GCSE Foundation Paper Number Q1.(a) Complete the table. Fraction Decimal Percentage 75% 0.9 0.3 30% Write, 0.9 and 30% in order with the smallest first. Q2.(a) Write 80% as a decimal. Answer...,...,... Write 0.7 as a fraction. (c) Write as a decimal. (d) Write 80%, 0.7 and in order with the smallest first. Answer...,...,... Q3.Arrange these numbers in order of size starting with the smallest. You must show your working. 27% 0.207... Page 1
... Q4.(a) Write 3.574 to 1 decimal place. Answer...,...,... (Total 2 marks) Put these decimals in order, starting with the smallest. 0.5 0.62 0.325 (c) Circle the two values that are equivalent to 0.8 Answer...,...,... 8% 80% Q5.Write these values in order, starting with the smallest. 0.2 11% You must show your working....... Q6.(a) Work out one-quarter of 240. Work out 10% of 390. Q7.(a) Three of these fractions are equivalent. (Total 2 marks) Circle the odd one out. Page 2
Write as a percentage. (c) Write 0.3 as a percentage.... %... % Q8.Work out of 180...... Q9. Work out (Total 2 marks) (a).... Q10.Kerry needs of a tank of petrol to drive home. She has of a tank of petrol. Does she have enough petrol to drive home? You must show your working.......... (Total 2 marks) Page 3
Q11.Use a calculator to work out the area of the rectangle. Not drawn accurately Give your answer as a mixed fraction............. m 2 (Total 2 marks) Q12.When a jug is full of water it weighs 250 grams. When the same jug is full of water it weighs 550 grams. How much does the jug weigh when it is empty?......... Page 4
... grams Q13.(a) Work out What fraction is half way between and? Q14. Mollie s Cookie Shop sells cookies individually or in bags of 5, 8, 13 or 18. 1 5 8 13 18 cookie cookies cookies cookies cookies 75p 2.25 2.99 3.99 4.9 What is the cheapest way to buy exactly 50 cookies? You must show your working.......... Answer... Q15. Work out (a) Write down your full calculator display.. Give your answer to one decimal place.. Page 5
Q16. Decide whether each answer is more than 10 or less than 10. Write MORE or LESS. (Total 2 marks) 10 0.7 Answer... 10 0.7 Answer... 0.1 1000 Answer... 0.1 0.001 Answer... Q17. Work out 45% of 330. (Total 2 marks)......... Q18.(a) Work out 70% of 986. Answer... (Total 2 marks)...... Answer... Circle the calculations that have the same answer as 57% of 372. A 58% of 371 B 5.7% of 37.20 C 372 D 0.57 0.372 E 5.7% of 3720 Q19.Work out 80% of 300......... Page 6
Q20.Shabir buys 30 bottles of lemonade for a party. He is given 20% discount off the total price. (Total 2 marks) One bottle costs 80p before the discount. How much does he pay?............ Q21.A train ticket costs 23.50 The price increases by 6%. Felix has 100. Can Felix buy four tickets at the new price?......... Q22.Here are three offers for a fridge freezer. Electric Supplies New Homes Fridges for Us Usual price 250 30% off Which offer is the cheapest? You must show your working. Usual price 240 off 50 deposit plus 20 a month for 6 months............ Page 7
(Total 6 marks) Q23. Work out the sale price.... Q24.Here are two ways of having a car for one year. Answer... Buy and sell Buy it for 12 000 Sell it for 10 000 after one year Rent Normal Price: 195 per month Special Offer 15% off Which way is cheaper? You must show your working....... Q25.Here are two bottles of the same perfume. (Total 5 marks) Normal price 40 55 20% off Which is the better value? You must show your working.......... Page 8
(Total 6 marks) Q26. Write 108 as the product of its prime factors. Give your answer in index form....... Q27. When written as the product of prime factors (a) Write 150 as the product of prime factors. Give your answer in index form. Work out the highest common factor (HCF) of 225 and 150. (Total 5 marks Q28.(a) Write 36 as the product of prime factors. Give your answer in index form Work out the Highest Common Factor (HCF) of 36 and 81. Q29. Divide 7200 in the ratio 2 : 3 : 7 (Total 5 marks)...... Q30.120 adults complete a survey. 45 are men. Answer......... Write the ratio men : women in its simplest form....... Page 9
(Total 2 marks) Q31.A toy is made from red bricks and yellow bricks. Number of red bricks : number of yellow bricks = 5 : 2 There are 210 more red bricks than yellow bricks. How many red bricks are in the toy?...... Q32.Three people share 180. Billy gets twice as much as Amy. Chloe gets three times as much as Billy. Is Chloe s share enough to buy a bike costing 115? You must show your working.......... (Total 5 marks) Q33. Alex and Ben share 520 in the ratio 1:3 (a) How much does Ben receive? Answer... What percentage of the 520 does Ben receive? % Q34. Andy and Trevor share 40 sweets in the ratio 11 : 9. How many more sweets does Andy receive than Trevor?...... Answer... (Total 2 marks Page 10
Algebra Q1. (a) Expand and simplify 4(2x 1) + 3(x + 6) Expand x 2 (4 2x) Q2. (a) Simplify a 2 a 4 Simplify b 9 b 3. (c) Simplify c 5 c c 5.. Q3. (a) Simplify x 2 x 3 Simplify y 8 y 5 (c) Expand x(x 3 3) Answer... Answer... Q4. (a) Expand 3(x 6) Answer... Factorise 5y 10 Page 11
(c) Expand and simplify 3(4w + 1) 5(3w 2) Q5.Expand w(w + 6) (Total 5 marks)... Q6. (a) You are given that 6x = 48 (Total 2 marks) Work out the value of 5x Solve the equation 2(4y 1) = 18 Answer... Q7.(a) Solve x + 3 = 7 Answer y =... (Total 5 marks) Solve 2x + 5 = 1 Answer x =... Q8.(a) Solve 8x = 32 Answer x =... x =... Solve y 9 = 14 Page 12
y =... (c) Solve Q9.(a) Solve 3w = 18 w =... w =... Solve (c) Solve 2y 5 = 12 x =... y =... Q10.(a) Solve Solve 2y 3 = 8 Answer x =... (c) Simplify fully 4m + 3p + m 10p Answer y =... (Total 5 marks) Page 13
Q11.(a) Solve Simplify fully 3c + 5d + 4c 2d Answer y=... (c) Given that P = 3e + 5f... work out the value of P when e = 4 and f = 2 Q12.Solve the equations. (a) x 19 = 43... (Total 5 marks) 9y = 72 x =... y =... (c) = 10 Q13.Solve 3(x + 2) = 2x 1 w =...... Q14.(a) Solve 5x = 20 x =... x =... Page 14
Solve y + 9 = 17 Q15.(a) Solve 6x 5 = 28 y =... (Total 2 marks) Simplify fully 3a + 5b a + 2b x =... Q16. (a) Expand and simplify 2(3x - 2) + 4(x + 5) Solve the equation 2(3x - 2) + 4(x + 5) Q17. (a) Solve 8t 5 = 19 Answer x =... (Total 5 marks) Answer t =... Nails cost 3 pence each. Screws cost 5 pence each. Write down an expression for the cost of x nails and y screws.... pence Page 15
(c) Expand and simplify 4(2w + 3) 5(3w + 7). (Total 6 marks) Q18. (a) Solve the equation = 4 Solve the equation 8w 5 = 3w + 1 Answer x =... (c) Simplify y + 2 y y Answer w =... (d) Factorise 15t + 25. (e) Factorise z 2 + 8z.. Q19. The triangle has lengths (4x 2) cm, (2x + 5) cm and (6x 9) cm. (Total 7 marks) Find the value of x that makes this triangle equilateral.... Page 16
...... Q20.(a) Solve 5x + 3 = 3(x + 2) Answer... 2(x + 16) + 4(x 5) simplifies to a(x + b) Answer x =... Work out the values of a and b. Q21.Solve 3(2x + 4) + 8 = 50 Answer a =..., b =... (Total 6 marks)......... Q22.The perimeter of this L-shape is 56 cm. x =... Set up and solve an equation to work out the value of x. x =... Page 17
Q23.Work out the value of 5x 2y when x = 3 and y = 4...... Q24.(a) Work out the value of 3c 4d when c = 5 and d = (Total 2 marks) Expand and simplify 3(2x + 4) + 2(x + 1) (Total 5 marks) Q25. Not drawn accurately Work out the length of the longest side of the triangle when x = 5......... cm Page 18
Q26.P = 2a + 3b Work out the value of P when a = 11 and b = 5......... Q27. This shape is made up of rectangles. (Total 2 marks) (a) Write down an expression, in terms of x and y, for the perimeter of the shape.... If x = 2 cm and y = 5 cm, find the area of the shape.. cm 2 Q28. (a) Find the value of 3x + 5y when x = 2 and y = 4 Find the value of 3a 2 + 5 when a = 4 (c) k is an even number. Jo says that k + 1 is always even. Give an example to show that Jo is wrong. Page 19
(d) The letters a and b represent prime numbers. Give an example to show that a + b is not always an even number. Q29. (a) Simplify (i) y 7 y 2... (Total 6 marks) (ii) y 7 y 2... (iii) (y 7 ) 2... (i) If y = 1 which answer in part (a) is positive? (ii)... If y = 0.5 which answer in part (a) has the greatest value?... Q30. (a) Simplify 2x + 8 + 4x 3 (Total 5 marks) Solve the equation. Answer x =... Page 20
(c) Tom is investigating the two expressions ab + c and a(b + c) (i) He finds that both expressions have the same value when a = 1, b = 3 and c = 4. Show that this is true. (ii)...... Tom says that this means that a(b + c) = ab + c. Explain why Tom is wrong.......... Q31. Two car hire firms use different ways of charging for the hire of a car. (Total 8 marks) (a) Cheap Days uses this formula. H = 50d + 120 H is the hire charge in pounds. d is the number of days the car is hired. Work out H when d = 2 Cheap Miles uses this formula. Answer... H is the hire charge in pounds. m is the number of miles the car travels. Work out m when H = 200 miles Page 21
Q32. After exercise you can work out your fitness index, F. You need to know your exercise time in seconds (T) the number of your pulse beats in three 30 second intervals after you have stopped exercising (a, b and c). Terry is working out his fitness index. (a) (i) Terry exercises for 3 minutes 30 seconds. Work out T... Answer... seconds (ii) After exercise he obtains a = 70, b = 55 and c = 45 (iii) Work out a + b + c.... Answer... pulse beats Work out F, Terry s fitness index, using the formula F =...... Answer... seconds Your fitness grade can be worked out from your fitness index, F, using this table. Fitness index, F less than 50 50 to 59 60 to 69 70 to 79 80 to 89 90 Fitness grade Very poor Poor Fair Good Excellent Superb What is Terry s fitness grade? Q33. (a) Work out the value of 8(16 1) Answer... (Total 5 marks). Page 22
Factorise 2x 2 x (c) Work out the value of 2x 2 x when x = 8.. Q34.(a) Solve Answer x =... Rearrange this formula to make t the subject. s = 3t + 4 Answer t =... (Total 5 marks) Q35.(a) Solve Answer x =... Rearrange this formula to make t the subject. s = 3t + 4 Answer t =... (Total 5 marks) Page 23
Shape Q1. (a) Two squares of side 4 cm are removed from a square of side 12 cm as shown. Work out the shaded area. Two squares of side x cm are removed from a square of side 3x cm as shown. Work out the fraction of the large square which remains. Give your answer in its simplest form. You must show your working. (Total 6 marks) Page 24
Q2. The length of a rectangle is 10.8 cm. The perimeter of the rectangle is 28.8 cm. Calculate the width of the rectangle.... cm Q3. A shop sells square carpet tiles in two different sizes. small carpet tile? (a) What is the area of a cm 2 What is the length of a side of a large carpet tile? cm (c) The floor of a rectangular room is 300 cm long and 180 cm wide. How many small tiles are needed to carpet the floor? (Total 6 marks) Q4. A circle of diameter 60 cm is cut out of a square of side 80 cm. Not drawn accurate Page 25
Calculate the shaded area.......... Q5. (a) The diagram shows a rectangle. Answer...cm 2 (Total 3 marks Not drawn accurately Work out the area of the rectangle. State the units of your answer.. The diagram shows a rectangle made from two congruent shapes A and B. (i) Write down the mathematical name of shape B.. (ii) Explain how you could work out the area of shape B....... (Total 6 marks) Page 26
Q6. ABCD is a square. PQRS is a square with vertices on the sides of ABCD. AS = DR = CQ = BP = 9 cm, PA = SD = RC = QB = 1 cm What is the area of the shaded square PQRS?......... cm 2 Q7. Work out the circumference of a circle of diameter 10.5 cm. Not drawn accurately...... Answer... cm (Total 2 marks) Q8.The diagram shows a trapezium. Not drawn accurately (a) Write down the length of AB when x = 6.2 Work out the perimeter when x = 7... cm... cm (Total 5 marks) Page 27
Q9.The diagram shows a rectangle. 4 cm (a) Four of these rectangles are put together as shown. Work out the shaded area.... cm 2 The four rectangles are now put together to make this shape. Not drawn accurately Work out the perimeter of the shape. You must show your working.... cm (Total 5 marks) Page 28
Q10.Work out the area of a circle of radius 6 m............. m 2 Q11.This shape is made by cutting out an equilateral triangle from a square. (Total 2 marks) Work out the perimeter of the shape....... Q12.The perimeter of the rectangle is 37 cm.... cm (Total 2 marks) Not drawn accurately x x + 3 Work out the value of x.......... x =... cm Page 29
Q13. What percentage of this shape is shaded?......... % Q14. This L-shape has measurements as shown on the diagram. The perimeter of the shape is 72 cm. Find the length marked h on the diagram................ Answer... cm Page 30
Q15.Work out the area of the triangle. Give your answer to 1 decimal place....... Q16.This circle is drawn accurately.... cm 2 Work out the area of the circle. Give your answer in terms of π. State the units of your answer....... Page 31
Q17.The hexagon is made from a rectangle and two congruent triangles. Work out the area of the hexagon............. cm 2 Q18.The perimeter of this square is 48 cm. (Total 5 marks) Semicircles are joined to two sides of the square. Work out the perimeter of this shape................ cm Page 32
Q19.This shape is made from identical quarter circles. Not drawn accurately Work out the perimeter of the shape............. cm Q20.Work out the area of a circle, radius 3.5 cm. Give your answer to 1 decimal place.......... cm 2 Q21.Work out the circumference of a circle, radius 4.2 cm. Give your answer to 1 decimal place.......... cm Q22.In the trapezium, a = 6.5 m, b = 8.3 m and h = 3.2 m Not drawn accurately (a) Work out the area of the trapezium.... m 2 Page 33
The trapezium is the cross-section of a tunnel. The tunnel is 200 metres long. Work out the volume of the tunnel.... m 3 Q23.DVD cases are packed in this box. (a) How many cases are there in a full box? A full box of cases costs 2.70 Work out the cost of one case.... pence Page 34
Q24.The diagram shows a cuboid. The cross-section (shaded) is a square. Work out the volume of the cuboid. State the units of your answer....... Q25. A school hall is in the shape of a cuboid. (a) The school hall is 30 m long, 12 m wide and 4 m high. Calculate the volume of the hall. m 3 The school buys ten 5 litre tins of paint to paint the hall. The area to be painted is 279 m 2. Each tin covers 30 m 2. Calculate the percentage of paint used.. % (Total 5 marks) Page 35
Q26. The diagram shows two boxes that are cuboids. The larger box measures 20 cm by 10 cm by 20 cm. It is partly filled with 70 smaller boxes each measuring 5 cm by 5 cm by 2 cm. The smaller boxes are packed so that there are no gaps between them. Not drawn accurately How many more smaller boxes could be fitted in the larger box?...... Q27. A support for a flagpole is attached at a height of 3 m and is fixed to the ground at a distance of 1.2 m from the base. Calculate the length of the support (marked x on the diagram)............. Answer... m Page 36
Q28.Work out the length AC.... Q29.Work out length AB as a decimal.... cm......... cm Q30.Work out the length x. Not drawn accurately Give your answer to 1 decimal place............. cm Page 37
Q31. Rebecca has three rectangular sheets of paper. She cuts each sheet into two pieces. She now has the six pieces, A to F, shown below. Not drawn accurately (a) Which piece is part of the same rectangle as A? Which piece is part of the same rectangle as B? (c) Calculate the size of angle x on piece D. Answer x =... degrees Page 38
Q32. Here are two rectangles, A and B. Not drawn accurately Is rectangle B an enlargement of rectangle A? Tick the correct box. Explain your answer. Yes No......... Q33.(a) The diagram shows three angles at a point. Work out the value of x... degrees This diagram also shows three angles at a point. Page 39
Work out the missing angle in terms of y. Give your answer in its simplest form. Q34.(a) In the diagram, AB = AC... degrees Not drawn accurately Work out the size of angle x.... degrees A rhombus is reflected as shown. DE is a straight line. Not drawn accurately Work out the size of angle y. Show your working, which may be on the diagram.... degrees (Total 5 marks) Page 40
Handling Data Q1. The diagram shows a probability scale. An ordinary fair six-sided dice is rolled. (a) Which arrow represents the probability of rolling a 5? Which arrow represents the probability of rolling a number less than 7? (c) Draw an arrow on the scale to represent the probability of rolling an odd number. Q2.A lunchbox contains one sandwich and one drink from this list. Sandwiches Cheese (C) Ham (H) Prawn (P) Drinks Blackcurrant (B) Lemonade (L) Water (W) (a) List all possible combinations. One has been done for you. One combination is chosen at random. What is the probability that it is Ham and Water? (Total 4 mark) People in a town voted in an election. The probability a vote was given to a particular party is shown. One value is missing. Party Probability Conservative 0.41 Labour 0.24 Liberal Democrat 0.22 UKIP Other 0.04 (a) Complete the table. Page 41
There are 15 000 people in the town. 8000 voted. How many people in the town did not vote Conservative? Q4.150 boys and 160 girls sit an examination. The table shows some of the probabilities that they came with or without a calculator. (Total 5 marks) With calculator Without calculator Boy 0.92 0.08 Girl 0.95 (a) What is the probability that a girl came without a calculator? Write your answer in the table. How many of the 150 boys came with a calculator? Q5. On her way to work Janice passes through four sets of traffic lights. She records the number of times she stops at traffic lights each day. The table shows her results for ten weeks. Number of stops each day Frequency (number of days) 0 1 1 6 2 12 3 15 4 16 (a) Calculate the mean number of stops each day. Answer... Page 42
Janice says that she stops at every set of traffic lights on most days. She is wrong. (c) Explain why she is wrong. On average, how many days per week does Janice work? Answer... Q6. The table shows the heights of 30 students in a class. (Total 5 marks) Height, h, (cm) Number of students 140 < h 144 4 144 < h 148 5 148 < h 152 8 152 < h 156 7 156 < h 160 5 160 < h 164 1 By using the midpoints of each group, calculate an estimate for the mean height of the students....... cm Q7. (a) The National Curriculum levels in Mathematics for 30 students in year 9 were recorded. Level Number of students 3 0 4 4 5 4 6 9 7 8 8 5 Page 43
Calculate the mean level. The 30 students study both French and Spanish. Answer... Their National Curriculum levels in these subjects are shown in the table. Level of Spanish 1 2 3 4 5 6 Total 1 0 0 0 0 0 0 0 2 1 0 0 0 0 0 1 Level of French 3 2 1 1 0 0 0 4 4 0 3 4 1 0 0 8 5 0 1 2 3 2 0 8 6 0 0 3 3 2 1 9 Total 3 5 10 7 4 1 30 (i) What is the median level for French? Show clearly how you obtain your answer. (ii)... Answer... The teacher claims that the students are better at French than at Spanish. How can you tell from the table that this is true?... Q8.80 patients gave information about how long they waited to see the doctor. (Total 6 marks) Time, T, (minutes) Frequency 0 T < 10 5 10 T < 20 22 20 T < 30 28 30 T < 40 21 (a) 40 T < 50 4 Work out an estimate of the mean time that the patients waited. Page 44
... minutes The doctor says, 70% of our patients wait less than 30 minutes to be seen. Is she correct? You must show your working. (4) Q9.Here are nine numbers. (Total 7 marks) 23 25 23 31 20 25 21 24 25 (a) Work out the median. Write down the mode. Q10.Here are five numbers. 5 9 10 7 9 (a) What is the mode? Show clearly that the median is 9. Q11.A shop manager counts the number of items bought by 15 customers. The results are shown in the stem-and-leaf diagram. Page 45 (Total 2 marks)
Key: 3 1 represents 31 items (a) Write down the median. Work out the range. (c) Another customer is included. The median does not change. How many items did this customer buy? Q12.The stem-and-leaf diagram shows the ages of people at a show. 2 3 4 Key: 2 3 represents 23 years 3 1 3 5 5 4 0 2 3 8 8 9 5 1 1 4 5 6 (a) (c) What is the range of the ages?... years How many people are represented in the stem-and-leaf diagram? How can you tell from the stem-and-leaf diagram that the median is 43 years? Page 46
(d) The age of another person is added to the stem-and-leaf diagram. The median increases by 2 years. What is the age of this person?... years Q13. A form teacher records the number of times her students were late during a term. She shows the data for those who were late in a stem and leaf diagram. Key 2 7 represents late 26 times 0 1 1 2 6 1 2 4 4 2 3 6 3 2 4 0 9 5 0 17 students were never late. Calculate the mean number of times students were late for the whole form....... Q14. The stem and leaf diagram shows the ages, in years, of 15 members of a badminton club. (a) What is the median age of the members? years What is the range of the ages? Page 47
years (Total 2 marks) Page 48