FOUNDATION REVISION PAPER 2

Transcription

1 Edexcel GCSE Mathematics (Linear) 1MA0 FOUNDATION REVISION PAPER 2 Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Items included with question papers Nil Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided there may be more space than you need. Calculators may be used. Information The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed you should take particular care on these questions with your spelling, punctuation and grammar, as well as the clarity of expression. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end.

2 1. Kaz rolled a dice 10 times. Here are her scores Work out the mean. (2 marks) 2. The table gives some information about the birds Paula sees in her garden one day. Bird Frequency Magpie 15 Thrush 10 Starling 20 Sparrow 27 Complete the accurate pie chart. (3 marks) 2

3 3. Sue has a bag of 18 sweets. 5 of the sweets are blue 7 of the sweets are red 6 of the sweets are green Sue takes at random a sweet from the bag. Write down the probability that Sue does not take a green sweet. (1 mark) 4. Here are 6 triangles drawn on a grid of centimetre squares. Write down the letters of the triangles which are congruent. (1 mark) 3

4 5. Use a calculator to work out Write down all the figures on your calculator display. Give your answer as a decimal.... (2 marks) 6. There are 3 counters in a bag. One counter is red. One counter is green. One counter is blue. Mike takes at random a counter from the bag. He puts the counter back in the bag. Then Ellie takes at random a counter from the bag. (a) Write a list of all the possible combinations of the two counters that Mike and Ellie can take (2) (b) Find the probability that Mike takes a blue counter and then Ellie takes a green counter. (1) (3 marks) 4

5 7. Jamal has a biased coin. He is going to throw the coin 200 times. The probability of getting heads is 0.7 Work out an estimate for the number of heads Jamal will get. (2 marks) 8. The scatter graph shows some information about 8 cars. For each car it shows the engine size, in litres, and the distance, in kilometres, the car travels on one litre of petrol. (a) What type of correlation does the scatter graph show?..(1) A different car of the same type has an engine size of 2.5 litres. (b) Estimate the distance travelled on one litre of petrol by this car. kilometres(2) (3 marks) 5

6 9. Linda is going on holiday to the Czech Republic. She needs to change some money into koruna. She can only change her money into 100 koruna notes. Linda only wants to change up to 200 into koruna. She wants as many 100 koruna notes as possible. The exchange rate is 1 = koruna. (a) How many 100 koruna notes should she get? (3) Linda buys a meal in the Czech Republic. The meal costs 400 koruna. (b) Work out the cost of the meal in pounds. (3) (6 marks) 10. (a) Change 4 kg to grams. (b) Change 3500 ml to litres. grams (1) litres (1) (2 marks) 6

7 11. Solve 4m + 6 = 15 m =... (2 marks) 11. You can use the graph to change between miles and kilometres. Change 60 kilometres into miles. miles (2 marks) 7

8 12. P = 3.5x y (a) Work out the value of P when x = 12 and y = 5 (b) Work out the value of P when x = 9 and y = 6 (2) (2) (4 marks) 13. y = 4x + c y = 18.8 c = 2.4 Work out the value of x. (2 marks) 15. Here is a 4-sided spinner. The sides of the spinner are labelled 1, 2, 3 and 4. The spinner is biased. The probability that the spinner will land on each of the numbers 2 and 3 is given in the table. The probability that the spinner will land on 1 is equal to the probability that it will land on 4. Number Probability x x Work out the value of x. x =. (2) 8

9 *16. Here is a diagram of a wall. Halima wants to cover all of the wall with tiles. The tiles are squares with sides of length 20 cm. The tiles are sold in packs. There are 10 tiles in each pack. Each pack of tiles costs Halima only has 1000 Can she buy enough packs of tiles to cover the wall? (6 marks) 17. Here are the first five terms of an arithmetic sequence (a) Find, in terms of n, an expression for the nth term of this sequence. (b) An expression for the nth term of another sequence is 10 n 2... (2) (i) Find the third term of this sequence. (ii) Find the fifth term of this sequence (2) (Total 4 marks) 9

10 18. Describe fully the single transformation that maps shape P onto shape Q (3 marks) 19. (a) Factorise 4x + 10y (b) Factorise x 2 + 7x (1) (1) (2 marks) 10

11 *20. Henry is thinking about having a water meter. These are the two ways he can pay for the water he uses. Henry uses an average of 180 litres of water each day. Henry wants to pay as little as possible for the water he uses. Should Henry have a water meter? (5 marks) 11

12 21. A, B and C are 3 service stations on a motorway. AB = 25 miles BC = 25 miles Aysha drives along the motorway from A to C. Aysha drives at an average speed of 50 mph from A to B. She drives at an average speed of 60 mph from B to C. Work out the difference in the time Aysha takes to drive from A to B and the time Aysha takes to drive from B to C. Give your answer in minutes. minutes (3 marks) 22. Pat and Julie share some money in the ratio 2 : 5 Julie gets 45 more than Pat. How much money did Pat get? (Total for Question 28 is 3 marks) 12

13 *23. ABCD is a parallelogram. Angle ADB = 38. Angle BEC = 41. Angle DAB = 120. Calculate the size of angle x. You must give reasons for your answer. 24. (4 marks) The angle marked x is 160. How do you know this? (1 mark) 13

14 *25. Mr Weaver s garden is in the shape of a rectangle. In the garden there is a patio in the shape of a rectangle and two ponds in the shape of circles with diameter 3.8 m. The rest of the garden is grass. Mr Weaver is going to spread fertiliser over all the grass. One box of fertiliser will cover 25 m2 of grass. How many boxes of fertiliser does Mr Weaver need? You must show your working. (5 marks) 14

15 26. Here is a square and a trapezium. (a) Mark, with the letter O, an obtuse angle. (1) (b) Find two lines that are perpendicular. Mark each of these lines with a letter P. (2 marks) 27. (a) n is an integer. 1 n < 4 List the possible values of n. (1) (b)... (2) Write down the inequality shown in the diagram. (c) Solve 3y 2 > 5 (2) (2) (6 marks) 15

16 26. The pie charts show some information about the numbers of medals won by Germany and by the Russian Federation in the 2010 Winter Olympics. Medals won by Germany Medals won by the Russian Federation Germany won 7 bronze medals. (a) How many gold medals did Germany win? (2) (b) Graham says, The pie charts show that Germany won more gold medals than the Russian Federation. Is Graham right?... You must explain your answer (1) (3 marks) 16

17 27. Triangle A and triangle B are drawn on the grid. (a) Describe fully the single transformation which maps triangle A onto triangle B (3) (b) Reflect triangle A in the line x = 4 (2) (5 marks) 17

18 28. The table shows information about the numbers of hours 40 children watched television one evening. (a) Write down the modal class interval. (1)... (b) Work out an estimate for the mean number of hours. 29. (4)... hours (5 marks) A 2.1 m D 1.9 m 3.2 m B C ABCD is a trapezium. AD is parallel to BC. Angle A = angle B = 90. AD = 2.1 m, AB = 1.9 m, CD = 3.2 m. Diagram NOT accurately drawn Work out the length of BC. Give your answer correct to 3 significant figures. m (4 marks) 18

19 30. The diagram shows the position of two ports P and Q on a map. (a) Measure the bearing of Q from P.... (1) A rock R is on a bearing of 150 from Q. On the map R is 6 cm from Q. (b) Mark the position of R with a cross ( ) and label it R. (2) (Total 3 marks) 31. (a) Use your calculator to work out Write down all the figures on your calculator display. You must give your answer as a decimal.... (3) (b) Write your answer to part (a) correct to 2 decimal places.... (1) (Total 4 marks) 19

20 32. The equation x 3 + 3x = 41 has a solution between 3 and 4 Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show all your working. x =... (Total 4 marks) 33. Here is a list of ingredients for making 14 Flapjacks. Ingredients for 10 Flapjacks 80 g rolled oats 60 g butter 30 ml golden syrup 36 g light brown sugar Work out the amount of each ingredient needed to make 21 Flapjacks.... g rolled oats... g butter... ml golden syrup... g light brown sugar (Total 3 marks) 20

21 students ran a cross-country race. Each student s time was recorded. The table shows information about these times. Time (t minutes) Frequency 10 < t < < t < < t < < t < < t < 30 3 On the grid, draw a frequency polygon to show this information. 15 Number of students Time (t minutes) (4 marks) 21

22 35. Here are the weights, in kilograms, of 16 parcels a) Draw a stem and leaf diagram to show this information b) Find the Median weight ( 3 marks) ( 2 marks) 36. Solve 5y + 1 = 3y + 13 y =... (3 marks) 22

23 37. Solve 3y + 10 = 5y + 3 y =... (3 marks) 38. The diagram shows a square and 4 regular pentagons. Work out the size of the angle marked x.... (4 marks) 23

24 39. A skip is in the shape of a prism with cross-section ABCD. AD = 2.3 m, DC = 1.3 m and BC = 1.7 m. The width of the skip is 1.5 m. Calculate the volume of the skip.... (3 marks) 24