TJC 2020 IP1 FM EOY (Questions & Answers)

1 [Turn over TemasekJC/IP1/FM/EoY/2020 TEMASEK JC INTEGRATED PROGRAMME YEAR ONE 2020 END-OF-YEAR EXAMINATION FUNDAMENTAL MATHEMATICS Date: 7 October 2020 Duration: 2 hours Additional materials required: Graph Paper READ THESE INSTRUCTIONS FIRST. Write in dark blue or black pen in the spaces provided in the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. Give non- exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The calculator value for should be used unless the question requires the answer in terms of π . The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. Marks will be deducted for poor or unclear presentation. The number of marks is given in brackets [ ] at the end of each question or part question. The total score for this paper is 80 marks. This paper consists of 22 printed pages and 0 blank pages. Question Marks 1 2 3 4 5 6 7 8 9 10 11 12 13 Presentation Deduction −1 Total Name: ________________________ Class: ________________________ ________________________ Parent’s Signature

2 TemasekJC/IP1/FM/EoY/2020 Answer all questions in the spaces provided. Show all working clearly. 1 Jack and Jill went to fetch a pail of water each from a well. The ratio of the amount of water that Jack fetched to Jill’s amount is 5 : 2. After pouring 0.3 litres of water from Jack’s pail to Jill’s pail, the ratio of the amount of water is now 11 : 5. Find (i) the total amount of water that the both of them had fetched , [3] (ii) the percentage change in the amount of water in Jack’s pail after pouring the water into Jill’s pail. [2] 2 (a) The numbers 3 888 000 000, 138 240 000 and 7 290 000 000 written as a product of their prime factors, are 3 888 000 000 = 2 10 × 35 × 56, 138 240 000 = 2 13 × 33 × 54, 7 290 000 000 = 2 7 × 36 × 57. Find (i) the greatest whole number that divides 3 888 000 000, 138 240 000 and 7 290 000 000, leaving your answers in index form, [1] (ii) the lowest common multiple of 3 888 000 000, 138 240 000 and 7 290 000 000, leaving your answers in index form, [1] (iii) the smallest positive integer n such that the product of n and the lowest common multiple of 3 888 000 000, 138 240 000 and 7 290 000 000 is a perfect cube. [1] (b) Ruhua has between 200 to 400 sweets. If he divides his sweets into groups of 11, he will have 10 sweets left. If he divides his sweets into groups of 13, he will have 12 sweets left. Find the number of sweets left if he divides his sweets into groups of 17. [3] 3 Without the use of a calculator, evaluate 2 34 3 64 23