plumiForming and solving equations: OCR GCSE Maths questions
Every OCR GCSE Maths exam question on A21 Forming and solving equations, 2017–2025, with its mark scheme and examiner’s report.
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All 34 questions on Forming and solving equations, as a list
- June 2025, Paper 5, Q10 (4 marks): Heidi is x years old. Finley is 5 years younger than Heidi. Zayn is 4 times Finley’s age. Find an expression in terms of x for the total age of Heidi, Finley an
- November 2024, Paper 5, Q4 (2 marks): An electrician charges £30 per visit plus £22 per hour. Write an expression for the cost, in £, charged by the electrician for one visit lasting n hours. £
- November 2024, Paper 6, Q11 (7 marks): (a) Here is a function. Input + 3 × 2 Output Complete the diagram below to show the inverse of the function. Input Output (b) Here is another function. Input ×
- June 2024, Paper 4, Q3 (5 marks): Four numbers are written, in ascending order, as algebraic expressions. a a b a 2 b 3 - a b + + The mean of these four numbers is 27. The range of these four nu
- June 2024, Paper 4, Q6 (4 marks): A regular polygon has n sides. The interior angle of the polygon is 15 times its exterior angle. Find the value of n. n =
- June 2024, Paper 4, Q8 (5 marks): The price of a television is increased by 35%. In a sale, the new price of the television is decreased by r %. The overall percentage increase in the price of t
- June 2024, Paper 5, Q10 (4 marks): The diagram shows an equilateral triangle and a rectangle. Not to scale a cm 14 cm (a + 5) cm The equilateral triangle has the same perimeter as the rectangle.
- November 2023, Paper 4, Q6 (5 marks): 2 kg of carrots and 5 kg of potatoes cost £6.36. 3 kg of carrots and 2 kg of potatoes cost £5.25. Find the cost of 1 kg of carrots and the cost of 1 kg of potat
- November 2023, Paper 6, Q6 (5 marks): The area of this rectangle can be written as ax bx 10 . - Not to scale 3x + 2 x + c Find the values of a, b and c. You must show your working. a = , b = and c =
- June 2023, Paper 4, Q6 (4 marks): A six-sided numbered spinner is thrown 50 times. The score for each throw is recorded. Some of the results are shown in the table. An 8 was thrown f times. An u
- June 2023, Paper 4, Q9 (8 marks): The sides of this triangle are given in centimetres. The perimeter of the triangle is 80 cm. Not to scale 3x + 1 x + 5 2x + 8 (a) Find the length of each side o
- June 2023, Paper 5, Q6 (4 marks): Taylor has a full bottle of medicine. The bottle holds 20 doses of medicine. Each day Taylor takes one dose of medicine out of the bottle. After 8 days, there a
- June 2023, Paper 6, Q11 (5 marks): The diagram shows a quadrilateral, PQRS. P Q Not to scale 10 cm S R PS = 10 cm. Angle QPS = Angle PSR = 90°. SR is 6 cm longer than PQ. The area of quadrilatera
- November 2022, Paper 5, Q7 (5 marks): The diagram shows a straight line crossing a pair of parallel lines. Not to scale (3x – 23)° (x + 35)° y° Find the value of y. You must show your working. y =
- June 2022, Paper 5, Q8 (5 marks): A bag only contains red marbles, blue marbles and yellow marbles. 2 . • The probability of picking a red marble is 5 • There are nine yellow marbles. • The prob
- June 2022, Paper 5, Q14 (6 marks): In a survey about music, some students were asked whether they like pop (P) and whether they like rap (R). The Venn diagram shows some of the results. x student
- June 2022, Paper 5, Q17 (6 marks): Charlie is making some wooden frames. Charlie has a strip of wood 1.6 m long and 2 cm wide. Not to scale 2 cm 1.6 m Each frame will be made from four pieces of
- November 2021, Paper 4, Q10 (7 marks): Alex, Blake and Charlie play a computer game. Alex goes first and scores n points. • Blake scores 8 points less than 3 times the number of points scored by Alex
- November 2021, Paper 6, Q16 (9 marks): The following kinematics formulas may be used in this question. v u at = + 1 2 s ut at = + 2 2 2 v u 2 as = + The initial velocity of a particle is 20 m/s. The
- November 2020, Paper 4, Q4 (5 marks): In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J). The number of students who had neither a ban
- November 2019, Paper 4, Q8 (5 marks): The diagrams show the price paid by two groups of people visiting a funfair. 5 adults £ 3 adults £ 4 children £ 6 children £ Total £ 78 Total £ 63 Assume each a
- November 2019, Paper 5, Q7 (4 marks): Sundip and Emma have some money. The ratio of Sundip’s money to Emma’s money is 3 : 5. Emma spends £450 of her money. The ratio of Sundip’s money to Emma’s mone
- November 2019, Paper 6, Q4 (5 marks): The diagram shows two rectangles, A and B. Rectangle A Rectangle B 12 cm Not to scale 25 cm Rectangle A has a width of 25 cm and a height of 12 cm. The width of
- November 2019, Paper 6, Q10 (6 marks): Nine consecutive numbers are written on a 3-by-3 grid. They are arranged, in ascending order, in a spiral as shown. (a) Karen writes the numbers 3 to 11 on her
- June 2019, Paper 4, Q5 (6 marks): Bennie is 7 years older than Ayesha. Chloe is twice as old as Bennie. The sum of their three ages is 57. Work out the ages of Ayesha, Bennie and Chloe. Ayesha’s
- June 2019, Paper 4, Q12 (7 marks): (a) Here are the first four terms of a sequence. -1 4 9 14 Write an expression for the nth term of this sequence. (a) (b) The nth term of another sequence is gi
- June 2019, Paper 5, Q4 (4 marks): (a) A sunflower grows at a rate of 4 cm each day. How many days does it take to grow from a height of 80 cm to more than 1.06 m? (a) (b) If the sunflower grows
- November 2018, Paper 4, Q5 (5 marks): Marcin buys 7 rulers and 15 crayons for £7. A ruler costs 12p more than a crayon. Find the cost of one crayon. cost of one crayon = p
- November 2018, Paper 5, Q5 (4 marks): The depth of water in a garden pond is 57.8 cm. The depth decreases by 0.3 cm per day. (a) Assume the depth continues to decrease at the same rate. After how ma
- November 2018, Paper 6, Q12 (6 marks): In the diagram, the square and the trapezium share a common side of length x cm. Not to scale x cm 6 cm 10 cm The area of the square is equal to the area of the
- June 2018, Paper 4, Q9 (6 marks): The dimensions, in centimetres, of this rectangle are shown as algebraic expressions. Not to scale 5x – y – 8 3x + y – 4 2x – 6y – 3 3x + 5y + 4 Work out the le
- November 2017, Paper 5, Q6 (5 marks): This rectangle has length (4x – 5) cm and width (x + 3) cm. Not to scale (x + 3) cm (4x – 5) cm The perimeter of the rectangle is 46 cm. Calculate the area of t
- November 2017, Paper 6, Q12 (6 marks): (a) A sequence is defined using this term-to-term rule. u 2 u 15 1 = + n n + If u1 = 5, find u2 . (a) (b) Another sequence is defined using this term-to-term ru
- June 2017, Paper 4, Q9 (6 marks): Each week Dan drives two routes, route X and route Y. One week he drives route X three times and route Y twice. He drives a total of 134 miles that week. Anothe
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