TJC 2022 IP1 EOY (Question & Answer)

TemasekJC/IP1/FM/EoY/2022 TEMASEK JUNIOR COLLEGE 2022 IP1 END-OF-YEAR EXAMINATION CANDIDATE NAME CG SUBJECT TUTOR’S NAME FUNDAMENTAL MATHEMATICS 5 October 2022 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 que stion. The calculator value for π should be used unless the question r equires the answer in terms of π . The use of an approved scient ific 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 17 printed pages and 1 blank page. For Examiner’s Use Q1 / 6 Q2 / 7 Q3 / 7 Q4 / 7 Q5 / 7 Q6 / 6 Q7 / 6 Q8 / 4 Q9 / 6 Q10 / 6 Q11 / 6 Q12 / 6 Q13 / 6 Presentation Deduction – 1 / – 2 Total / 80

2 TemasekJC/IP1/FM/EoY/2022 Answer all questions in the spaces provided. Show all working clearly. 1 (a) Identify all the irrational numbers in the list of numbers below. 2 322, , , 3437 0π24, 1.6 3 , − [2] (b) Without the use of a calculator, evaluate 3 2 51255 2 63 642  −−+   ++ . [4] [Answers for Question 1]

3 TemasekJC/IP1/FM/EoY/2022 [Turn over] 2 (a) It is given that 3 5 1.71= , correct to 3 significant figures. Find, without the use of a calculator, the length of an edge of a cube which has a volume of 35000 cm . [3] (b) The numbers 36 and 56, written as the products of their prime factors, are 2236 2 3= and 356 2 7= . (i) Find the highest common factor of 36 and 56. [1] (ii) Find the smallest positive integer k such that 56 k is a perfect square. [1] (iii) Ash, Misty and Brock are each given a rope of length n cm. Ash cuts his rope into smaller pieces of equal length of 36 cm. Misty cuts her rope into smaller pieces of equal length of 56 cm. Brock cuts his rope into smaller pieces of equal length of 54 cm . If there is no rope leftover, find the smallest possible value of n. [2] [Answers for Question 2]

4 TemasekJC/IP1/FM/EoY/2022 3 (a) Express 3 2( 1) 4 5 1 32 p q p q− − − +− as a single fraction in its simplest form. [3] (b) Expand and simplify