TKSS 2021 Sec 1 EOY Maths P2

This document consists of 5 printed pages and 1 blank page. [Turn over CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4048/02 Paper 2 1 October 2021 1 hour 15 minutes Additional Materials: Writing Paper Graph 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. 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. You are expected to use a scientific calculator to evaluate explicit numerical expressions. 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 End-of-Year Examination 2021 Secondary 1

2 4048/2/Sec 1EOY21 [Turn over 1 The first four terms of a sequence are 33, 26, 19 and 12. (a) Write down the seventh term of the sequence. [1] (b) Write down an expression, in terms of n, for the nth term of the sequence. [1] (c) Determine, with a reason, if the number 206 is in the sequence. [2] 2 (a) Find the smallest possible value of a whole number if it leaves a remainder of 3 when divided by 5, 6 or 9. [2] (b) For a charity event, a group of student leaders has to pack 252 bread rolls and 210 packets of biscuit equally into identical goodie bags with no leftover. Find the largest possible number of goodie bags that can be packed. [2] 3 (a) Solve the inequality 6 40 2 7 4 2x x x     . [3] (b) Illustrate the solution on a number line. [1] (c) State the smallest prime value of x that satisfies the inequality. [1] 4 (a) Given that 1 7 x  and 5 3 y   find (i) the greatest possible value of x y , [1] (ii) the smallest possible value of 2y . [1] (b) By showing your working clearly, estimate the value of 42100 2.95×996 , correct to one significant figure. [2] (c) Simplify (i) 6x  5 )113(2 x , [3] (ii) 2 9 3 3 12 4 216 27 v v u u . [2]

3 4048/2/Sec 1EOY21 [Turn over 5 Andy bought 40 pencils for x cents. If he buys erasers using the same amount of money, he would have 10 erasers more than pencils. (a) Express the cost of one pencil in terms of x. [1] (b) Express the cost of one eraser in terms of x. [1] (c) An eraser costs 5 cents less than a pencil. (i) Write down an equation in terms of x to represent this information. [1] (ii) Solve the equation and find the cost of one pencil. [2] 6 Answer the whole of this question on a sheet of graph paper. The values of x and y shown in the table below are related through a straight line. (a) Using a scale of 2 cm to 1 unit on the y-axis and 4 cm to 1 unit on the x-axis, plot the points given in the table above and join them with a straight line. [3] (b) The point ( 0.5 , d ) lies on the graph. Use your graph to find the value of d. [1] (c) Using your graph, find the (i) gradient of the line, [2] (ii) equation of the line. [1] x – 1 0 1 2 y 8 5 2 – 1

4 4048/2/Sec 1EOY21 [Turn over 7 (a) ABCD is a rhombus and E is the intersection of the two diagonals. Given that 58CBD   , find angle DAE, stating your reason(s) clearly. [2] (b) PQRST is a pentagon in which 113PQR QPT    , 67QRS   . RST PTS  . QP and ST produced meet at X. (i) Calculate PTS . [2] (ii) Explain whether PQ is parallel to SR. [1] (iii) Prove that triangle PXT is an isosceles triangle. Showing your working and reasons clearly. [2] X T S P Q R A B D C E 58o

5 4048/2/Sec 1EOY21 [Turn over 8 Concrete solid barriers are used for guiding traffic and securing property from automobile traffic. Figure 1 shows a concrete traffic control barrier. Figure 1 The barrier can be modelled by a prism with uniform cross section of length 3 m, as shown in Figure 2. The sloping sides PQAB and SRDC are rectangles. The uniform cross-section of the prism is made up of a trapezium PQRS and a semi-circle with diameter RQ. The perpendicular height between RQ and SP is 0.5 m. RQ = 0.2 m and SP = 0.6 m. SR = PQ = 0.7m. Figure 2 (a) (i) Show that the cross-sectional area of the barrier is 0.2157 m2, correct to 4 significant figures.