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Forming and solving equations: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on A21 Forming and solving equations, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q4

    June 2025 · Paper 3H

    4 marksA21 Forming and solving equationsA17 Linear equations
    The whole paper ↗
    June 2025 Paper 3H, question 4: Here is an equilateral triangle. All measurements are in centimetres. Not drawn accurately Work out the value of the perimeter of the triangle. Answer cm

  2. Q15

    November 2024 · Paper 2H

    4 marksG3 Angles and polygonsA21 Forming and solving equations
    The whole paper ↗
    November 2024 Paper 2H, question 15: AB and CD are straight, parallel lines. P is a point on AB. Q is a point on CD. AP = AQ Work out the value of x. Not drawn accurately x = °

  3. Q5

    November 2024 · Paper 3H

    2 marksA21 Forming and solving equations
    The whole paper ↗
    November 2024 Paper 3H, question 5: The total cost of a taxi ride is calculated by adding a fixed charge of £4 and a charge of £2 per mile. Write a formula to work out the total cost, £C, of a jou

  4. Q17

    June 2024 · Paper 2H

    4 marksA21 Forming and solving equationsG3 Angles and polygons
    The whole paper ↗
    June 2024 Paper 2H, question 17: AB is a straight line. Both angles are given in degrees. By working out the value of x, work out the ratio smaller angle : larger angle Not drawn accurately Ans

  5. Q10

    June 2023 · Paper 1H

    5 marksA21 Forming and solving equationsA17 Linear equations
    The whole paper ↗
    June 2023 Paper 1H, question 10: Sunita is x years old. Beth is one year younger than Sunita. Joel is double Sunita’s age. The mean of their ages is 5 How old is Joel? Answer

  6. Q20

    June 2023 · Paper 1H

    3 marksA21 Forming and solving equations
    The whole paper ↗
    June 2023 Paper 1H, question 20: K, L and M are weights. Both of the scales balance exactly. How many M weights are needed to balance one L weight? Answer

  7. Q8

    November 2022 · Paper 2H

    3 marksG17 Circles, surface area and volumeA21 Forming and solving equations
    The whole paper ↗
    November 2022 Paper 2H, question 8: (a) Here is a cuboid. w, x and y are different whole numbers. The total length of all the edges of the cuboid is 80 cm The volume is greater than 200 cm3 Work o

  8. Q12

    November 2022 · Paper 2H

    4 marksA21 Forming and solving equationsR4 Ratio notation
    The whole paper ↗
    November 2022 Paper 2H, question 12: The length of this rectangle is 6 times the width. Two of these rectangles are joined, with no overlap, to make this L-shape. The perimeter of the L-shape is 98

  9. Q19

    June 2022 · Paper 3H

    5 marksA18 Quadratic equationsA21 Forming and solving equations
    The whole paper ↗
    June 2022 Paper 3H, question 19: Here is the plan of the floor of an L-shaped room. All lengths are in metres. Not drawn accurately 19 (a) The area of the floor is 75 m2 Show that x2 + x – 90 =

  10. Q24

    November 2021 · Paper 2H

    5 marksA21 Forming and solving equationsA18 Quadratic equations
    The whole paper ↗
    November 2021 Paper 2H, question 24: The flight of a plane was in two stages. The table shows information about the flight. Distance (miles) Speed (mph) Time (hours) 1st stage 731 x x 731 2nd stage

  11. Q9

    November 2020 · Paper 2H

    4 marksG17 Circles, surface area and volumeA21 Forming and solving equations
    The whole paper ↗
    November 2020 Paper 2H, question 9: Here is a cuboid. 9 (a) Assume that the total surface area of the cuboid is 200 cm2 Work out the volume of the cuboid. Answer cm3 9 (b) In fact, the total surfa

  12. Q17

    November 2020 · Paper 3H

    4 marksA21 Forming and solving equationsA17 Linear equations
    The whole paper ↗
    November 2020 Paper 3H, question 17: Here are two rectangles. The area of the shaded rectangle is 4 1 the area of the large rectangle. Work out the value of x. Not drawn accurately Answer

  13. Q18

    November 2019 · Paper 2H

    4 marksA21 Forming and solving equationsA18 Quadratic equations
    The whole paper ↗
    November 2019 Paper 2H, question 18: Kate has the following question for homework. 18 (a) Show that Kate can form the equation x2 + 5x – 1400 = 0 18 (b) Kate correctly factorises the equation to ge

  14. Q17

    June 2019 · Paper 1H

    3 marksA21 Forming and solving equations
    The whole paper ↗
    June 2019 Paper 1H, question 17: Toby is forming and solving equations. 17 (a) Toby uses y to represent the number. Write an equation that Toby could form. The product of half of a number and t

  15. Q9

    June 2019 · Paper 3H

    4 marksA21 Forming and solving equations
    The whole paper ↗
    June 2019 Paper 3H, question 9: Towns P, Q and R are connected by roads PQ, PR and QR. PR is 10 km longer than PQ. QR is twice as long as PR. The total length of the three roads is 170 km Work

  16. Q19

    November 2018 · Paper 1H

    5 marksA21 Forming and solving equationsA19 Simultaneous equations
    The whole paper ↗
    November 2018 Paper 1H, question 19: In a chess club, there are x boys and y girls. 19 (a) If 5 more boys and 8 more girls join, there would be half as many boys as girls. Show that y = 2x + 2 19 (

  17. Q10

    November 2018 · Paper 2H

    5 marksA21 Forming and solving equationsA17 Linear equations
    The whole paper ↗
    November 2018 Paper 2H, question 10: This triangle is equilateral. Is the perimeter of the triangle greater than one metre? You must show your working. Not drawn accurately

  18. Q11

    June 2018 · Paper 1H

    4 marksA21 Forming and solving equationsG17 Circles, surface area and volume
    The whole paper ↗
    June 2018 Paper 1H, question 11: A large rectangle is made by joining three identical small rectangles as shown. The perimeter of one small rectangle is 15 cm Work out the perimeter of the larg

  19. Q8

    June 2018 · Paper 2H

    3 marksA21 Forming and solving equationsR4 Ratio notation
    The whole paper ↗
    June 2018 Paper 2H, question 8: Theo starts with savings of £18 James starts with no savings. Each week from now, Theo will save £4.50 and James will save £4 In how many weeks will Theo and Ja

  20. Q9

    November 2017 · Paper 1H

    1 markA21 Forming and solving equations
    The whole paper ↗
    November 2017 Paper 1H, question 9: Circle the expression for the range of n consecutive integers. 2 1 + n n – 1 n n + 1
All 25 questions on Forming and solving equations, as a list
  1. June 2025, Paper 3H, Q4 (4 marks): Here is an equilateral triangle. All measurements are in centimetres. Not drawn accurately Work out the value of the perimeter of the triangle. Answer cm
  2. November 2024, Paper 2H, Q15 (4 marks): AB and CD are straight, parallel lines. P is a point on AB. Q is a point on CD. AP = AQ Work out the value of x. Not drawn accurately x = °
  3. November 2024, Paper 3H, Q5 (2 marks): The total cost of a taxi ride is calculated by adding a fixed charge of £4 and a charge of £2 per mile. Write a formula to work out the total cost, £C, of a jou
  4. June 2024, Paper 2H, Q17 (4 marks): AB is a straight line. Both angles are given in degrees. By working out the value of x, work out the ratio smaller angle : larger angle Not drawn accurately Ans
  5. June 2023, Paper 1H, Q10 (5 marks): Sunita is x years old. Beth is one year younger than Sunita. Joel is double Sunita’s age. The mean of their ages is 5 How old is Joel? Answer
  6. June 2023, Paper 1H, Q20 (3 marks): K, L and M are weights. Both of the scales balance exactly. How many M weights are needed to balance one L weight? Answer
  7. November 2022, Paper 2H, Q8 (3 marks): (a) Here is a cuboid. w, x and y are different whole numbers. The total length of all the edges of the cuboid is 80 cm The volume is greater than 200 cm3 Work o
  8. November 2022, Paper 2H, Q12 (4 marks): The length of this rectangle is 6 times the width. Two of these rectangles are joined, with no overlap, to make this L-shape. The perimeter of the L-shape is 98
  9. June 2022, Paper 3H, Q19 (5 marks): Here is the plan of the floor of an L-shaped room. All lengths are in metres. Not drawn accurately 19 (a) The area of the floor is 75 m2 Show that x2 + x – 90 =
  10. November 2021, Paper 2H, Q24 (5 marks): The flight of a plane was in two stages. The table shows information about the flight. Distance (miles) Speed (mph) Time (hours) 1st stage 731 x x 731 2nd stage
  11. November 2020, Paper 2H, Q9 (4 marks): Here is a cuboid. 9 (a) Assume that the total surface area of the cuboid is 200 cm2 Work out the volume of the cuboid. Answer cm3 9 (b) In fact, the total surfa
  12. November 2020, Paper 3H, Q17 (4 marks): Here are two rectangles. The area of the shaded rectangle is 4 1 the area of the large rectangle. Work out the value of x. Not drawn accurately Answer
  13. November 2019, Paper 2H, Q18 (4 marks): Kate has the following question for homework. 18 (a) Show that Kate can form the equation x2 + 5x – 1400 = 0 18 (b) Kate correctly factorises the equation to ge
  14. June 2019, Paper 1H, Q17 (3 marks): Toby is forming and solving equations. 17 (a) Toby uses y to represent the number. Write an equation that Toby could form. The product of half of a number and t
  15. June 2019, Paper 3H, Q9 (4 marks): Towns P, Q and R are connected by roads PQ, PR and QR. PR is 10 km longer than PQ. QR is twice as long as PR. The total length of the three roads is 170 km Work
  16. November 2018, Paper 1H, Q19 (5 marks): In a chess club, there are x boys and y girls. 19 (a) If 5 more boys and 8 more girls join, there would be half as many boys as girls. Show that y = 2x + 2 19 (
  17. November 2018, Paper 2H, Q10 (5 marks): This triangle is equilateral. Is the perimeter of the triangle greater than one metre? You must show your working. Not drawn accurately
  18. June 2018, Paper 1H, Q11 (4 marks): A large rectangle is made by joining three identical small rectangles as shown. The perimeter of one small rectangle is 15 cm Work out the perimeter of the larg
  19. June 2018, Paper 2H, Q8 (3 marks): Theo starts with savings of £18 James starts with no savings. Each week from now, Theo will save £4.50 and James will save £4 In how many weeks will Theo and Ja
  20. November 2017, Paper 1H, Q9 (1 mark): Circle the expression for the range of n consecutive integers. 2 1 + n n – 1 n n + 1
  21. November 2017, Paper 2H, Q19 (3 marks): The length of a rectangle is five times the width. The area of the rectangle is 1620 cm2 Not drawn accurately Work out the width of the rectangle. Answer cm
  22. June 2017, Paper 2H, Q17 (4 marks): P is a rectangle with length 50 cm and width x cm Q is a rectangle with width y cm Not drawn accurately P Q The length of Q is 20% more than the length of P. Th
  23. June 2017, Paper 3H, Q10 (7 marks): AB, CD and EF are straight lines. Not drawn accurately 10 (a) Ava assumes that AB and CD are parallel. What answer should she get for the size of angle y? Answe
  24. June 2017, Paper 3H, Q26 (6 marks): Here is an L-shape. All dimensions are in centimetres. Not drawn accurately The area of the L-shape is 65 cm2 Work out the value of x. Answer
  25. Specimen, Paper 1H, Q18 (4 marks): In this question all dimensions are in centimetres. A solid has uniform cross section. The cross section is a rectangle and a semicircle joined together. x x 2x

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