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 2 4( ) 2 ( 6 )ay xy ab x y b+ − + − completely, leaving your answer in its factorised form. [4] [Answers for Question 3]

5 TemasekJC/IP1/FM/EoY/2022 [Turn over] 4 (a) Solve the equation 2 3 1 2 1 3 5 2 mm−− =− + . [4] (b) Given that 3 4 2 7 2 3 xy xy − =−+ , find the value of x y . [3] [Answers for Question 4]

6 TemasekJC/IP1/FM/EoY/2022 5 There are four numbers. The first number is half of the second number. The third number is 6 less than the first number. The fourth number is 2 7 times the third number. (i) Given that the first number is x, write down e xpressions, in terms of x, to represent the second, third and fourth numbers. [3] The average of the four numbers is 27. (ii) Form an equation, in terms of x, and solve it. [3] (iii) Hence find the sum of the first and third numbers. [1] [Answers for Question 5]

7 TemasekJC/IP1/FM/EoY/2022 [Turn over] 6 (a) Every year, the value of a car depreciates by 11% of the previous year’s value. Given that the value of a car is $158 000 now, find the value of the car 2 years ago, giving your answer to the nearest dollar. [2] (b) The breadth of a rectangle is x cm and the length of the same rectangle is 5 times that of its breadth. If the length is decreased by 40% and the breadth is increased by 35%, determine the percentage decrease of its perimeter. [4] [Answers for Question 6]

8 TemasekJC/IP1/FM/EoY/2022 7 A triathlete takes 31 4 hours to complete a sprint triathlon which consists of swimming, cycling and running. He takes x minutes to run, 25 mi nutes less than running to swim and 1.25 minutesx to cycle. (i) Form an equation, in terms of x, and solve it to find the time taken for him to complete running, leaving your answer in minutes. [2] The total distance completed during the triathlon is 25 750 m. Given that the triathlete swims at an average speed of 50 m etres per minute , and the ratio of the distance s covered is 3:80 : y for swimming, cycling, and running respectively, (ii) find the value of y, [2] (iii) calculate the average cycling speed in m/min. [2] [Answers for Question 7]

9 TemasekJC/IP1/FM/EoY/2022 [Turn over] 8 Tom claims that 3 of the exterior angles of an irregular nonagon (9-sided polygon) are ( )30x+ , ( )26x−  and ( )5 14x+  , and the remaining exterior angles are 55 each. Is his claim accurate? Justify your answer. [4] [Answers for Question 8]

10 TemasekJC/IP1/FM/EoY/2022 9 In the diagram below (not drawn to scale), AGEF is a rhombus, AGB is an isosceles triangle, and FED is a straight line. It is given that 44GAF =  , AGE x =  , 88AGB =  , GED y =  , EDB z =  and 90DBC =  . Find the value of (i) x, [1] (ii) y, [1] (iii) z. [4] [Answers to Question 9] A B C D E F G