Maths 2020 paper 2

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01 24 Total Marks Turn over ► ? Pearson Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 (a) Write 84 as a product of its prime factors. (b) Find the lowest common multiple (LCM) of 60 and 84 2 (2) (2) (Total for Question 1 is 4 marks) P6 2 2 7 8 RA02 2 4 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 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {even numbers} B = {factors of 10} (a) Complete the Venn diagram for this information. E o A number is chosen at random from the universal set, & (b) Find the probability that this number is in the set AB B (3) (Total for Question 2 is 5 marks) P 6 2 2 7 8 RA 0 3 2 4 Turn over ► 3 Carlo puts tins into small boxes and into large boxes. He puts 6 tins into each small box. He puts 20 tins into each large box. Carlo puts a total of 3000 tins into the boxes so that number of tins in small boxes: number of tins in large boxes = 2:3 Carlo says that less than 30% of the boxes filled with tins are large boxes. Is Carlo correct? You must show all your working. (Total for Question 3 is 5 marks) P6 2 2 7 8 RA0424 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 (a) Complete the table of values for y = 5 - x³ X y -2 -2 -1 -1 6 (b) On the grid below, draw the graph of y=5-x³ for values of x from -2 to 2 УА 14 -12 10 8 6 4 M. 2 O -2 0 4 1 2 P 6 2 2 7 8 RA052 4 2 X (2) (2) (Total for Question 4 is 4 marks) 5 Turn over ► 5 Work out the value of x. Give your answer correct to 1 decimal place. 6 a = -() 6 b = Find 2a 3b as a column vector. 34° 178 mm x mm (Total for Question 5 is 2 marks) (Total for Question 6 is 2 marks) P 6 2 2 7 8 RA 062 4 I 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 7 The diagram shows a right-angled triangle and a quarter circle. 9m 6m The right-angled triangle ABC has angle ABC = 90° The quarter circle has centre C and radius CB. Work out the area of the quarter circle. Give your answer correct to 3 significant figures. You must show all your working. B D (Total for Question 7 is 4 marks) P 6 2 2 7 8 RA 0 7 2 4 m² 7 Turn over ► 8 Tariq buys a laptop. He gets a discount of 5% off the normal price. Tariq pays £551 for the laptop. (a) Work out the normal price of the laptop. Joan invests £6000 in a savings account. The savings account pays compound interest at a rate of 2.4% for the first year 1.7% for each extra year. (b) Work out the value of Joan's investment at the end of 3 years. 8 £ P6 2 2 7 8 RA 082 4 £. (2) (3) (Total for Question 8 is 5 marks) 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 9 Aisha recorded the heights, in centimetres, of some girls. She used her results to work out the information in this table. 1 2 130 Least height Lower quartile 140 Interquartile range Median Range 142 cm 150 154 cm Aisha drew this box plot for the information in the table. The box plot is not fully correct. 17 cm 162 cm 40 cm 170 160 Height (centimetres) Write down the two things Aisha should do to make the box plot fully correct. 180 P6 2 2 7 8 RA09 2 4 190 (Total for Question 9 is 2 marks) Turn over ► 10 (a) Simplify (b) Simplify m² 8(x4) (x-4)² (c) Simplify (3n²w²)³ 11 Jack is in a restaurant. There are 5 starters, 8 main courses and some desserts on the menu. 10 Could Jack be correct? You must show how you get your answer. (1) (2) (Total for Question 10 is 4 marks) Jack is going to choose one starter, one main course and one dessert. He says there are 240 ways that he can choose his starter, his main course and his dessert. (1) P 6 2 2 7 8 RA 0 1 0 2 4 (Total for Question 11 is 2 marks) 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 12 The graph gives information about the volume, v litres, of petrol in the tank of Jim's car after it has travelled a distance of d kilometres. Volume (v litres) 30 20 10 0 50 (a) Find the gradient of the graph. 100 150 Distance (d kilometres) 200 (b) Interpret what the gradient of the graph represents. 250 P 6 2 2 7 8 RA 0 1 1 2 4 300 (2) (1) (Total for Question 12 is 3 marks) 11 Turn over ► 13 Here is triangle ABC. 34° 12 A Work out the length of AB. Give your answer correct to 1 decimal place. 23.8 cm 26° B (Total for Question 13 is 3 marks) P6 2 2 7 8 RA 01 2 2 4 cm 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 14 Here are two squares, A and B. A B The length of each side of square B is 4 cm greater than the length of each side of square A. The area of square B is 70 cm² greater than the area of square A. Find the area of square B. Give your answer correct to 3 significant figures. You must show all your working. (Total for Question 14 is 4 marks) P 6 2 2 7 8 RA 01 3 2 4 cm² 13 Turn over ► 15 -6 14 y 6 B V 5 4 3 2 1 -5 -4 -3 -2 -1 0 -1 --2 -3 -4 -5 -6 -7 -8 1 2 3 A 4 5 6 Describe fully the single transformation that maps triangle A onto triangle B. P 6 2 2 7 8 RA 0 14 24 7 X (Total for Question 15 is 2 marks) 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 16 Here are the first five terms of a quadratic sequence. 10 21 38 61 90 Find an expression, in terms of n, for the nth term of this sequence. (Total for Question 16 is 3 marks) 17 Write down the coordinates of the turning point on the graph of y = (x+12)² - 7 (Total for Question 17 is 1 mark) P6 2 2 7 8 RA 0 1 5 2 4 15 Turn over ► 18 The diagram represents a solid cone. 25 cm 20 cm 16 10 cm Curved surface area of cone = πrl The cone has a base diameter of 20 cm and a slant height of 25 cm. A circle is drawn around the surface of the cone at a slant height of 10 cm above the base. The curved surface of the cone above the circle is painted grey. Work out the area of the curved surface of the cone that is not painted grey. Give your answer as a multiple of You must show all your working. (Total for Question 18 is 4 marks) P6 2 2 7 8 RA 0 1 6 24 cm² 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 19 A hot air balloon is descending. The height of the balloon n minutes after it starts to descend is h metres. The height of the balloon (n +1) minutes after it starts to descend, h n+1 h₁+₁=Kx h₁ +20 where K is a constant. n+1 The balloon starts to descend from a height of 1200 metres at 09 15 At 09 16 the height of the balloon is 1040 metres. Work out the height of the balloon at 09 18 metres, is given by (Total for Question 19 is 4 marks) P 6 2 2 7 8 RA 0 17 24 m 17 Turn over ► 20 There are only red sweets and yellow sweets in a bag. There are n red sweets in the bag. There are 8 yellow sweets in the bag. Sajid is going to take at random a sweet from the bag and eat it. 7 He says that the probability that the sweet will be red is 10 (a) Show why the probability cannot be 7 10 After Sajid has taken the first sweet from the bag and eaten it, he is going to take at random a second sweet from the bag. 3 Given that the probability that both the sweets he takes will be red is 5 (b) work out the number of red sweets in the bag. You must show all your working. 18 P6 2 2 7 8 RA 01 8 2 4 (3) 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 (Total for Question 20 is 8 marks) P6 2 2 7 8 RA 0 19 2 4 19 Turn over ► 21 The graph of the curve with equation y = f(x) is shown on the grid below. YA -4 curve C 20 -2 (1,6) 2 O -2 (a) On the grid above, sketch the graph of the curve with equation y = f(-x) 2 (4, 6) 4 curve S X The curve C with equation y = 5 + 2x - x² is transformed by a translation to give the curve S such that the point (1, 6) on C is mapped to the point (4, 6) on S. (b) Find an equation for S. P6 2 2 7 8 RA 0 2 0 2 4 X (2) (2) (Total for Question 21 is 4 marks) 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 22 C is a circle with centre the origin. A tangent to C passes through the points (-20, 0) and (0, 10) Work out an equation of C. You must show all your working. (Total for Question 22 is 5 marks) TOTAL FOR PAPER IS 80 MARKS P 6 2 2 7 8 RA 0 2 1 2 4 21 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA BLANK PAGE DO NOT WRITE IN THIS AREA 22 P6 22 7 8 RA02 2 2 4 6 2 2 7 8 RA 0 2 3 2 4 23 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA BLANK PAGE DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA BLANK PAGE DO NOT WRITE IN THIS AREA 24 P6 22 7 8 RA 0 2 4 24