TJC 2023 IP1 FM EOY (Questions & Answers)

TemasekJC/IP1/FM/EOY/2023 TEMASEK JUNIOR COLLEGE 2023 IP1 END-OF-YEAR EXAMINATION CANDIDATE NAME CG SUBJECT TUTOR’S NAME FUNDAMENTAL MATHEMATICS 5 October 2023 2 hours READ THESE INSTRUCTIONS FIRST Write your name, CG and tutor’s name on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid. Answer all questions. Write your answers in the spaces provided in the question paper. You may request for additional writing materials if there is insufficient space. These should be attached to the back of the booklet. 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 π should be used unless the question requires the answer in terms of π . The use of an approved scientific and/or graphing 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. This document consists of 10 printed pages and 0 blank pages. For Examiner’s Use Q1 / 6 Q2 / 7 Q3 / 6 Q4 / 6 Q5 / 6 Q6 / 7 Q7 / 6 Q8 / 5 Q9 / 6 Q10 / 7 Q11 / 7 Q12 / 5 Q13 / 6 Presentation Deduction −1 / −2 Total / 80

2 TemasekJC/IP1/FM/EOY/2023 Answer all questions in the spaces provided. Show all working clearly. 1 (a) Express the following numbers on a number line. [1] π , 1.654, 24 312, − − (b) Without the use of a calculator, estimate the value of the expression ( ) 2 2.054 0.98 102 4 +− , leaving your answer correct to the nearest integer. [5] 2 (a) A prime number, x , is greater than 75 but less than 81. (i) State the value of x . [1] It is given that x can be expressed as a product of 22h− and 56h+ , where h is a positive integer. (ii) Find the value of h , showing your working clearly. [2] (b) (i) Express 127 008 as a product of its prime factors. [1] (ii) Hence find the largest possible value of 3 127 008 2k and the corresponding value of k , where k is a positive integer. [3] 3 A rectangular tank measures 48 cm by 72 cm by 252 cm. If it is to be filled completely with small identical cubes, find (i) the greatest possible volume of each cube, [4] (ii) the least possible number of cubes required. [2]

3 TemasekJC/IP1/FM/EOY/2023 [Turn over 4 (a) Convert 20 m/s to km/h . [2] (b) It is given that the value of a limited-edition pair of sneakers increases by 5% every year. In 2020, the value of the pair of sneakers is $3000. Find the value of the pair of s