GCSE Mathematics. Foundation Tier

Transcription

1 For Edexcel Name GCSE Mathematics Paper 2E (Calculator) Foundation Tier Time: 1 hour and 30 minutes Materials required Ruler, protractor, compasses, pen, pencil, eraser. Tracing paper may be used. Instructions and Information for Candidates Write your name in the box at the top of the page. Answer all the questions in the spaces provided in this question paper. The marks for each question and for each part of a question are shown in brackets. The total number of marks for this paper is 100. There are 25 questions in this paper. Calculators may be used. If your calculator does not have a π button, take the value of π to be unless the question instructs otherwise. Advice to Candidates Show all stages in any calculation. Work steadily through the paper. Do not spend too long on one question. If you cannot answer a question, leave it and attempt the next one. Return at the end to those you have left out. Written by Shaun Armstrong Only to be copied for use in the purchaser's school or college EF2E Page 1

2 GCSE Mathematics Formulae: Foundation Tier a Area of a trapezium = 1 (a + b)h 2 h b Volume of a prism = area of cross section length cross section length EF2E Page 2

3 Answer ALL TWENTY FIVE questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1. Here is part of a bus timetable. Bus Stop Time Time Worcester Saint Johns and every Bransford minutes Leigh Sinton until Malvern Link Great Malvern How long should the journey from Worcester to Great Malvern take? minutes Zack arrives at the Bransford bus stop at How long should he wait for a bus to arrive? Brian is in Worcester and needs to get to Malvern Link by minutes (c) At what time does the latest bus he can catch leave Worcester? (Total 3 marks) Q1 EF2E Page 3

4 2. Write down the mathematical name of the shaded shape. On the grid, show how the shaded shape tesselates. You should draw at least 6 shapes. (Total 3 marks) Q2 EF2E Page 4

5 3. Solder is an alloy made from tin and lead. The ratio of the weight of tin to the weight of lead in solder is 5 : 3 Work out the weight of lead in 20 grams of solder. g Q3 (Total 2 marks) 4. Each CD in a bargain box costs 2.50 Liam has 14. He wants to buy as many CDs as he can. The Chatters Bargain Box CDs 2.50 (i) How many CDs can Liam buy from the bargain box? (ii) How much money will Liam have left after buying the CDs? 45% of the CDs that Nick owns are by Heavy Metal bands. What percentage of the CDs that Nick owns are not by Heavy Metal bands. % (Total 3 marks) Q4 EF2E Page 5

6 5. Measure the length of the line AB. A B cm C D The line CD is 8 cm long. Draw a rectangle with an area of 24 cm 2. Use the line CD as one side of the rectangle. (c) 1 cm The grid above is made up of equilateral triangles of side length 1 cm. On the grid, draw a regular hexagon with a perimeter of 18 cm. (Total 5 marks) Q5 EF2E Page 6

7 6. y W X 1 O x Write down the coordinates of the point (i) W, (, ) (ii) X. (, ) Y is the point (1, 3). On the grid, mark and label the point Y. Z is a point on the x-axis. XZ is parallel to WY. (c) On the grid, mark and label the point Z. (Total 4 marks) Q6 EF2E Page 7

8 7. This pie chart shows the favourite television channel of 60 adults. Other ITV1 Channel 4 BBC1 Sky One (i) Measure the angle for BBC1. (ii) What fraction of these adults said BBC1 is their favourite channel? (iii) How many of these adults said ITV1 is their favourite channel? (4) EF2E Page 8

9 Susie is writing a questionnaire about how much television children watch. This is one of her questions. How much television do you watch? This is not a good question. Design a better question to find out how much television children watch. You should include some response boxes. (Total 6 marks) Q7 8. Sanjay asked 20 people coming out of the library how many books they had borrowed. Here are his results. Number of books Number of people (c) Write down the modal number of books borrowed. Work out the range of the number of books borrowed. Work out the mean number of books borrowed. (3) (Total 5 marks) Q8 EF2E Page 9

10 9. Change 2 litres into millilitres. ml Change 23 millimetres into centimetres. cm (c) A table weighs 20 kilograms. Roughly what is the weight of the table in pounds? pounds (Total 4 marks) Q9 10. Element Melting Point ( C) Bromine 7 Chlorine 101 Gallium 30 Mercury 39 Oxygen 223 The table gives the melting point, in C, of five elements. Which of these elements has the highest melting point? Which of these elements has the lowest melting point? (c) Work out the difference between the melting points of Bromine and Mercury. C (Total 3 marks) Q10 EF2E Page 10

11 11. The scatter graph shows information about 8 companies. For each company, it shows the percentage of employees doing unskilled jobs and the mean weekly pay of all employees. Mean weekly pay ( ) Percentage of employees doing unskilled jobs Describe the relationship between the mean weekly pay and the percentage of employees doing unskilled jobs. (c) Draw a line of best fit on the diagram. Use your line of best fit to estimate the mean weekly pay at another company where 59% of employees are doing unskilled jobs. (Total 3 marks) Q11 EF2E Page 11

12 12. A shaded shape is shown on a grid of centimetre squares. Find the perimeter of the shaded shape. cm Find the area of the shaded shape. (c) cm 2 On the grid, rotate the shaded shape 180 about the point marked with a cross. (Total 4 marks) Q12 EF2E Page 12

13 13. Here are some patterns made of lines and dots. pattern 1 pattern 2 pattern 3 Find out the number of dots in (i) pattern 4, (ii) pattern 8. (3) (i) Find the number of the pattern with 34 dots. (ii) Explain how you worked out your answer. (3) (Total 6 marks) Q13 EF2E Page 13

14 14. This travel graph shows Dawn's journey when delivering a present to her sister's house, 40 km from her home Distance from home (km) Time How long did Dawn spend at her sister's house? minutes Work out Dawn's average speed on her way home from her sister's house. km/h (Total 3 marks) Q14 EF2E Page 14

15 15. P = 4m 6 Work out the value of P when m = 5. P = Work out the value of m when P = 30. m = (Total 3 marks) Q Ben is going to America. The exchange rate is 1 = $1.86 Work out how many dollars Ben will get for 300. $ Ian is returning from America. The exchange rate is the same. Work out how many pounds Ian will get for $64. (Total 4 marks) Q16 EF2E Page 15

16 17. Here is Will's shopping bill. Milk Bread Cheese 2 litres at 1.15 per litre 3 loaves at 0.85 per loaf 500g at 6.50 per kg Total Complete this bill. (4) Will has these two vouchers. Save 25 p on each loaf of bread Save 20% all cheese Work out how much he saves if he uses both vouchers when paying his bill. (3) (Total 7 marks) Q A mobile phone weighs 82 grams correct to the nearest gram. Write down the least possible weight of the phone. g Write down the greatest possible weight of the phone. g (Total 2 marks) Q18 EF2E Page 16

17 19. R Diagram NOT Q accurately drawn P x y S T 41 U 102 V PQR and STUV are parallel lines. (i) Write down the value of x. (ii) Give a reason for your answer. Find the value of y. (Total 4 marks) Q19 EF2E Page 17

18 20. In a fitness test, children have to do as many star jumps as they can in two minutes and then as many sit-ups as they can in one minute. Each child's score is worked out using this rule. Multipy the number of sit-ups by 2 and then add the number of star jumps Emma did 30 star jumps and 10 sit-ups. Work out Emma's score. Ros did 16 sit-ups and got a score of 57. Work out how many star jumps Ros did. (c) Linda's score was an even number. Becky says Linda must have done an even number of star jumps. Explain why Becky is correct. (Total 5 marks) Q20 EF2E Page 18

19 21. Simplify w w w Simplify 5 3p (c) Expand y(y + 6) (d) Factorise fully 6 18m (Total 4 marks) Q21 EF2E Page 19

20 22. C Diagram NOT accurately drawn N 10 km A 10 km B A boat is at the point A. The boat sails 10 km due East to the point B. It then sails 10 km on a bearing of 020 to the point C. Work out the size of angle ABC. What type of triangle is ABC. (c) Find the size of angle BAC. (Total 5 marks) Q22 EF2E Page 20

21 23. Complete this table of values for y = x 2 + 3x + 1 x y On the grid, draw the graph of y = x 2 + 3x + 1 y O x 2 (c) Use your graph to estimate the minimum value of y. y = (Total 5 marks) Q23 EF2E Page 21

22 24. Part of a multiplication table is shown Rafiq is looking at the numbers in 2 by 2 squares drawn on the table. This is one of the squares Rafiq looks at Fill in the missing number. This is another of the squares Rafiq looks at Fill in the missing numbers. (Total 3 marks) Q24 EF2E Page 22

23 25. Diagram NOT accurately drawn 30 cm 42 cm One end of a rod is attached to a wall. The other end of the rod is attached to a wire which keeps the rod horizontal. The wire is also attached to the wall, 30 cm vertically above the rod. The rod is 42 cm long. Find the length of the wire. Give your answer correct to an appropriate degree of accuracy. cm Q25 (Total 4 marks) TOTAL FOR PAPER: 100 MARKS END EF2E Page 23