GCSE MATHS 2018 PAPER 2

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5 8 7 A 0 1 2 0 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 Write down the value of the 4 in the number 542.3 2 Write down a square number that is also an odd number. 3 (a) Change 4560g into kg. (b) Change 7.3 m into mm. 4 Work out the cube root of 64 5 Write 0.31 as a fraction. 2 (Total for Question 1 is 1 mark) (Total for Question 2 is 1 mark) (1) (1) (Total for Question 3 is 2 marks) (Total for Question 4 is 1 mark) (Total for Question 5 is 1 mark) P 5 5 5 8 7 A 0 2 2 0 kg mm 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 6 Here are four fractions. 314 Write the fractions in order of size. Start with the smallest fraction. 7 (a) Simplify 3m - m - m + 3m (b) Simplify 2 x nx px 4 5 7 19 25 11 15 (Total for Question 6 is 2 marks) (1) (Total for Question 7 is 2 marks) 8 A map has a scale of 1 cm to 14 km. On the map, the distance between Manchester and London is 18.8 cm. What is the real distance, in km, between Manchester and London? (1) P 5 5 5 8 7 A 0 3 2 0 (Total for Question 8 is 2 marks) km Turn over ► 9 (a) The nth term of a sequence is 3n+4 Explain why 21 is not a term of this sequence. (b) Here are the first three terms of a different sequence. 1 2 Write down two numbers that could be the 4th term and the 5th term of this sequence. Give the rule you have used to get your numbers. 10 Here is a number machine. input x5 (a) Work out the output when the input is 8 (b) Work out the input when the output is 28 4 (2) (Total for Question 9 is 4 marks) -2 (2) >output P 5 5 5 8 7 A 04 20 (1) (2) (Total for Question 10 is 3 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 11 Adam gets a bonus of 30% of £80 Katy gets a bonus of £28 Work out the difference between the bonus Adam gets and the bonus Katy gets. 12 There are 49 counters in a bag. 20 of the counters are red. The rest of the counters are blue. One of the counters is taken at random. Find the probability that the counter is blue. £. (Total for Question 11 is 3 marks) (Total for Question 12 is 2 marks) P 5 5 5 8 7 A 0 5 20 5 Turn over ► 13 A square has an area of 81 cm² (a) Find the perimeter of the square. The diagram shows a right-angled triangle and a parallelogram. 16 cm 6 81 cm² 9 cm The area of the parallelogram is 5 times the area of the triangle. The perpendicular height of the parallelogram is h cm. (b) Find the value of h. hcm -30 cm- h = P 5 5 5 8 7 A 0 6 20 (2) (3) (Total for Question 13 is 5 marks) .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 Victoria throws an ordinary fair 6-sided dice once. She says, "The probability of getting a 3 is half the probability of getting a 6" (a) Is Victoria correct? You must explain your answer. Andy throws the dice twice. He says, "The probability of getting a 6 on both throws is (b) Is Andy correct? You must explain your answer. Indre throws the dice once. She also throws a coin to get Heads or Tails. (c) List all the possible outcomes she can get. 2/6 STO (1) P 5 5 5 8 7 A 0 7 20 (1) (2) (Total for Question 14 is 4 marks) Turn over ► 15 Remi invests £600 for 5 years in a savings account. By the end of the 5 years he has received a total of £75 simple interest. Work out the annual rate of simple interest. 16 -5 -4 -3 --2 8 M 5 -4 -3 -2 1 O -2 -3 -4 -5 (Total for Question 15 is 3 marks) A B 3 Describe fully the single transformation that maps shape A onto shape B. X (Total for Question 16 is 2 marks) P 5 5 5 8 7 A 0 8 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 DO NOT WRITE IN THIS AREA 17 Adrian is going to make concrete. He is going to use 180 kg of cement 375 kg of sand 1080 kg of stone Cement, sand and stone are sold in bags. Adrian already has 1 bag cement 25 kg 1 bag sand 22.5 kg 10 bags of cement 20 bags of sand 20 bags of stone Work out what bags he needs to buy to make the concrete. 1 bag stone 50 kg (Total for Question 17 is 3 marks) P 5 5 5 8 7 A 09 20 Turn over ► 18 Bill wants to increase 150 by 3% He writes down Bill's method is wrong. (a) Explain why. Sally wants to decrease 150 by 3% (b) Complete this statement to show how Sally can decrease 150 by 3% 19 (a) Solve 3(x-4)= 12 150 x 1.3 195 (b) Factorise fully 9b3b² 10 150 x (1) (Total for Question 18 is 2 marks) (1) X = P 5 5 5 8 7 A 0 1 0 20 (2) (2) (Total for Question 19 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 20 {even numbers between 1 and 25} A = {2, 8, 10, 14} B = {6, 8, 20} C={8, 18, 20, 22} (a) Complete the Venn diagram for this information. E A B Q A number is chosen at random from 8. (b) Find the probability that the number is a member of AB. (4) (2) (Total for Question 20 is 6 marks) P 5 5 5 8 7 A 0 1 1 2 0 11 Turn over ► 21 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. 1 2 Weight (kg) 12 105 100 95 90 85 140 160 170 X X X 180 Height (cm) Sean has plotted the points accurately. Write down two things that are wrong with his answer. X X X X 190 P 5 5 5 8 7 A 0 1 2 20 200 (Total for Question 21 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 22 BEG is a triangle. A D 110° E ABC and DEF are parallel lines. Work out the size of angle x. Give a reason for each stage of your working. B 25° 35° x P 5 5 5 8 7 A 0 1 3 2 0 с G (Total for Question 22 is 4 marks) 13 Turn over ► 23 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. (a) Work out who will get the most interest by the end of 3 You must show all your working. 14 Shares account Interest 3.5% per annum years. 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. (4) (1) (Total for Question 23 is 5 marks) P 5 5 5 8 7 A 0 14 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 DO NOT WRITE IN THIS AREA 24 The diagram shows a floor in the shape of a trapezium. 10m 7m 16m 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. 5 litres P 5 5 5 8 7 A 0 15 20 £16.99 (Total for Question 24 is 5 marks) 15 Turn over ► 25 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. 16 (Total for Question 25 is 3 marks) P 5 5 5 8 7 A 0 16 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 DO NOT WRITE IN THIS AREA 26 (a) Expand and simplify (5x + 2)(2x - 3) (b) Factorise x² + 4x + 3 27 (a) Write the number 0.000 075 47 in standard form. (b) Write 3.42 x 104 as an ordinary number. (c) Work out 2.3 × 10 × 6.7 × 10³ 5 x 10-⁹ (2) (2) (Total for Question 26 is 4 marks) (1) P 5 5 5 8 7 A 0 1 7 20 (1) (2) (Total for Question 27 is 4 marks) TOTAL FOR PAPER IS 80 MARKS 17 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA BLANK PAGE DO NOT WRITE IN THIS AREA 18 P 5 5 5 8 7 A 0 1 8 20 P 5 5 5 8 7 A 01920 19 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 20 P 5 5 5 8 7 A 0 2 0 20