AQA GCSE Mathematics Specification (8300/3F)

AQA GCSE Mathematics Specification (8300/3F) NEW SPECIMEN PAPERS PUBLISHED JUNE 2015 GCSE Mathematics Specification (8300/3F) Paper 3 Foundation tier Date Morning 1 hour 30 minutes Materials Instructions • Use black ink or black ball-point pen. Draw diagrams in pencil. • Fill in the boxes at the bottom of this page. • Answer all questions. • You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages. • Do all rough work in this book. • In all calculations, show clearly how you work out your answer. Information • The marks for questions are shown in brackets. • The maximum mark for this paper is 80. • You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer book. Version 1.0 8300/3F Answer all questions in the spaces provided. 1 Here are seven numbers. 13 6 12 7 6 4 8 1 (a) Work out the range of the seven numbers. Circle your answer. [1 mark] 5 6 7 8 9 1 (b) What is the mode of the seven numbers? Circle your answer. [1 mark] 5 6 7 8 9 2 Which shape has two lines of symmetry and its diagonals intersecting at 90˚? Circle the correct letter. A B C D [1 mark] 3 Which of these is a cube number? Circle your answer. [1 mark] 3 9 27 100 Turn over for the next question 4 Liz buys a car for £7500 She pays a deposit of £1875 She pays the rest in 36 equal monthly payments. Work out the amount of each monthly payment. [3 marks] Answer £ 5 120 men and 80 women were asked if they drive to work. Altogether 1 4 of the people said yes. 1 of the men said yes. 3 What fraction of the women said yes? [4 marks] Answer 6 Boxes A, B, C and D contain balls with numbers on them. Box A Box B Box C Box D 1 2 1 2 2 3 2 3 1 1 2 1 2 2 3 3 3 3 A ball is picked at random from each box. 6 (a) Which box gives the greatest chance of picking a 3? You must show your working. [2 marks] Box 6 (b) Which two boxes give the same chance of picking a 1? [1 mark] Box and Box 7 Zayn records his weekly sales. 300 Sales (£) 250 200 150 100 50 0 Week 1 Week 2 Week 3 Week 4 Every week his costs are £87.50 7 (a) Work out his profit in Week 1 [2 marks] Answer £ 7 (b) His sales in Week 4 were half of his sales in Week 1 Zayn says, “This means that my profit in Week 4 was half of my profit in Week 1” Is he correct? You must show your working. [2 marks] 8 Work out the value of 5x + 9y when x = 7 and y = –2 [2 marks] Answer 9 The points (1, 0) and (1, 4) are the diagonally opposite corners of a square. y 5 4 3 2 1 -5 -4 -3 -2 -1 O -1 1 2 3 4 5 x -2 Work out the coordinates of the other two corners of the square. [2 marks] Answer ( , ) and ( , ) 10 In an experiment, different masses are hung on a spring. The length of the spring is measured for each mass. Mass (g) 10 20 30 40 Length (cm) 20.8 21.6 22.4 23.2 10 (a) Draw a graph to show the length of the spring for masses from 10 g to 40 g [2 marks] 23.5 23.0 22.5 Length (cm) 22.0 21.5 21.0 20.5 20.0 19.5 0 0 5 10 15 20 25 30 35 40 Mass (g) 10 (b) Estimate the length of the spring with no mass hung on it. [1 mark] Answer cm 10 (c) How much longer is the spring with a 35 g mass than with a 15 g mass? [2 marks] Answer cm Turn over for the next question 11 A sequence of patterns uses grey squares and white squares. Here are the first four patterns. Pattern 1 Pattern 2 Pattern 3 Pattern 4 11 (a) Work out the total number of squares in Pattern 100 [3 marks] Answer 11 (b) Complete this number machine for the sequence of patterns. [1 mark] Number of grey squares Number of + white squares Turn over for the next question 12 In Scotland, squirrels are red or grey in the ratio red : grey = 1 : 2 1 2 12 (a) What fraction of the squirrels in Scotland are red? [2 marks] Answer 12 (b) In Scotland there are 120 000 red squirrels. How many squirrels are there altogether in Scotland? [2 marks] Answer 13 Hayley and Tom have £2000 to spend on food at their wedding. Here are their two options. Kim the Caterer Number of people Price per person 100 & over £24.50 80 to 99 £26.50 60 to 79 £28.50 up to 59 £30.50 Work out the maximum number of people they can pay for. Show working to compare the maximum number of people for both options. [5 marks] Answer 14 Solve 4(x + 5) = 15 [3 marks] x = 15 The mass of 40 cm3 of copper is 356 grams. Work out the mass of 90 cm3 of copper. [2 marks] Answer grams 16 24 boys, 45 girls and 281 adults are the members of a badminton club. 50 more children join the club. The number of girls is now 18% of the total number of members. How many of the 50 children were boys? [4 marks] Answer Turn over for the next question 17 The table shows information about the marks of 30 students in a test. Mark Frequency 14 2 15 10 16 2 17 3 18 13 Total = 30 Students who scored less than the mean mark have to retake the test. How many students have to retake the test? You must show your working. [3 marks] Answer 18 Work out the square root of 100 million. Circle your answer. [1 mark] 1000 10 000 100 000 1 000 000  5    2  19 a = 2 and b =  3      Circle the vector a – b   3    5   7    1  3   1  7  5 [1 mark]         20 Circle the decimal that is closest in value to 2 3 [1 mark] 0.6 0.66 0.667 0.67 Turn over for the next question 21 When x2 = 16 the only value that x can be is 4 Is this true or false? Tick a box. [1 mark] True False Reason 22 In 1999 the minimum wage for adults was £3.60 per hour. In 2013 it was £6.31 per hour. Work out the percentage increase in the minimum wage. [3 marks] Answer % 23 Use ruler and compasses to answer this question. Point P is • the same distance from AB and AD • 6 cm from C. D C A B Show the position of P on the diagram. [3 marks] Turn over for the next question 24 (a) Use your calculator to work out 19.422 – ÷ 4.95 Write down your full calculator display. [1 mark] Answer 24 (b) Use approximations to check that your answer to part (a) is sensible. You must show your working. [2 marks] 25 Three cups, A, B and C, contain only salt and water. The different mixtures are A salt : water = 3 : 22 B salt = 1 8 C salt = 12.75% Which cup has the greatest proportion of salt? You must show your working. [3 marks] Answer Turn over for the next question 26 y is directly proportional to x. Which graph shows this? Circle the correct letter. [1 mark] A B y y O x O x C D y y O x O x 27 A bag contains counters that are red, blue, green or yellow. red blue green yellow Number of counters 9 3x x – 5 2x A counter is chosen at random. The probability it is red is 9 100 Work out the probability it is green. [4 marks] Answer Turn over for the next question 28 The pressure at sea level is 101 325 Pascals. Any rise of 1 km above sea level decreases the pressure by 14% For example, at 3 km above sea level the pressure is 14% less than at 2 km Work out the pressure at 4 km above sea level. Give your answer to 2 significant figures. [4 marks] Answer Pascals 29 ABC is a triangle with AB = AC BA is parallel to CD. A Not drawn accurately D P x 15° B C Show that angle x = 30 [3 marks] END OF QUESTIONS Version 1.0 8300/3F There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Copyright © 2015 AQA and its licensors. All rights reserved.