Mathematics Mock Set 6 Higher Edexcel

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over > P Pearson 1 ayram Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. between 1 and 25} 6 ZA = {even numbers A = {2, 8, 10, 14} B = {6, 8, 20} C= {8, 18, 20, 22} (a) Complete the Venn diagram for this information. oin 1 E A 2 10 p. 14 W n 18 22 A number is chosen at random from E. (b) Find the probability that the number is a member of AB. B 24 12 ib 12 (Total for Question 1 is 6 marks) P 5 5 5 8 8 A 0 2 2 0 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA PowertraitE IN THIS AREA DURU, MALE HELEUS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2 Sean has information about the height, in cm, and the weight, in kg, of each of ten rugby players. He is asked to draw a scatter graph and a line of best fit for this information. Here is his answer. Weight (kg) 105 100 95 90 85 140 2 The live of Height goes 160 tip 170 Sean has plotted the points accurately. Write down two things that are wrong with his answer. 1. The line of best fit da X 180 Height (cm) intieto 190 only goes through one pont - 200 fit starts from &* (150, 85) inconsistupt values. (Total for Question 2 is 2 marks) P5 5 5 8 8 A0320 3 Turn over > | 3 BEG is a triangle. 110° E - Co- interion ABC and DEF are parallel lines. Work out the size of angle x. Give a reason for each stage of your working. 180-110=20 ^ ABE -70% line DR 70° 450 -angles - - 180-70-35= 75° EBG =75% angles on line 180-110-125 = 45 BÊG=45" 745⁰ - angles in a triangle : 180-75-45 = 60° 172 A * B&B= 60° x = 60° B 75⁰ 25° 35⁰ G 60 (Total for Question 3 is 4 marks) P 5 5 5 88 A 04 20 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WHITE IN THIS A AREA Maun Enst in Sim DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4 Northern Bank has two types of account. Both accounts pay compound interest. Cash savings account Interest 2.5% per annum Ali invests £2000 in the cash savings account. Ben invests £1600 in the shares account. 22153.78 K (a) Work out who will get the most interest by the end of 3 years. You must show all your working. Ali 2000×10253 2153-78-2000 2153.78 2215378€ No effect, at feel who Bon Afi gels more X. Ben gets (156 more No, because then Ali, Ben gele even Shares account Interest 3.5% per annum 2/77395 1773.45-1600- =173.95 In the 3rd year the rate of interest for the shares account is changed to 4% per annum. (b) Does this affect who will get the most interest by the end of 3 years? Give a reason for your answer. Ali Ben 200071 02832 Ben 1600×1-0333 the screase. B will gol most. already gets more more 2 1600×1.035 ²1. 04. =1782.52 € tvo MELANIA. small to Total for Question 4 is 5 marks) P 5 5 5 8 8 A 0 5 20170 WX 5 Turn over I Foor. VSI ETT 5 The diagram shows a floor in the shape of a trapezium. (10f1b)=7 2 you = 10m 7m John is going to paint the floor. Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of 2 m² John has £160 to spend on paint. Has John got enough money to buy all the paint he needs? You must show how you get your answer. Area of traperium 16m 91 m 2 Paint needed. 91=2=45-5s = 46 temes 9x16.491529 46=510s tins 10x16-992 169.9 jo, ". Not enough enough E 5 litres P 5 5 5 8 8 A06 20 £16.99 (Total for Question 5 is 5 marks) DO NOT WRITE IN THIS AREA CADO WINa M wwwwwww DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA BENCI WRITEIN ITS AKER DU NUI WHITE MV THIS AREA. w tanecunch DIMLAR te 6 A is the point with coordinates (5,9) B is the point with coordinates (d, 15) The gradient of the line AB is 3 Work out the value of d. y=3x+c 9=3(5)+c c=~6 y=3x-b 15=30-6 x=√ (Total for Question 6 is 3 marks) 1 for . 170840 7 P 5 5 5 8 8 A07 20 7 Turn over ► | I 7 (a) Write the number 0.000 086 23 in standard form. 3.2 x 10³ +5.1 x 10-² 4.3 x 10 Give your answer in standard form, correct to 3 significant figures. 744 0000-00 =744x x 106 (b) Work out 8 8.623×108 (1) 2.44 тов (2) (Total for Question 7 is 3 marks) P 5 5 5 8 8 A08 20 DO NOT WRITE IN THIS AREA DO NOT WHILE IN THIS ARER DO NOT WRITE IN THIS Maust onar su mu down SAREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA UO NOT WRITE IN THIS AREA www DO NOT WRITE IN THIS AREA AKAN KULI MEHEDIANZILIMderet -6 -5 -4. --B -2 Ø T 6 9 Martin truncates the number N to 1 digit. The result is 7 Write down the error interval for N. 5 6-5≤N<2.5 4- 3 -2- O -2 -3 t i Triangle P is reflected in the line y = -x to give triangle Q. Triangle Q is reflected in the line x = -1 to give triangle R. P 2 Describe fully the single transformation that maps triangle R to triangle P. Cockwise 9.0⁰ around (0₂0) (1) (Total for Question 8 is 3 marks) 6 P 5 5 5 8 8 A 09 20 7SN <8 (Total for Question 9 is 2 marks) 9 Turn over - 10 Robert makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 2:3 Yellow paint is sold in 5 litre tins. Each tin of yellow paint costs £26 Blue paint is sold in 10 litre tins. Each tin of blue paint costs £48 Robert sells all the green paint he makes in 10 litre tins. He sells each tin of green paint for £66.96 Work out Robert's percentage profit on each tin of green paint he sells. 10 Y 2:3 50÷5=0 Y 20 : 30 20+ 5x26 = 104. 30710×48=144²) #25 50÷10*66.96=3348 334.77-248 334.8 •*108/10 2 1948 2.18 211.25 15 multiplier 3348-248 248 =35% *100% P 5 5 5 8 8 A 0 1 0 20 $35 (Total for Question 10 is 5 marks) % www DO NOT WRITE IN THIS AREA Mountai DO NOT WRITE IN THIS AREA DO NOT WRITERN THIS AREA DO NOT WRITE IN THIS AREA માં તાપા નાmthat DO NOT WRITE IN THIS AREA. DO NORTECOMEZARER YOU NOT WRITE IN THIS AREA Mau CHSimintak iew Ofl 11 In a restaurant there are 9 starter dishes 15 main dishes 8 dessert dishes Janet is going to choose one of the following combinations for her meal. a starter dish and a main dish or a main dish and a dessert dish or a starter dish, a main dish and a dessert dish Show that there are 1335 different ways to choose the meal. 9x15x8 Starter Main Mam dessert starter man dessert 15x8x9= w 9x15=135 15x8 = 120 1350120 + 1080 = 1335 (Total for Question 11 is 3 marks) for P 5 5 5 8 8 A 0 1 1 2 0 11 Turn over 12 (a) Write 4x² - 9 6x + 9 (2x-3)(2x13) 2 8x²-18 2-12x+12x-18 - 4 4x (2x-3) + 6(2x-3) (4x+6)(2x-3) X (b) Express 12 2x x² – 3x 3*x+3)(x-³) 2 (2x-3) 3 (x-3) 4x² 9 6x9x²3x (Qx+9) (x²-3x) 8x3-18x1 2% 4x-6 3 1 x+1 x-2 4x2 2 4x² - 6x + bx - 9 = 2x(2x-3) +3(2x-3) 2(2x-3)(2x+3) ax + b in the form cx + d 2 x²-3x = x (x-3) (4x²9)(2x) + = where a, b, c and d are integers. 6x+9 = 3 (2x + 3) 6x²-9x-27 6x³-18/²+93-27x = 2x(3x79) + 3(3x-9) = (2x+3)(3-9 Z 8³-18x 6x²/4x²-27x 2 18x²-18 8x²9x-27 (4x+6)(2x-3) (2x+3)(3x-9) 34TH 3 (x-2) x + (x+1)x - 4(x+1)(x-2) (+1)(x-2)x 4 as a single fraction in its simplest form. z Z 2 = 6 x ²²-18 x + 9x-27 3x² - 6x + x² + x = 4(x²-x-2) ²-x²² - 2x 4x² - 5x (4x14x13) -2x x+8 X -x²³²-2x X 4x-t 3x-9 (3) (Total for Question 12 is 6 marks) P 5 5 5 8 8 A 0 1 2 2 0 Î DO NOT WRITE IN THIS AREA HOWN CON ASTMA mina DO NOT WRITE IN THIS ARGA DO NOT WADDY 1995 AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS ARES DO NOT VIRITE IN THIS AREA DO NOT WRITE IN THIS AREA e Chien d TIVETICIRIS AREAS 13 The diagram shows a circle and an equilateral triangle. One side of the equilateral triangle is a diameter of the circle. The circle has a circumference of 44 cm. Work out the area of the triangle. Give your answer correct to 3 significant figures. da 244 d 3.14 = 44 #d=44 2 44 x² = -( 32 14 4 ² 4 ) ² + ( 4 4 4 ) ² X (3.14) 3.14 44 ( x + ( + 1 + x + 1) = 2 X 3.14 Sin 30 √ MALWM 45 1=20 Y-intercept (0.1) AT 601√ 90 Aren of 10 14 On the grid, sketch the curve with equation y = 2* Give the coordinates of any points of intersection with the axes. Y=2x for 44 3.14 P 5 5 5 8 8 A 0 1 3 2 0 60 = 1/2 ab Sin (C) 1 44 23.1 3.142 2 849 (Total for Question 13 is 3 marks) 44 xsin (60) =-343,142² 晕 1=549 (1d,p.) (Total for Question 14 is 2 marks) t .cm² 13 Turn over 31 ster into the 15 The equation of a circle is 2+² = 42.25 "1 into t Find the radius of the circle. y that! 16 There are only red counters and blue counters in a bag. Joe takes at random a counter from the bag. The probability that the counter is red is 0.65 Joe puts the counter back into the bag. 142.25/€ 6.5 Mary takes at random a counter from the bag. She puts the counter back into the bag. 14 ters are (a) What is the probability that Joe and Mary take counters of different colours? the J M P Bz Bp (blue) = 1065 = 0.39 0.65 x 0.35 +0.35×0-65 =0.45/5 There are 78 red counters in the bag. (b) How many blue counters are there in the bag? 78 0.65 ×0.35 784-0.63) 788 0.38 = 42 6.5 (Total for Question 15 is 1 mark) b=1-0.65 20-35 0.485 (2) P 5 5 5 8 8 A 0 1 4 2 0 42 (2) (Total for Question 16 is 4 marks) DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT TIANG IN HEID ARCHY DONGERBITZINE TIRE ANCH, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA and q are two numbers such that p > q 17 P 9 103 When you subtract 5 from p and subtract 5 from q the answers are in the ratio 5:1 When you add 20 to p and add 20 to q the answers are in the ratio 5:2 Find the ratio p:q Give your answer in its simplest form. P-59-5=5=1 zoep = 20eq = 5:2 5 20 ep = 12/20 weq 126 40+2p=100+59 of B 80-592-20 -59 2-100 9320 = 80=20 4 N P-5 5 9-57 P-5=59-28 are it t 2p-59260 P-59==20 =80 P/PP 3 P 5 5 5 88 A015 20 3 3 4:1 (Total for Question 17 is 5 marks) 15 Turn over 18 The straight line L, passes through the points with coordinates (4, 6) and (12, 2) The straight line L₂ passes through the origin and has gradient -3 The lines L, and L, intersect at point P. Find the coordinates of P. L₂=y=-3x L₁ = y=-3x+0 by=-3x+49 -Syz -48 yz 9.6 16 m= 2-6 224 -4 === 6* = - 1212 (4) + C 8 = t y=-1/232x+8 y=-3x+0 y = -√2/2 x+8 952-0-5xt8 162-05x x=-3/2 -32 qb (Total for Question 18 is 4 marks) P 5 5 5 8 8 A 0 1 6 20 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DU NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 1 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITEINADIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAS m² + 7 4 Show all your working. 19 Solve 22 < << 32 287 4432 => 88<m² +7 <128 => 81 < m² sizi => q< <MX 샌 +9<m<ll 22 < m * ±9 <m<#11 or -9 cm (-11 £9 km K±11 gamass (Total for Question 19 is 5 marks) P5 5 5 8 8 A 0 1 7 20 17 Turn over - 7 20 Here is a frustum of a cone URLE Solid S 18 0421 -7.2 cm- -7.2 cm- 3.2 cm Folume Volume of s.f. 3.2 cm The density of the frustum is 2.4 g/cm³ The density of the hemisphere is 4.8 g/cm³ Calculate the average density of solid S. The diagram shows that the frustum is made by removing a cone with height 3.2 cm from a solid cone with height 6.4 cm and base diameter 7.2 cm. The frustum is joined to a solid hemisphere of diameter 7.2 cm to form the solid S shown below. 80.41784S t 3.2 cm Volume of sphere fustrum: Volume of cone = = 4 π13 3xx 3.6² * 6.4 = 86. g Adp) b 2 31,8²x3,2x{ x== 1. (idop) 3² 86.9-10.9=96.0 cm Volume of hemisphere: 3.6³xxx=97.7 cm³ (Id.p.) P 5 5 5 8 8 A 0 18 20 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA www.DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WHITE IN THIS AREA T DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Average density of S: 76x24 +977 x 4.8 764977 =3,7/ (ld.p.) glem 3 3.7 (Total for Question 20 is 5 marks) for t P 5 5 5 8 8 A 0 1 9 2 0 g/cm³ 19 Turn over 21 mis en 20 the ig A, B, R and P are four points on a circle with centre O. A, O, R and Care four points on a different circle. The two circles intersect at the points A and R. CPA, CRB and AOB are straight lines. Prove that angle CAB= angle ABC. EA RÂD=180-* ARÃO= : opposite angles. in a cydre quadrilateral add up to 180. LORC Let the angle of MAÎR bey. Angles in a straight = 180-X line Anyles Ma triangle :: ORB = 180- (180-X) 2 • AO and OR are radii ..RÃO = ORA ORB = 180 - 180-X 2 " OR and OB .. OBR = ORB are B Angles radii. CAB = X bias irrectes triangle zx "RO=DB → isoceles liangle .. ORB = DÊR at a right angle .. CAB - ABC (Total for Question 21 is 4 marks) TOTAL FOR PAPER IS 80 MARKS P 5 5 5 8 8 A 0 2 0 20 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA