SJI 2025 Prelim Paper 1 With Answer Key

1 [Turn over] ST JOSEPH’S INSTITUTION PRELIMINARY EXAMINATION 2025 (YEAR 4) CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Candidates answer on the Question Paper. 4052/01 15 August 2025 2 hours 15 minutes (10:15 – 12:30) 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 27 printed pages and 1 blank page.

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 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] Answer all the questions. 1 At a football match, the attendance was reported as 26 500 people, rounded to the nearest hundred. Using x to represent the possible number of people who attended the match, write down an inequality in x. Answer …………………………………… [1] 2 Joseph invested $50 000 at a simple interest of r% per year. After q months the interest was $I. Write down and simplify an expression for I, in terms of q and r. Answer I = ……………………………. [2]

4 3 ABD is a triangle. ADC is a straight line. AB = 8 cm, AD = 9 cm and BD = 10 cm. Without using a calculator, find the exact value of cos BDC . Answer cos BDC = …………… [2] A D B C 9 10 8

5 [Turn over] 4 Jane either walks or cycles to school. The probability that she cycles to school is 1 5 . (a) Write down the probability that Jane walks to school. Answer …………………………… [1] (b) There are 190 days in a school year. Find the number of days Jane is likely to walk to school in a school year. Answer …………………….. days [1] 5 A polygon has n sides. When the number of sides is doubled, the interior angle is increased by 20o. Find the value of n. Answer n = …………………….. [2]

6 6 The marks of 19 students in a Science test are shown in the stem-and-leaf diagram. 0 1 7 7 8 2 6 8 9 9 9 3 1 4 6 7 8 9 4 3 4 6 6 x Key 2 6 means 26 marks (a) Write down the median mark. Answer …………………………… [1] (b) The range of marks for the Science test is 32. Find the value of x. Answer x = …………………….. [1]

7 [Turn over] 7 The graph shows the average daily household water consumption per person in Singapore over the years. Source: PUB Straits Times Graphics (a) Under the Singapore Green Plan 2030, find the projected percentage reduction in household water consumption from 2024 to 2030. Answer ……………………....... % [1] (b) State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. …………………………………………………..……………………………… …………………………………………………..……………………………… …………………………………………………..……………………………… [2]

8 8 Simplify 3 6 2 8 16 9 m q −   . Answer …………………………… [2] 9 The number N is a multiple of 18 and is both a perfect square and a perfect cube. Find the smallest possible value of N. Answer N = …………………….. [2]

9 [Turn over] 10 Write as a single fraction in its simplest form 2 1 3 2 2 7 10 x x x x +−− − + . Answer …………………………… [3]

10 11 The first four terms in a sequence of numbers are given below. 22 1 1 1 2T = + = 22 2 5 2 29T = + = 22 3 9 3 90T = + = 22 4 13 4 185T = + = (a) Evaluate 5T . Answer T5 = …………………... [1] (b) nT is the nth term of the sequence. Find an expression, in terms of n, for nT , in the form 2an bn c++ where a, b and c are integers. Answer Tn = …………………... [3]