vv w v u=+ Rearrange the formula to make v the subject. Answer v = ……………… [3] y x O • P (−2, 96) • Q (0, )

9 [TURN OVER 12 On a coordinate plane, P is the point ( )0,12 and 8 10PR =− . (a) Calculate PR . Answer …………………… [2] (b) Find the equation of the line PR. Answer …………………… [2] 13 (a) Write down 252 as product of its prime factors in index notation. Answer …………………… [1] (b) The highest common factor (HCF) of two numbers is 6. The lowest common multiple (LCM) of the two numbers is 252. One of the numbers is a perfect square. Find the two numbers. Answer ……… and ……… [2]

10 [TURN OVER 0 2 4 6 8 10 12 14 16 18 Time (seconds) h 2h 3h Height of water level (h cm) 14 A container is a prism with a triangular cross-section. The container has a height of 3h cm and uniform width. Water is poured into the container at a constant rate. It takes 18 seconds to fill the container. (a) Find the time taken for the water level to reach a depth of 2h. Answer …………… seconds [2] (b) On the axes in the answer space, sketch the graph of the height of the water level against time. Answer …………………… [3] 3h 2h 3h