TJC 2021 IP1 FM EOY (Questions & Answers)

1 [Turn over TemasekJC/IP1/FM/EOY/2021 TEMASEK JC INTEGRATED PROGRAMME YEAR ONE 2021 END-OF-YEAR EXAMINATION FUNDAMENTAL MATHEMATICS Date: 8 October 2021 Duration: 2 hours No additional materials required Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College Temasek Junior College READ THESE INSTRUCTIONS FIRST. Write your answer 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 the questions. Write your answers in the spaces provided in the question paper. Additional writing materials can be used 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 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 16 printed pages, and no 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/2021 Answer all questions in the spaces provided. Show all working clearly. 1 (a) Without the use of a calculator, evaluate 3 4 18 1 6412 39  −×−−  . [4] (b) The table below shows the number of people and the respective entrance fees for a carnival on a specific day. Age group Number of people Entrance Fee (per person) Adult 18 $14.15 Child 11 $9.95 Without the use of a calculator, estimate the total amount collected on that day. [2] 2 (i) Find the HCF of 1 470 and 300. [3] (ii) Paperclips are sold in packs of 1 470. Thumbtacks are sold in packs of 300. Beatrice buys the same number of paperclips as thumbtacks for her office. Find the least number of packs of paperclips that she could have bought. [3] 3 (a) The numbers A, B and C, written as a product of their prime factors, are given below, where p, q and r are positive integers. 2 7 11 42 322 7 13 Ap q r Bpqr C =×× =×× = ×× Using the prime factors given above, find (i) the cube root of AB× , [2] (ii) the smallest integer, k, such that C k is a perfect square. [1] (b) The area of a square is 22 601 cm . Using prime factorisation, find the perimeter of the square. [3] 4 (a) Expand and s implify ( ) ( )114 23 3426x yx xy++ − − − completely. [3] (b) Factorise ( )( ) ( )( )2 2 3 75 2pq pq p q p qq p− +− −++ − completely. [3]

3 [Turn over TemasekJC/IP1/FM/EOY/2021 5 (a) Solve the equation 32 2 23 26 3 x xx+− +−= . [4] (b) Given that 31 2 11 5 pq pq − =− , find the value of p q . [3] 6 Bruno has some money to buy textbooks and workbooks for the new school year. If he buys x textbooks at $12 each, he will have $2 left. If he buys (x – 2) workbooks at $16 each, he will have $6 left. (i) Form an equation, in terms of x, and solve it to find the amount of money Bruno has. [4] (ii) Bruno decides to buy 2 textbooks at $12 each. He uses the remaining money to buy workbooks at $16 each. How many workbooks can he buy? [3] 7 (a) Given that the exchange rate between the Singapore dollar (S$) and the Canadian dollar (C$) is S$1 = C$0.93, convert C$10 000 into Singapore dollars. Leave your answer correct to the nearest cent. [2] (b) A man deposited $30 000 into a savings account that pays a simple interest of 2.2% per annum. Calculate the number of years required for the money in the account to exceed $34 000. [4]

4 TemasekJC/IP1/FM/EOY/2021 8 A straight line, L1 , is given in the grid below. (i) Find the equation of the straight line L 1 . [2] The equation of another straight line, L2 , is 0.5 1yx= + . (ii) Determine if the point ( )3, 2.5 lies on the straight line L2 . [2] (iii) On the same grid above, draw the straight line L 2 for 44 x−≤≤ . [1] (iv) Estimate the area of the triangle bounded by L1, L2 and the x-axis. [1] x y – 4 – 3 – 2 – 1 0 1 2 3 4 4 2 – 1 5 3 1 L1

5 [Turn over TemasekJC/IP1/FM/EOY/2021 9 The graph below shows Penelope’s journey from her house to Hudson’s house. During the journey, she stopped at a café for lunch, after which she continued her journey to Hudson’s house. Find the gradient of each of the following line segments, stating clearly what each gradient represents. (i) AB [2] (ii) BC [2] (iii) Hudson claimed that Penelope travelled at a faster speed from Penelope’s house to the café than from the café to his house. Is his claim accurate? Justify your answer, showing all working clearly. [2]

6 TemasekJC/IP1/FM/EOY/2021 10 (a) John intends to train for a 21- km half marathon and decides to adopt a training programme. The distance he runs each day is reflected in the table below. Day Distance ran by John (in km) 1 1 2 1.4 3 1.8 4 2.2 5   n Complete the table above. [2] (b) Tom also intends to train for the 21- km half marathon but decides to adopt a different training programme. The distance he runs each day is reflected in the table below. Day Distance ran by Tom (in km) 1 0.5 2 1 3 2 4 4 5 8  n (i) Find, showing your working clearly, the distance Tom ran on the thn day leaving your answer in terms of n . [2] (ii) Find the value of n such that the distance ran by Tom on Day n is at least the distance required to complete the half marathon. [2]

7 [Turn over TemasekJC/IP1/FM/EOY/2021 11 The diagram below (not drawn to scale) shows a metal statue that comprises of a closed half-cylinder that is mounted on a cuboid. The dimensions of the cuboid are 1.1 m by 0.2 m by 2.5 m. The radius of the semi -circular cross-section of the half-cylinder is 1.5 m and the breadth is 0.4 m. (a) Find the volume of metal, in 3m , used to make the statue. [3] (b) Find the total surface area, in 2m , of the statue. [4] 12 In the figure below (not drawn to scale), AB is parallel to CD and EF. PQRST is a straight line. Find the values of x and of y. [5] A B F D E P C Q R S T 0.4 m 1.1 m 2.5 m 0.2 m 1.5 m

8 TemasekJC/IP1/FM/EOY/2021 13 In the diagram below (not drawn to scale), ABCDE is part of a regular n-sided polygon where 146.25ABD∠= ° . (i) Explain why triangle BCD is an isosceles triangle. [1] (ii) Find the value of n. [5]  End of Paper  A B