GCSE Mathematics Specification Paper 1 Foundation Tier

Transcription

1 For AQA Name Class GCSE Mathematics Specification Paper 1 Foundation Tier F Churchill Paper 1C 1 hour 30 minutes Materials For this paper you must have: mathematical instruments You must not use a calculator Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Write your name and class in the box at the top of the page. all questions. You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages. 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. Written by Shaun Armstrong Only to be copied for use in a single school or college having purchased a licence 2017 AF1C Page 1 Churchill Maths Limited

2 all questions in the spaces provided. 1 At 5 am the temperature is 3º C. Over the next 6 hours the temperature increases by 8º C. What is the temperature at 11 am? Circle your answer. 11ºC 5ºC 5ºC 11ºC 2 Work out 25% of 180 kg. Circle your answer. 36kg 40kg 45kg 48kg 3 Circle the number of minutes in hours? AF1C Page 2 Churchill Maths Limited

3 4 (a) Simplify 2p 4p Circle your answer. 8p 2 6p 2 16p 8p 4 (b) Solve 5y + 2 < AF1C Page 3 Churchill Maths Limited

4 5 This bar chart gives information about the staff at four pet shops. 10 Number of Staff 8 Full-time Part-time Fur Petsus Paws Animalz Shop 5 (a) Which shop employs the most staff? 5 (b) What fraction of the staff at Petsus are part-time? 2017 AF1C Page 4 Churchill Maths Limited

5 Esme says Across these 4 shops, more than half the staff are part-time. 5 (c) Is Esme correct? Show working to support your answer. 6 Work out 6 (a) (b) 5 8 (4 2) 6 (c) AF1C Page 5 Churchill Maths Limited

6 7 Circle the number that is not a prime number Here are five cards. Each card has a number and a shape on it The cards are turned over and mixed up. One card is then chosen at random. What is the probability that the card chosen 8 (a) has a circle on it, 8 (b) has an odd number on it, 8 (c) has an odd number and a triangle on it AF1C Page 6 Churchill Maths Limited

7 9 (a) 120º a º Not drawn accurately The diagram shows a parallelogram. Work out the value of a. 9 (b) 81º 45º b º Not drawn accurately The diagram shows a kite. Work out the value of b AF1C Page 7 Churchill Maths Limited

8 10 Here is a conversion graph between litres and pints. Pints Litres 10 (a) Convert 20 litres into pints. pints 10 (b) Convert 60 pints into litres. litres 10 (c) Describe the two features of the graph that show that the number of pints is directly proportional to the number of litres AF1C Page 8 Churchill Maths Limited

9 11 Box A Box B Box C Each week, the winner of a game show has to pick one of the boxes shown above. They then get to keep the money in that box. The amounts of money in the boxes are always in the ratio 1 : 10 : 200 Which amount of money is in which box is unknown. The total amount of money is different for each game. 11 (a) Will wins one week and chooses box B which has 50 in it. Work out the largest amount of money that could have been in box C for Will's game. 11 (b) On another week, Emma wins and chooses box A which has 300 in it. Work out the smallest amount of money that could have been in the three boxes altogether for Emma's game AF1C Page 9 Churchill Maths Limited

10 12 Some students were asked whether they had been on holiday in the UK or abroad in the last year. This Venn diagram gives some information about their answers. ξ UK Abroad N (a) How many of the students had not been on holiday in the UK or abroad? 12 (b) How many students had been on holiday abroad? One region of the diagram has N students in it. 12 (c) What do we know about these students? 2017 AF1C Page 10 Churchill Maths Limited

11 Half of all the students asked had been on holiday in the UK. 12 (d) Work out the value of N students took part in a sponsored walk. The mean amount of money raised by the students was (a) Work out an estimate for the total amount of money raised. Last year, the same event raised a total of (b) Work out an estimate for the percentage increase in how much was raised this year. % 2017 AF1C Page 11 Churchill Maths Limited

12 14 These are the scores recorded for Pippa on 6 tests One of the scores has been recorded wrongly and has to be corrected. Circle the largest amount the median of her scores could change by when the correction is made In a table tennis competition no matches are drawn each match is won or lost. In each round of the competition, only the winners go into the next round. 50 members of the Tabletop club enter a competition. 40% of them win their 1st round matches. 75% of the Tabletop club members in the 2nd round win their 2nd round matches. 9 members of the Tabletop club reach the 4th round of the competition. Work out the percentage of the Tabletop club members in the 3rd round who win their 3rd round matches. [3 marks] % 2017 AF1C Page 12 Churchill Maths Limited

13 16 Not drawn accurately 10 cm Leona cuts a square piece of card into four identical strips. She arranges the strips to form a larger square with a hole in the middle as shown. The side length of the larger square is 10 cm. Work out the area of the original square of card. [4 marks] cm AF1C Page 13 Churchill Maths Limited

14 17 Work out 17 (a) (b) [3 marks] 18 (a) Work out (b) Given that 7 4 = 2401, find the value of AF1C Page 14 Churchill Maths Limited

15 19 In a flash sale, a shop reduces all prices by (a) Work out the sale price of a pair of trainers that usually cost (b) Paula pays 48 for a pair of boots in the sale. Work out the usual price of the boots AF1C Page 15 Churchill Maths Limited

16 20 y = x y = x 2 5 y = x 3 y = 3x + 1 y = 2x 2 x y = 1 x y = 4 x 2 y = x 2 Write down the equation from the list above that could be represented by each graph. 20 (a) y O x 20 (b) y O x 2017 AF1C Page 16 Churchill Maths Limited

17 21 The straight line L passes through the origin, (0, 0) and the point ( 3, 2). Circle the equation of a line that is parallel to L. y = x y = 2 3 x 1 3 y = x y = 3 2 x Martha is playing with Minibricks. She has 300 of each type of brick the twospot, the fourspot and the eightspot. Martha uses some of her bricks to make zombies. To make zombies, she uses twospots, fourspots and eightspots in the ratio 3 : 1 : 2 When she has finished making zombies, she has twice as many fourspots left as twospots. Work out how many eightspots Martha has left. [3 marks] 2017 AF1C Page 17 Churchill Maths Limited

18 Stage 1 Stage 2 Stage 3 Nathan is making a zig-zag shape from rectangles. Not drawn accurately Stage 1 is a rectangle measuring 2 cm by 4 cm. For stage 2, Nathan adds a second rectangle measuring 2 cm by 5 cm as shown above. For stage 3, Nathan adds a third rectangle measuring 2 cm by 6 cm as shown above. He continues adding rectangles like this. Each rectangle is 1 cm longer than the one before. 23 (a) Show that the perimeter of stage 2 is 22 cm. The perimeter, P cm, of stage n is given by the formula P = n 2 + 7n (b) Work out the perimeter of stage 11. cm 2017 AF1C Page 18 Churchill Maths Limited

19 23 (c) By solving a suitable equation, find out which stage has a perimeter of 82 cm. [3 marks] 24 Here are five numbers (a) Which of the numbers above is the largest? 24 (b) Which of the numbers above is the smallest? 24 (c) Which two of the numbers above have the same value? and 2017 AF1C Page 19 Churchill Maths Limited

20 25 The first five terms of a sequence are 12, 18, 24, 30, 36, Circle the expression for the nth term of this sequence. 18n 6 12n + 6 6n 6 6n Solve the simultaneous equations 2x + y = 13 3x y = 2 [3 marks] x = y = END OF QUESTIONS 2017 AF1C Page 20 Churchill Maths Limited