Quadratic equations: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 2.7 Quadratic equations, 2019–2025, with its mark scheme and examiner’s report.

All 103 questions on Quadratic equations, as a list

June 2025 (R), Paper 1 Foundation, Q23 (8 marks): (a) Expand x x ( − 3 ) t 4 (b) Make t the subject of m 5 (c) Simplify a × a 6 10 (d) Simplify c 30 ÷ c 12 (e) (i) Factorise y y 2 10 21 (ii) Hence, solve y y 2
June 2025 (R), Paper 1 Higher, Q22 (5 marks): Solve the simultaneous equations x y 2 2 41 x y 2 + 3 Show clear algebraic working.
June 2025, Paper 1 Foundation, Q23 (6 marks): (a) Solve x – 4 = 3 + 2 x 6 Show clear algebraic working. x = (b) (i) Factorise y2 – 11y + 30 (ii) Hence solve y2 – 11y + 30 = 0
June 2025, Paper 1 Higher, Q6 (6 marks): (a) Solve x – 4 = 3 + 2 x 6 Show clear algebraic working. x = 2 – 11y + 30 (b) (i) Factorise y 2 – 11y + 30 = 0 (ii) Hence solve y
June 2025, Paper 1 Higher, Q22 (5 marks): Solve the simultaneous equations 2 + 3y + y 2 = 7 x y = x + 2 Show clear algebraic working.
June 2025, Paper 2 Higher, Q25 (6 marks): (a) Write 28 x x in the form a 2 − b x − c )2 where a, b and c are integers. 24 6 ( (b) On the axes below, sketch the graph of y x x 2 28 24 6 Show clearly the
November 2024, Paper 1 Foundation, Q25 (6 marks): (a) (i) Factorise x x 2 5 24 (ii) Hence, solve x 5 x 24 0 2 (b) Solve the inequality 3 y y 5 7 10 Show clear algebraic working.
November 2024, Paper 1 Higher, Q8 (6 marks): (a) (i) Factorise x x 2 5 24 (ii) Hence, solve x 2 5 x 24 0 (b) Solve the inequality 3 y y 5 7 10 Show clear algebraic working.
November 2024, Paper 1 Higher, Q23 (5 marks): The curve C has equation y x x 9 2 8 The straight line L has equation y k where k is an integer. = C and L intersect at the points A and B The coordinates of po
November 2024, Paper 2 Higher, Q22 (5 marks): Solve the simultaneous equations x y y 2 2 3 x 2 y Show clear algebraic working.
June 2024 (R), Paper 1 Foundation, Q22 (9 marks): (a) Simplify g ÷ g 9 2 (b) Expand 5 k k 2 ( 3 + 4 ) (c) (i) Factorise x − x − 2 2 63 (ii) Hence, solve x − x − = 0 2 2 63 (d) Solve the inequality 7 2 y
June 2024 (R), Paper 1 Higher, Q7 (9 marks): (a) Simplify g ÷ g 9 2 (b) Expand 5 k k 2 ( 3 + 4 ) (c) (i) Factorise x − x − 2 2 63 (ii) Hence, solve x − x − = 0 2 2 63 (d) Solve the inequality 7 2 y
June 2024 (R), Paper 1 Higher, Q20 (5 marks): (a) Express 2 x x in the form a x − b − c where a, b and c are numbers to 2 11 9 ( ) 2 be found. The curve C has equation y 2 ( x 3 ) 2 11 ( x 3 ) 9 The point
June 2024 (R), Paper 1 Higher, Q21 (5 marks): There are 25 counters in a bag such that 6 counters are blue x counters are orange, where x > 9 the rest of the counters are pink Maalam takes at random two of
June 2024 (R), Paper 2 Higher, Q22 (5 marks): Solve the simultaneous equations Show clear algebraic working.
June 2024, Paper 1 Higher, Q25 (4 marks): f (x) = 17 − 3x 2 + 12x Write f (x) in the form a – b(x − c) 2 where a, b and c are constants. f (x) =
June 2024, Paper 2 Foundation, Q27 (3 marks): (i) Factorise x (ii) Hence, solve x 2 + 9x – 22 = 0
June 2024, Paper 2 Higher, Q11 (3 marks): (i) Factorise x 2 + 9x – 22 2 + 9x – 22 = 0 (ii) Hence, solve x
June 2024, Paper 2 Higher, Q22 (5 marks): The straight line L has equation x + y = 5 The curve C has equation 2x 2 + 3y 2 = 210 Find the coordinates of the points where L and C intersect. Show clear alg
November 2023, Paper 2 Higher, Q21 (5 marks): The line with equation x y 5 intersects the curve with equation 2 at the points A and B x 2 3 y 2 13 Find the coordinates of A and the coordinates of B Show cle
November 2023, Paper 2 Higher, Q24 (5 marks): Solve x x x x x 2 3 4 3 4 5 8 Show clear algebraic working. x =
June 2023 (R), Paper 1 Higher, Q25 (6 marks): Here is a triangle ABC B Diagram NOT C accurately drawn (2x – 1) cm (2x + 1) cm 30° A The area of the triangle is (x2 + x – 3.75) cm2 Find the size of the large
June 2023 (R), Paper 2 Higher, Q21 (5 marks): Work out the coordinates of the points of intersection of y – 2x = 1 and y2 + xy = 7 Show clear algebraic working. ( , ) ( , )
June 2023, Paper 1 Foundation, Q21 (8 marks): (a) Simplify (2c 4d 7) 3 (b) Find the value of 5y 0 where y > 0 2b 3 + 20a 3b (c) Factorise fully 16a 2 + 9x – 22 (d) (i) Factorise x 2 + 9x – 22 = 0 (ii) Hence
June 2023, Paper 1 Higher, Q6 (8 marks): (a) Simplify (2c 4d 7) 3 (b) Find the value of 5y 0 where y > 0 2b 3 + 20a 3b (c) Factorise fully 16a 2 + 9x – 22 (d) (i) Factorise x 2 + 9x – 22 = 0 (ii) Hence
June 2023, Paper 2 Higher, Q19 (3 marks): Express 3x2 – 6x + 5 in the form a(x – b)2 + c
June 2023, Paper 2 Higher, Q21 (5 marks): Solve the simultaneous equations 2x2 + 3y2 = 11 x = 3y – 1 Show clear algebraic working.
January 2023 (R), Paper 1 Foundation, Q23 (5 marks): (a) Factorise fully 18c3d2 – 21c2 (b) (i) Factorise y2 – 3y – 18 (ii) Hence, solve y2 – 3y – 18 = 0
January 2023 (R), Paper 1 Higher, Q8 (5 marks): (a) Factorise fully 18c3d2 – 21c2 (b) (i) Factorise y2 – 3y – 18 (ii) Hence, solve y2 – 3y – 18 = 0
January 2023 (R), Paper 1 Higher, Q16 (6 marks): The function f is such that 2 where x ≠ 5 f(x) = 3 x − 5 3 (a) Find f 1     3 (b) Find f –1(x) f –1(x) = The function g is such that g(x) = 5x2 – 20x + 23
January 2023 (R), Paper 2 Higher, Q22 (5 marks): Solve the simultaneous equations 2y2 + x2 = –6x + 42 2x + y = –3 Show clear algebraic working.
January 2023 (R), Paper 2 Higher, Q23 (5 marks): AEC and BED are chords of a circle. B Diagram NOT accurately drawn A x cm (x + 5) cm 48° E (5x – 12) cm C (x + 12) cm D AE = (x + 5) cm BE = x cm CE = (5x – 12)
January 2023, Paper 2 Higher, Q20 (5 marks): Solve the simultaneous equations y = 7 – 2x x2 + y2 = 34 Show clear algebraic working.
June 2022 (R), Paper 1 Foundation, Q21 (5 marks): (a) Expand 3c 3(c + 4) (b) (i) Factorise x 2 + 8x – 9 2 + 8x –9 = 0 (ii) Hence, solve x
June 2022 (R), Paper 1 Foundation, Q27 (6 marks): The diagram shows a quadrilateral ABCD D Diagram NOT accurately drawn A 7.5 cm 6 cm B C In the diagram, ABC and DAC are right‑angled triangles. BC = 6 cm AC = 7
June 2022 (R), Paper 1 Higher, Q5 (5 marks): (a) Expand 3c 3(c + 4) (b) (i) Factorise x 2 + 8x – 9 2 + 8x –9 = 0 (ii) Hence, solve x
June 2022 (R), Paper 1 Higher, Q11 (6 marks): The diagram shows a quadrilateral ABCD D Diagram NOT accurately drawn A 7.5 cm 6 cm B C In the diagram, ABC and DAC are right‑angled triangles. BC = 6 cm AC = 7
June 2022 (R), Paper 1 Higher, Q23 (5 marks): (a) Express 2x 2 – 12x + 3 in the form a(x + b) 2 + c where a, b and c are integers. The curve C has equation y = 2(x + 4) 2 – 12(x + 4) + 3 The point M is the
June 2022 (R), Paper 1 Higher, Q24 (5 marks): Elliot has x counters. Each counter has one red face and one green face. Elliot spreads all the counters out on a table and sees that the number of counters sho
June 2022 (R), Paper 2 Higher, Q21 (5 marks): Solve the simultaneous equations x – 2y = 3 2 – y 2 + 2x = 10 x Show clear algebraic working.
June 2022, Paper 1 Higher, Q19 (5 marks): A (r + 7) m Diagram NOT 45° accurately drawn O B OAB is a sector S of a circle with centre O and radius (r + 7) metres. Angle AOB = 45° A circle C has radius (r
June 2022, Paper 1 Higher, Q24 (4 marks): Express each of a, b and c in terms of q so that q + 12x − qx2 can be written as a − b (x − c) 2 a = b = c =
June 2022, Paper 2 Foundation, Q27 (3 marks): (i) Factorise x2 + 5x − 24 (ii) Hence, solve x2 + 5x − 24 = 0
June 2022, Paper 2 Higher, Q11 (3 marks): (i) Factorise x2 + 5x − 24 (ii) Hence, solve x2 + 5x − 24 = 0
January 2022 (R), Paper 1 Higher, Q19 (3 marks): Given that xm 3 x (a) find the value of m m = Given that a, b and c are integers, (b) express 3x2 + 12x + 19 in the form a(x + b)2 + c
January 2022 (R), Paper 2 Higher, Q18 (5 marks): The line with equation 2y = x + 1 intersects the curve with equation 3y2 + 7y + 16 = x2 – x at the points A and B Find the coordinates of A and the coordinates
January 2022, Paper 1 Foundation, Q21 (5 marks): (a) Solve the inequality 5x – 7  2 (b) (i) Factorise y2 – 2y – 35 (ii) Hence, solve y2 – 2y – 35 = 0
January 2022, Paper 1 Higher, Q6 (5 marks): (a) Solve the inequality 5x – 7  2 (b) (i) Factorise y2 – 2y – 35 (ii) Hence, solve y2 – 2y – 35 = 0
January 2022, Paper 1 Higher, Q19 (5 marks): Solve the simultaneous equations 3x2 + y2 – xy = 5 y = 2x – 3 Show clear algebraic working.
January 2022, Paper 1 Higher, Q20 (4 marks): (a) Express 7 + 12x – 3x2 in the form a + b(x + c)2 where a, b and c are integers. C is the curve with equation y = 7 + 12x – 3x2 The point A is the maximum poi
November 2021, Paper 1 Higher, Q17 (8 marks): (a) Factorise 6y2 – y – 5 2 f + 3 (b) Make f the subject of w = 8 - f (c) Express 4x2 – 8x + 7 in the form a(x + b)2 + c where a, b and c are integers.
November 2021, Paper 1 Higher, Q19 (6 marks): ABCED is a five-sided shape. E Diagram NOT accurately drawn D C y cm A x cm B ABCD is a rectangle. CED is an equilateral triangle. AB = x cm BC = y cm The perim
November 2021, Paper 2 Foundation, Q18 (4 marks): Here are two rectangles, rectangle A and rectangle B. rectangle A rectangle B Diagram NOT accurately drawn (2x – 1) cm (5 – x) cm 4 cm 5 cm The area of rectangl
November 2021, Paper 2 Foundation, Q24 (4 marks): (a) Simplify (3x2y)0 (b) (i) Factorise x2 – 5x – 36 (ii) Hence solve x2 – 5x – 36 = 0
November 2021, Paper 2 Higher, Q2 (4 marks): Here are two rectangles, rectangle A and rectangle B. rectangle A rectangle B Diagram NOT accurately drawn (2x – 1) cm (5 – x) cm 4 cm 5 cm The area of rectangl
November 2021, Paper 2 Higher, Q8 (4 marks): (a) Simplify (3x2y)0 (b) (i) Factorise x2 – 5x – 36 (ii) Hence solve x2 – 5x – 36 = 0
November 2021, Paper 2 Higher, Q19 (6 marks): The straight line L has equation x – y = 3 The curve C has equation 3x2 – y2 + xy = 9 L and C intersect at the points P and Q. Find the coordinates of the midpo
November 2021, Paper 2 Higher, Q21 (6 marks): The curve C has equation y = f(x) where f(x) = 9 – 3(x + 2)2 The point A is the maximum point on C. (a) Write down the coordinates of A. ( , ) 4 The curve C is
June 2021, Paper 1 Foundation, Q24 (5 marks): (a) Factorise fully 25a4c7d + 45a9c3h (b) Solve (2x + 5)2 = (2x + 3)(2x – 1) x =
June 2021, Paper 1 Higher, Q9 (5 marks): (a) Factorise fully 25a4c7d + 45a9c3h (b) Solve (2x + 5)2 = (2x + 3)(2x – 1) x =
June 2021, Paper 2 Foundation, Q23 (3 marks): (i) Factorise x2 + 2x – 24 (ii) Hence solve x2 + 2x – 24 = 0
June 2021, Paper 2 Higher, Q9 (3 marks): (i) Factorise x2 + 2x – 24 (ii) Hence solve x2 + 2x – 24 = 0
June 2021, Paper 2 Higher, Q19 (5 marks): Solve the simultaneous equations y = 3 – 2x x2 + y2 = 18 Show clear algebraic working.
June 2021, Paper 2 Higher, Q22 (4 marks): The curve S has equation y = f(x) where f(x) = x2 The curve T has equation y = g(x) where g(x) = 2x2 – 12x + 13 By writing g(x) in the form a(x – b)2 – c, where
June 2021, Paper 2 Higher, Q23 (5 marks): Pippa has a box containing N pens. There are only black pens and red pens in the box. The number of black pens in the box is 3 more than the number of red pens.
January 2021 (R), Paper 1 Higher, Q16 (5 marks): (a) Expand and simplify (x + 4)(x – 2)(x + 1) (b) Express x 2 – 10x + 40 in the form (x + a) 2 + b, where a and b are integers.
January 2021 (R), Paper 1 Higher, Q17 (5 marks): Solve the simultaneous equations x – 6y = 5 xy – 2y 2 = 6 Show clear algebraic working.
January 2021 (R), Paper 2 Foundation, Q20 (3 marks): Solve x 2 – 21x + 20 = 0 Show your working clearly.
January 2021 (R), Paper 2 Higher, Q9 (3 marks): Solve x 2 – 21x + 20 = 0 Show your working clearly.
January 2021 (R), Paper 2 Higher, Q18 (5 marks): Solve the equation 5 3 + = 2 x 2 + 2 x + 2 x Show clear algebraic working.
January 2021 (R), Paper 2 Higher, Q21 (6 marks): A bag contains n beads. 6 of the beads are red and the rest are blue. Ravi is going to take at random 2 beads from the bag. The probability that the 2 beads wil
January 2021, Paper 1 Foundation, Q25 (5 marks): (a) Simplify (2x 3y 5) 4 (b) (i) Factorise x 2 + 5x – 36 (ii) Hence, solve x 2 + 5x – 36 = 0
January 2021, Paper 1 Higher, Q9 (5 marks): (a) Simplify (2x 3y 5) 4 (b) (i) Factorise x 2 + 5x – 36 (ii) Hence, solve x 2 + 5x – 36 = 0
January 2021, Paper 1 Higher, Q19 (5 marks): Solve the simultaneous equations 2 – 9y – x = 2y 2 – 12 x x + 2y – 1 = 0 Show clear algebraic working.
November 2020 (R), Paper 1 Higher, Q23 (4 marks): In a bag, there are only 3 blue beads 4 white beads and x orange beads. Jean is going to take at random two beads from the bag. The probability that Jean will
November 2020 (R), Paper 2 Higher, Q22 (6 marks): The curve with equation x2 – x + y2 = 10 and the straight line with equation x – y = –4 intersect at the points A and B. Work out the exact length of AB. a Show
November 2020 (R), Paper 2 Higher, Q24 (5 marks): (a) Write 7 + 12x – 3x2 in the form a + b(x + c)2 where a, b and c are integers. The curve C has equation y = 7 + 12x – 3x2 The point A is the turning point on
November 2020, Paper 1 Foundation, Q20 (8 marks): (a) Solve 5(4 – x) = 7 – 3x Show clear algebraic working. x = (b) Factorise fully 16m3g3 + 24m2g5 (c) (i) Factorise y2 – 2y – 48 (ii) Hence, solve y2 – 2y – 48
November 2020, Paper 1 Higher, Q7 (8 marks): (a) Solve 5(4 – x) = 7 – 3x Show clear algebraic working. x = (b) Factorise fully 16m3g3 + 24m2g5 (c) (i) Factorise y2 – 2y – 48 (ii) Hence, solve y2 – 2y – 48
November 2020, Paper 2 Higher, Q16 (5 marks): Solve the simultaneous equations 3xy – y2 = 8 x – 2y = 1 Show clear algebraic working.
November 2020, Paper 2 Higher, Q17 (5 marks): The diagram shows a rectangle. (2x – 4) cm Diagram NOT accurately drawn (3x + 2) cm The area of the rectangle is A cm2 Given that A < 3x + 27 find the range of
November 2020, Paper 2 Higher, Q20 (5 marks): A bag contains X counters. There are only red counters and blue counters in the bag. There are 4 more blue counters than red counters in the bag. Finty takes at
November 2020, Paper 2 Higher, Q21 (7 marks): The function f is such that f(x) = 5 + 6x – x2 for x  3 (a) Express 5 + 6x – x2 in the form p – (x – q)2 where p and q are constants. (b) Using your answer to
January 2020 (R), Paper 1 Foundation, Q20 (3 marks): Solve x2 − 5x − 36 = 0 Show clear algebraic working.
January 2020 (R), Paper 1 Higher, Q6 (3 marks): Solve x2 − 5x − 36 = 0 Show clear algebraic working.
January 2020 (R), Paper 2 Higher, Q23 (3 marks): Express 7 – 12x – 2x2 in the form a + b(x + c)2 where a, b and c are integers.
January 2020, Paper 1 Higher, Q20 (4 marks): The curve C has equation y = 4(x − 1)2 − a where a > 4 Using the axes below, sketch the curve C. On your sketch show clearly, in terms of a, (i) the coordinates
January 2020, Paper 2 Foundation, Q23 (5 marks): (a) Solve the inequality 2x + 7 > 4 (b) Solve x2 – 3x – 40 = 0 Show clear algebraic working.
January 2020, Paper 2 Higher, Q7 (5 marks): (a) Solve the inequality 2x + 7 > 4 (b) Solve x2 – 3x – 40 = 0 Show clear algebraic working.
January 2020, Paper 2 Higher, Q22 (5 marks): The line with equation y = x + 2 intersects the curve with equation x2 + y2 – 2y = 24 at the points A and B. Find the coordinates of A and B. Show clear algebra
June 2019 (R), Paper 1 Higher, Q22 (5 marks): Solve the simultaneous equations 2x2 + 3y2 = 5 y = 2x + 1 Show clear algebraic working.
June 2019 (R), Paper 2 Higher, Q22 (4 marks): Write 5 + 12xíx2 in the form a + b(x + c)2 where a, b and c are integers.
June 2019 (R), Paper 2 Higher, Q24 (5 marks): A box contains marbles. 4 of the marbles are red. The rest of the marbles are yellow. Antonia takes at random a marble from the box and does not replace it. Ser
June 2019, Paper 1 Higher, Q22 (6 marks): The graph of y = sinx° for 0 - x - 360 is drawn on the grid. y 3 2 1 O x 60 120 180 240 300 360 í í í (a) On the grid, draw the graph of y = 2sin(x + 30)° fo
June 2019, Paper 2 Higher, Q20 (5 marks): The equation of the line L is y íx The equation of the curve C is x2íxy + 2y2 = 0 L and C intersect at two points. Find the coordinates of these two poi
June 2019, Paper 2 Higher, Q23 (5 marks): Boris has a bag that only contains red sweets and green sweets. Boris takes at random 2 sweets from the bag. The probability that Boris takes exactly 1 red swee
January 2019 (R), Paper 1 Higher, Q21 (5 marks): Here is a triangle XYZ. X Diagram NOT accurately drawn 60° 5 cm y cm Y x cm Z The perimeter of the triangle is k cm. Given that x = y − 1 find the value of k. S
January 2019 (R), Paper 2 Higher, Q20 (4 marks): (a) Write 3x2 − 12x + 7 in the form a(x + b)2 + c The line L is the line of symmetry of the curve with equation y = 3x2 − 12x + 7 (b) Using your answer to part
January 2019 (R), Paper 2 Higher, Q21 (6 marks): The curve with equation y = (10x − 3)(x + 1) and the line with equation y − 6x = 0 intersect at the points A and B. Find the coordinates of the midpoint of AB.
January 2019, Paper 1 Foundation, Q13 (8 marks): (a) Expand and simplify (e + 3)(e – 5) 2 y + 1 (b) Solve y = 5 Show clear algebraic working. y = (c) Solve x2 + 3x – 18 = 0 Show your working clearly.
January 2019, Paper 1 Higher, Q6 (6 marks): (a) Complete the table of values for y = x2 – 5x + 6 x 0 1 2 3 4 5 y 6 0 0 2 (b) On the grid, draw the graph of y = x2 – 5x + 6 for 0  x  5 y 7 6 5 4 3 2 1 O
January 2019, Paper 1 Higher, Q20 (6 marks): A bowl contains n pieces of fruit. Of these, 4 are oranges and the rest are apples. Two pieces of fruit are going to be taken at random from the bowl. The proba
January 2019, Paper 2 Higher, Q15 (6 marks): The diagram shows a trapezium. (x + 5) Diagram NOT accurately drawn (2x – 3) (3x – 2) All measurements shown on the diagram are in centimetres. The area of the

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