CEDAR GIRLS SECONDARY SCHOOL Preliminary Examination Secondary Four. MATHEMATICS 4016/01 Paper 1 19 August 2008

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CEDAR GIRLS SECONDARY SCHOOL Preliminary Examination Secondary Four CANDIDATE NAME CENTRE NUMBER INDEX NUMBER MATHEMATICS 4016/01 Paper 1 19 August 008 Candidates answer on the Question Paper.

1 CEDAR GIRLS SECONDARY SCHOOL Preliminary Examination Secondary Four CANDIDATE NAME CENTRE NUMBER INDEX NUMBER MATHEMATICS 4016/01 Paper 1 19 August 008 Candidates answer on the Question Paper. hours READ THESE INSTRUCTIONS FIRST Write your Centre number, index number and name on all the work you hand in. Write in dark blue or black pen. You may use a 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., use either your calculator value or.14, 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 number of marks for this paper is This document consists of 17 printed pages and 1 blank page. [Turn over

2 Mathematical mulae Compound interest Total amount = r P1 100 n Mensuration Curved surface area of a cone = Surface area of a sphere = rl 4 r Volume of a cone = 1 r h Volume of a sphere = 4 r Area of triangle ABC = 1 ab sin C Arc length = r, where is in radians Sector area = 1 r, where is in radians Trigonometry a sin A b sin B c sin C a b c bc cos A Statistics Mean = fx f Standard deviation = fx f fx f Cedar Girls Secondary School 4016/01/S4/Prelim08

3 Answer all the questions. 1 Beng and Lian want to buy some towels. A store displays the following signs. Mid-Year Sale All towels 60% off Normally $10 $ July sale price $4 $4 $ -Day Special EXTRA 5% off the July sale price.. Beng Lian. Who is correct, Beng or Lian? Show working to explain your answer. Answer [] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

4 If 1 men can build a platform in 0 days, how many days would it take 15 men to build of these similar platforms, assuming that they work at the same rate? 4 Answer [] The day temperature in a remote island in December is p C and the night temperature is q C where p and q are positive integers and p q. Write down an expression for (a) the difference between the two temperatures, (b) the mean of the two temperatures. Answer (a) [1] (b) [1] 4 Mrs Lee buys a large cylindrical can of fruit juice. She decides to store all the fruit juice in smaller cans. The smaller cans are geometrically similar to the large can and they have radius and height half of that of the large can. Explain, with working, how many small cans she will need to use. Answer [] Cedar Girls Secondary School 4016/01/S4/Prelim08

5 5 5 (a) Find the lowest common multiple of 40 and 540. (b) Find the smallest positive integer which can be multiplied by 540 to give a cube number. Answer (a) [1] (b) [1] 6 The actual distance between two towns P and Q is 6.5 km. The distance between the two towns is represented by a line of 6 cm on a map. Calculate (a) the scale of the map in the form of 1 : n, (b) the actual area, in km, of a town represented by 0 cm on the map. Answer (a) [1] (b) [1] 7 $4 500 is invested at.% compound interest per annum. Find, to the nearest dollar, the amount that the investment will yield after 6 years. Answer [] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

6 6 8 The proton, which is the nucleus of a hydrogen atom, can be pictured as a sphere whose radius is 160 nanometres. (a) Express 160 nanometres in metres, giving your answer in standard form. (b) How many protons must be placed in a straight line to make a length of 64 cm? Give your answer in standard form. Answer (a) [1] (b) [1] 9 7c (a) Simplify 4 (c) 4c, leaving your answer in positive indices. a 4 x (b) Simplify the expression. 4 x x a Answer (a) [] (b) [] Cedar Girls Secondary School 4016/01/S4/Prelim08

7 7 10 In the diagram, PQ = 15 cm, PR = 17 cm, PQR 90, QR = RS and PRS is a straight line. Q 15 cm P 17 cm R S Find (a) the length of QR, (b) as a fraction, the value of cos (c) the area of QRS. QRS, Answer (a) [1] (b) [1] (c) [] 11 Evaluate (a) (b) , Give both answers correct to significant figures. Answer (a) [] (b) [] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

8 8 1 The figure shows a square VWXY of sides 15 cm each. The side YX is produced to M such that XM = 10 cm. VM cuts WX at L and WL = a cm. V W a 15 L Y 15 X 10 M (a) (i) Name a triangle that is similar to VWL. (ii) Hence or otherwise, calculate the value of a. (b) Determine the ratio Area of VLX Area of VWY. Answer (a) (i) [1] (ii) [] Answer (b) [] Cedar Girls Secondary School 4016/01/S4/Prelim08

9 9 1 (a) Find the gradient of the line AB. [] (b) Find the angle that AB makes with the x-axis. (c) On the grid, draw the lines (i) y, (ii) x y 0. (d) Find the area of the triangle enclosed by these three lines. Answer (a) [1] (b) [1] (d) [1] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

10 10 14 (a) x Sketch the graph of y ( x 4)( 1). Answer (a) y x [] (b) (i) Express x 4x 1 in the form b ( x a). (ii) Sketch the graph of y x 4x 1. Answer (b) (ii) y (b) (i) [1] x [] Cedar Girls Secondary School 4016/01/S4/Prelim08

11 15 The maximum daily temperature, in C, was recorded throughout the month of April. The results are shown in the table below 11 Temperature ( o C) Number of days 4 T T T T T 1 4 (a) Calculate, showing your working and giving your answers correct to 1 decimal place, an estimate of (i) (ii) the mean temperature, the standard deviation. the month of June, the mean maximum daily temperature was 14.9 C and the standard deviation was.7 C. (b) Compare the information and state two observations about the temperature for the months of April and June. (a) (i) [] (ii) [] Answer (b) [] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

12 1 16 (a) Solve the simultaneous equations y 6x 60 x y 0 Answer x= y= [] (b) Consider the pattern, 1 = = = = 64 (i) Write down the 6 th line in the pattern. (ii) Find the value of (iii) Given that to n terms = 11, find the value of n. Answer (b) (i) [1] (b) (ii) [1] (b) (iii) [1] Cedar Girls Secondary School 4016/01/S4/Prelim08

13 1 17 In sector AOB, OA = OB = 7 cm and chord AB = 5 cm. The side OA is drawn in the answer space below. (a) Complete the two possible sectors. (b) one of these sectors, (i) construct the perpendicular bisector of OB, (ii) locate and mark point P in the sector which is equidistant from the points O and B, and equidistant from the lines OA and OB. Answers (a) and (b) O A [5] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

14 14 18 Distance from A (metres) Time (t seconds) The diagram is the distance-time graph for the first 5 seconds of a car s journey towards a point, A. (a) Find the initial distance of the car from A. (b) Find the speed of the car when t 15. (c) Find the initial speed of the car. (d) The car moved with a constant acceleration for the last 5 seconds and passes A with a speed of 70 m/s. Find this acceleration. (e) On the grid in the answer space on the next page, draw the speed-time graph for the same journey. Answer (a) [1] (b) [] (c) [1] (d) [] Cedar Girls Secondary School 4016/01/S4/Prelim08

15 15 Answer (e) Speed (metres per second) Time (t seconds) [] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

16 16 19 A spinner is in the shape of a square. The four triangular parts are numbered 1,, and each spin, the probability of scoring 1 is 0.5, the probability of scoring is 0.5 and the probability of scoring 4 is The spinner is used in a board game in which a player s counter is moved to the right at each turn by the score shown on the spinner. A B C C D E F If the player s counter lands on the blank square, the player is out of the game. (a) Amanda s counter is on square B. Calculate the probability that she will not be out of the game after one more turn. (b) Beatrice s counter is on square B. Calculate the probability that, after two more turns, her counter will be on square D. (c) Cherry s counter is on square A. Calculate the probability that, after three more turns, her counter will be on square E. Answer (a) [1] (b) [] (c) [] Cedar Girls Secondary School 4016/01/S4/Prelim08

17 17 0 A star is made up of a regular hexagon, centre X, surrounded by 6 equilateral triangles. OA a and OB b. (a) Write the following vectors in terms of a and/or b, giving your answers in their simplest form. (i) OS, (ii) AB, (iii) OR (iv) CF. (b) If b 6 units, find the value of OR. (a) (i) [1] (ii) [1] (iii) [1] (iv) [1] (b) [] Cedar Girls Secondary School 4016/01/S4/Prelim08 [Turn over

18 CEDAR GIRLS SECONDARY SCHOOL SECONDARY 4 MATHEMATICS Answer Key for 008 Preliminary Examination PAPER 4016/1 1 Lian is correct. 14a days a p q b p q y x y ( x 4)( 1) a 160 5b x 6a 1 : b 0 sq. km 7 $ 96 8a b 10 7 m 1 ( 1, 4 ) 4 9a 1 1c 17 9b 10a 10b 10c 4 14bi ( x ) a 8 cm sq. cm 17 14bii y (, ) y x 4x 1. 11a b ai 1aii 9 1b MXL or MYV 5 1 x 1a 1 6 1b 9.5 or ai 1.7 C 1c 15aii.7 C y = 15b Mean daily temp for June > Mean daily temp for April June is hotter than April Std Deviation for April > Std Deviation for June Hence there is a greater variation of temperature in the month of April. x y 0 1d.5 sq. units

19 PAPER 4016/1 16a x= 9, y = 6 19a 0. 16bi = 16 19b bii 51 19c biii ai a 18a 400 m 0aii b a 18b aiii a b 10ms 0 18c 0aiv ( b a) ( a b) 10 ms 1 18d ms 5 18e Speed (metres per second) 70 0b 0.8 units Time (t seconds)

20 CEDAR GIRLS SECONDARY SCHOOL SECONDARY 4 MATHEMATICS Answer Key for 008 Preliminary Examination PAPER 4016/ 1(a) S$ 550 5(i) (b) US$ (ii) 1(c) S$ (iii) 1(d)(i) Gain: S$ (iv) 1(d)(ii) Percentage increase: 7.58% 6(a)(i) 6(a)(ii) 6(a)(iii) The cost price of the coffee in the morning, afternoon and evening (a)(iv) 9 1(e) $5 61 6(b).9 cm (a)(i)(a) A B { x : x 9} 7(a)(i) 9.17 cm The total profit made from the sales (a)(ii) 09 cm 9 7(a)(iii) 187 cm 7(b) 7.0 cm (a)(i)(b) A ' B' { x : 0 x or 8 x 15} 8(a) (a)(ii) 8(b) 0.97 (b)(i) 7 p 5q (b)(ii) (a)(i) (a)(ii) (c) 8(c) 10.7 cm 6 8(d) 4 cm 7 8(e) 1.85 cm 1 4r 9(a)(i) 49 marks 14r 9(a)(ii) 0 marks 1 cm 9(a)(iii) 9(a)(iv) 8 marks 18 marks (d) 8 9(b) 7 marks 1 cm 9 9(c) No. Median for SMO is lower. 4(b)(i)(a) 11 10(a)(i) y = 6.64, x =.5 4(b)(i)(b) 4(b)(i)(c) 4(b)(ii) 1.1km 10(a)(ii).4 < x < (b). 7.5km 10(c) x = 1.65 or x = 6.45

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