07_HENDERSON_4EMP1 3-7

2 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER (a) Evaluate ÷ as a fraction in its lowest term (b) Evaluate − (− ) Answer (a) (b) (a) [1] (b) [1] Find, in its simplest form the fraction which is exactly half-way between and 9 Arrange the following fractions in ascending order 31%, , , − 6.2, 1.4 20 Answer (a) _ [1] (b) _ [1] HSS/Prelim2007/4017_01 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER (a) (b) Express, correct to two significant figures, (i) 347.12 (ii) 0.0016489 Hence, estimate, correct to one significant figure, the value of 347.12 × (0.0016489) Answer (ai) [1] (aii) [1] (b) [1] Three people A, B and C participated in a race The time taken by A is times that of B The time taken by B is times that of C B took 40 seconds to complete the race (a) Find the ratio of the time taken by A to the time taken by B to the time taken by C (b) Find the shortest time taken among these three participants to complete the race Answer HSS/Prelim2007/4017_01 (a) _: _: [1] (b) _seconds [1] NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER Given that − ≤ y ≤ −2 and − 10 ≤ z ≤ , where y and z are integers, find (a) (b) z , y the smallest value of z − y the largest value of Answer (a) (a) [1] (b) [1] A circular pail can be filled up with water by taps running at the same time in minutes, given that water from each tap flows at the same rate How long would it take taps running at the same time to fill the tank? (b) Employees of Burger King were given an increase amounting to 8% in the monthly salaries If an employee earned $1500 per month originally, find his monthly salary after the increase Answer HSS/Prelim2007/4017_01 (a) _ minutes [2] (b) _ [1] NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER Expressed as the product of prime factors, 9295 = × 11× 13 and 1573 = 112 ×13 Use these results to find (a) The highest common factor of 9295 and 1573 (b) The smallest integer, h, such that 9295h is a perfect square (c) The smallest integer, n, such that 1573n is a multiple of 9295 Answer (a) [1] (b) [1] (c) [1] Solve the equations 3x − y = 23 x + y = −4 Answer x = , y = [3] HSS/Prelim2007/4017_01 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER The table shows the temperature in four cities at 8pm on a particular day Singapore 26°C Sydney 18°C Berlin −6°C Tokyo −2°C (a) Find the difference in temperature between Singapore and Tokyo (b) The temperature in Seoul was exactly midway between the temperature in Berlin and Sydney Find the temperature in Seoul Answer 10 (a) °C [1] (b) °C [1] Ah Seng would like to save $5000 for years He has to decide from the two banks below Bukit Merah Bank: a simple interest of % per annum Redhill Bank: a compound interest of 2% per annum Determine with working, which bank Ah Seng should deposit his money with Answer HSS/Prelim2007/4017_01 _ [3] NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 11 A television station bought the rights to telecast the NBA finals live each time the game was on When it is 21 00 in Singapore, the time in San Antonio, USA, is 07 00 the same day (a) On a particular Thursday, a game ended at 2015 in San Antonio Calculate the duration of the game, assuming the game started at 1535, San Antonio time (b) On a particular Wednesday, the game in San Antonio started at 19 30 Calculate the time and day the game started in Singapore Give your answers in 24 hour clock system Answer 12 (a) _ [1] (b) _ [1] A polygon has n sides Three of its exterior angles are 36o, 55o, 65o and the remaining angles are each equal to 1o Find the value of n Answer HSS/Prelim2007/4017_01 _ [2] NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 13 ABCD is a quadrilateral, in which AD is parallel to BC and DC = 13 units If B is the point (a, -1), C is the point (a, 4), D is the point (0,6) and the gradient of AB is , (a) calculate the x-coordinates of the point C D (0, 6) (b) calclate the y-coordinates of point A (c) write down the name of the quadrilateral ABCD C (a, 4) (d) find the area of the quadrilateral ABCD B (a, -1) A (0, b) Answer HSS/Prelim2007/4017_01 (a) x-coordinates = [1] (b) y-coordinates = [1] (c) _ [1] (d) _units2 [2] NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 14 A cement truck manufacturer made a miniature of its cement truck using a scale of 1:20 (a) If the diameter of miniature’s wheel is 2.5 cm, what is the actual diameter of the wheel of the cement truck? Leave your answers in metres (b) The windscreen of the actual cement truck has a surface area of 1.5 m2 Find the surface area of the windscreen of the miniature cement truck Leave your answers in square centimeters (c) The cement truck can carry a load of 80 m of cement How much cement can the miniature load? Leave your answers in cubic metres Answer HSS/Prelim2007/4017_01 (a) m [1] (b) cm2 [2] (c) m3 [2] 10 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 15 The diagram shows the graph of y = x( x − p ) and y = x( p − x) A and B are two points of intersection on the x -axis (a) Write down the order of rotational symmetry (b) If (1, -2) lies on the curve y = x( x − p ) , determine the value of p y y = x( x − p) x B A Answer (a) (b) y = x( p − x) Order of rotational symmetry = [1] p = _ [1] 16 In the diagram, AC is parallel to EF, and AE is parallel to BD Given that ∠DEF = 37° and reflex ∠BDE = 244° , calculate E F (a) Find ∠AED, 37o (b) Find ∠CBD D A B Answer HSS/Prelim2007/4017_01 244° C (a) ∠AED = o [1] (b) ∠CBD = o [1] 11 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 17 The diagram represents a simplified snake and ladder board Start In each turn of a game played on this board, the player throws a fair 6-sided die and moves the number of squares indicated by the die If the player lands on a square containing the snake’s head, the player moves down the snake to the square containing the end of the tail If the player lands on a square containing the foot of a ladder, the player moves up the ladder to the square containing the end of the ladder In this game, the players begin from the ‘Start’ square (a) When a player is at the ‘Start’ square, find the probability of him landing on square in a single throw (b) At the completion of his first throw, a player is at square Find the probability that he will land on square in his next throw Answer HSS/Prelim2007/4017_01 (a) _ [1] (b) _ [1] 12 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 18 The diagram below shows the building of pyramids using playing cards Number of levels (a) Complete the 4th row of the following table Number of levels, L Total number of cards used, T Number of cards added to previous level, A (b) 2 15 Write down, in terms of L, an expression for A (c) How many complete levels can be built with a pack of 52 playing cards? Answer HSS/Prelim2007/4017_01 (a) T = , A = [1] (b) _ _ [1] (c) _ levels [1] 13 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 19 In the diagram, ABCD is a square whose diagonals are each cm long BD and AD are the diameters of the bigger and smaller circle respectively Take π = 22 Find, (a) the perimeter of the shaded region., giving your answers in surd form (b) the area of the shaded region A B D C Answer HSS/Prelim2007/4017_01 (a) cm2 [2] (b) cm2 [3] 14 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 20 (a) The graph below shows the line y - x = On the same diagram, sketch y - + 3x = [1] y -2 O x (b) Write down the coordinates of the points of intersection of the lines y - x = and y - + 3x = Answer (c) x = , y = _ [2] A container is being filled with water flowing at a constant rate from a tap At time t seconds after the tap is turned on, the height of the water in the container is h centimetres Initially the container is empty If the container is a bottle, as shown below, sketch the graph of h against t h O t [2] HSS/Prelim2007/4017_01 15 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 21 In a survey, the heights of 120 adults were measured The result is shown in the pie chart 1.7 ≤ h < 1.9 1.5 ≤ h < 1.6 1500 1.6 ≤ h < 1.7 (a) Find the value of a and b in the table below Height (h metres) 1.5 ≤ h < 1.6 1.6 ≤ h < 1.7 Number of adults 50 a Answer 1.7 ≤ h < 1.9 b a = _, b = [2] (b) The information is also to be represented in a histogram Complete the histogram 600 500 400 Frequency Density 300 200 100 1.5 1.6 1.7 1.8 Height (m) 1.9 2.0 [2] HSS/Prelim2007/4017_01 16 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 22 The diagram below shows a map of an island A treasure was hidden in the island There are three locations A, B and C on the map The map is being drawn to a scale of cm to km (a) Express the scale in the form 1: n Answer (a). _[1] (b) Some clues on the location of the treasure (T) are given below: I TA ≤ TC II It is less than km from C, III It is nearer to BC than BA Using the above clues, construct the locus of possible positions of the treasure Shade the region defined by the clues above [4] N A ² C ² ² HSS/Prelim2007/4017_01 B 17 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 23 The diagram below shows triangles A, B, C and D (a) Triangle A is mapped onto triangle B by a reflection in the line l Find the equation of the line l (b) Triangle B is mapped onto triangle C by a shear If the invariant line is y = 3, find the shear factor (c) Describe fully the single transformation which maps triangle A onto triangle D (d) Find the value of the ratio area of triangle C area of triangle D y 10 C B D A −4 −2 10 12 x Answer (a) [1] (b) [1] (c) [2] (d) [1] HSS/Prelim2007/4017_01 18 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 24 (a) ⎛ ⎞ ⎛ ⎞ ⎛ − 2⎞ Given that OP = ⎜⎜ ⎟⎟ , OQ = ⎜⎜ ⎟⎟ and OR = ⎜⎜ ⎟⎟ Find ⎝ − 2⎠ ⎝ − 6⎠ ⎝ k ⎠ (i) PQ , (ii) the value of k if OR is parallel to OP Answer (ai) PQ = _ (aii) k = (b) [1] [2] The diagram shows vectors OA and OB Given that OC = 3OA − 2OB , mark and label clearly point C on the diagram A O B [1] HSS/Prelim2007/4017_01 19 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER 25 The diagram is the speed-time graph of Ahmad's journey Speed (km/h) 40 30 20 10 1100 1200 1400 1300 Time (hr) Find (a) the acceleration at 1325 hr, (b) the distance traveled during the first hour of the journey Answer (c) (a) _ km/h2 [1] (b) km [1] Sketch on the grid below, the distance-time graph for the journey Distance (km) 80 60 40 20 1100 1200 HSS/Prelim2007/4017_01 1300 1400 Time [2] 20 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER Answers 1a 1b 2a -48 16b 17a 17b 2b − 6.2, 3ai 3aii b 4a 4b 350 0.0016 10 15:5:1 sec 18a 18b 18c 19a 5a 5b -16 19b 20a 6a 20b 6b 7a 7b 7c 9a 9b 10 11a 11b 12 13 mins $1620 143 55 65 x = 5, y = -2 28oC oC Bukit Merah Bank hrs 40 mins Thursday 0930 n = 27 13a 13b 13c -3 trapezium 13d 14a 14b 14c 15a 15b 16a 21 units 0.5m 37.5m2 0.01m3 64 o 3 ,31%,1.4,1 20 79 o T = 26, A = 11 A = 3L - 11 ( + 1) 0.5cm2 steeper graph, cut at (0,2) and ( ,0) (0,2) 20c 21a 21b 22a 23a 23b 23c 30, 40 300, 200 1:200000 y=x+2 enlargement with centre (8,2) and scale factor − 23d 24ai 24aii 24b (0,-6) 25a -40 25b 30 25c HSS/Prelim2007/4017_01 21 NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER HSS/Prelim2007/4017_01