TKSS 2022 Sec 1 EOY Maths P1

This document consists of 10 printed pages. CANDIDATE NAME MATHEMATICS 4052/01 Paper 1 Thursday 6 October 2022 1 hour 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid/tape. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 50. TANJONG KATONG SECONDARY SCHOOL Year End Examination 2022 Secondary 1 CLASS INDEX NUMBER For Examiner’s Use

2 4052/Sec1YearEnd2022 [Turn over 1 (a) Calculate 376 4.37 1.82 0.195   , giving your answer correct to 4 significant figures. Answer...………………………………… [1] (b) Mike evaluates 150.91 29.8 using a calculator and he says that the answer is 8407.136. Without doing the actual calculation, use estimation to determine whether Mike’s answer is reasonable. Answer .…… .………...……………………………...……………………… ……… … …………………...……………………………...………………………… …… .… .… .[2] 2 (a) Solve the inequality 1 2 5 13x x x     . Answer...………………………………… [3] (b) Hence, write down the smallest integer x which satisfies the inequality above. Answer x = ……………………………… [1]

3 4052/Sec1YearEnd2022 [Turn over 3 (a) Given that 28 20 9 12x y x y   , find the value of x y . Answer x y = ..…………………………… [2] (b) (i) Factorise 15 9 18 30a b bk ak   completely. Answer...………………………………… [2] (ii) By factorising 2t t , show that it is always even for all positive integers of t. Answer .…… .………...……………………………...………………………………… …………………...……………………………...……………………………… .… … [2] 4 (a) Write down the next two terms in the sequence, 1 2 3 4, , , , ...4 9 16 25 . Answer...………………………………… [1] (b) Write down an expression, in terms of n, for the nth term of the sequence. 8, 5, 2, 1, 4, ...  Answer...………………………………… [2]

4 4052/Sec1YearEnd2022 [Turn over 5 (a) (i) Find the prime factorisation of 196. Answer...………………………………… [1] (ii) Find the smallest positive integer value of k such that 196k is a perfect cube. Answer k = …………… … ……………… [1] (b) A rectangular block of wood has dimension 196 cm by 116 cm by 80 cm. Find the smallest number of identical cubes John can cut from the block of wood such that no wood is left. Answer...………………………………… [2] 196 cm 116 cm 80 cm

5 4052/Sec1YearEnd2022 [Turn over 6 On average, SUSA Company sells 300 computers at $2000 each daily. When the price of each computer increases by 15%, the total sales drops by 20%. What is the percentage change in the earnings with the increase in price and the drop in sales? Answer...……………………………… % [4] 7 Mr Tan can mark 30 scripts in 2.5 hours. Mrs Lim can mark 25 scripts in 1.25 hour. Working at constant rates, Mr Tan and Mrs Lim work together to complete marking the scripts for a class of 42 students. How long will it take to complete the marking? Leave your answer in hours and nearest minutes. Answer … …… … … h ……… … … mins [3]

6 4052/Sec1YearEnd2022 [Turn over 8 In the diagram, PQRS is a quadrilateral that is enclosed by 4 identical semicircles. (a) What is the special name of the quadrilateral PQRS? Answer...………………………………… [1] (b) The diameter of each of the semicircle is 5 cm. Find the total area of the 4 semicircles, in terms of π. Answer...…………………………… cm2 [2] (c) It is given that the area of quadrilateral PQRS is 24 cm2 and the length of the diagonal PR is 6 cm. Find (i) the perpendicular length of P to QR, Answer...…………………………… cm [2] (ii) the length of the diagonal QS. Answer...…………………………… cm [2] P Q R S x

7 4052/Sec1YearEnd2022 [Turn over 9 Two bicycle rental companies, X and Y, offer bicycle rental at the charges as shown in the graph below. (a) Which company has a greater rate of increase in charges? Explain your answer. Answer Company ……… because ………………...………………………… …… .……… …………………...……………………………...……………………………… .…[ 1] (b) If Henry has a budget of $60, which company should he rent a bicycle from? Explain your answer. Answer Company ……… because ………………...……………………………… .……… …………………...……………………………...……………………………… .…[ 1] Time (hours) Charges($) 20 Y 1 60 3 4 5 80 100 120 40 X 0 2

8 4052/Sec1YearEnd2022 [Turn over 10 In the figure, ADE and BCF are straight lines. AE is parallel to BF and BC = CD. 126BAE   and 58FCD   . (a) Stating your reasons clearly, find (i) reflex BAD , Answer...………………………………… [1] (ii) CBD . Answer...………………………………… [2] (b) Explain whether the line BD is an angle bisector of ABC . Show your workings clearly. Answer .…… .………...……………………………...……………………………… .… .… . …………………...……………………………...……………………………… .………… . [2] C D A B E F

9 4052/Sec1YearEnd2022 [Turn over 11 On the axes shown, A is a point (6, 0), B is a point (0, 2) and C is a point on the negative y-axis. The area of triangle AOB is half that of triangle AOC. (a) Plot point C on the diagram above and state the coordinates of C. Answer (…………… , …………… ) [2] (b) State the equation of the vertical line BC. Answer...……………………… ……… [1] (c) State the coordinates of D such that ABCD is a parallelogram. Answer (…………… , …………… ) [2] x y −4 × B −4 −2 O 2 4 6 2 4 6 −2 A × −6

10 4052/Sec1YearEnd2022 [Turn over 12 (a) Construct a triangle ABC such that AC = 7.3 cm and angle BAC =30. The line AB has been provided below. [1] (b) Construct the perpendicular bisector of line AB. [1] (c) Construct the angle bisector of angle BAC. [1] (d) Label the point M which is equidistant from the lines AC and AB and equidistant from the points A and B. [1] Answer END OF PAPER A B