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 ……