Question Simulator

AS & A Level Mathematics (9709)

Quadratics Banker

49 questions · about 2% of the marks we indexed · examined in 9 of 9 sessions.

Questions by year

2026

  • 2026 May/June · Paper 11 · Q9 (b(ii))5 marksDiscriminant / tangency
  • 2026 May/June · Paper 12 · Q13 marksDisguised quadratic
  • 2026 May/June · Paper 12 · Q10 (a)3 marksDiscriminant / tangency
  • 2026 May/June · Paper 13 · Q1 (a, b)5 marksLine-curve intersection
  • 2026 May/June · Paper 13 · Q2 (a, b)4 marksDisguised quadratic
  • 2026 May/June · Paper 15 · Q15 marksLine-curve intersection
  • 2026 May/June · Paper 15 · Q5 (a, b)6 marksCompleting the square · Disguised quadratic
  • 2026 May/June · Paper 15 · Q64 marksDiscriminant / tangency

2025

  • 2025 Oct/Nov · Paper 11 · Q14 marksDiscriminant / tangency
  • 2025 Oct/Nov · Paper 11 · Q4 (a)3 marksCompleting the square
  • 2025 Oct/Nov · Paper 12 · Q1 (a, b, c)5 marksCompleting the square · Discriminant / tangency · Disguised quadratic
  • 2025 Oct/Nov · Paper 13 · Q10 (a(i), b)8 marksCompleting the square
  • 2025 Oct/Nov · Paper 15 · Q3 (a, b)3 marksCompleting the square · Discriminant / tangency
  • 2025 Oct/Nov · Paper 15 · Q53 marksDisguised quadratic
  • 2025 May/June · Paper 11 · Q6 (a, b)9 marksDiscriminant / tangency · Line-curve intersection
  • 2025 May/June · Paper 12 · Q24 marksLine-curve intersection
  • 2025 May/June · Paper 12 · Q11 (a)2 marksCompleting the square
  • 2025 May/June · Paper 15 · Q3 (a)2 marksCompleting the square

2024

  • 2024 Oct/Nov · Paper 11 · Q45 marksDiscriminant / tangency
  • 2024 Oct/Nov · Paper 11 · Q5 (a)3 marksDisguised quadratic
  • 2024 Oct/Nov · Paper 11 · Q11 (a, c)5 marksCompleting the square · Sketching quadratics
  • 2024 Oct/Nov · Paper 12 · Q7 (a)3 marksCompleting the square
  • 2024 Oct/Nov · Paper 12 · Q9 (a, b)10 marksDiscriminant / tangency · Line-curve intersection
  • 2024 Oct/Nov · Paper 13 · Q8 (a)2 marksCompleting the square
  • 2024 Oct/Nov · Paper 13 · Q9 (a)3 marksLine-curve intersection
  • 2024 May/June · Paper 11 · Q1 (a, b)5 marksOfficial paper ↗Completing the square · Disguised quadratic
  • 2024 May/June · Paper 13 · Q11 (b)6 marksDiscriminant / tangency

2023

  • 2023 Oct/Nov · Paper 11 · Q24 marksDiscriminant / tangency
  • 2023 Oct/Nov · Paper 11 · Q8 (a)4 marksDisguised quadratic
  • 2023 Oct/Nov · Paper 11 · Q9 (a)2 marksCompleting the square
  • 2023 Oct/Nov · Paper 12 · Q6 (a)2 marksCompleting the square
  • 2023 Oct/Nov · Paper 12 · Q9 (a)4 marksDisguised quadratic
  • 2023 Oct/Nov · Paper 13 · Q67 marksDiscriminant / tangency
  • 2023 May/June · Paper 11 · Q55 marksDiscriminant / tangency
  • 2023 May/June · Paper 12 · Q3 (a, b)3 marksCompleting the square · Discriminant / tangency
  • 2023 May/June · Paper 12 · Q43 marksDisguised quadratic
  • 2023 May/June · Paper 13 · Q24 marksDiscriminant / tangency

2022

  • 2022 Oct/Nov · Paper 11 · Q13 marksDisguised quadratic
  • 2022 Oct/Nov · Paper 11 · Q9 (a, b, c)4 marksCompleting the square
  • 2022 Oct/Nov · Paper 12 · Q3 (a)2 marksDiscriminant / tangency
  • 2022 Oct/Nov · Paper 12 · Q6 (a, b, c)9 marksCompleting the square · Sketching quadratics
  • 2022 Oct/Nov · Paper 12 · Q11 (a)3 marksCompleting the square
  • 2022 Oct/Nov · Paper 13 · Q2 (a)2 marksCompleting the square
  • 2022 May/June · Paper 11 · Q1 (a, b)4 marksCompleting the square
  • 2022 May/June · Paper 11 · Q7 (a)4 marksLine-curve intersection
  • 2022 May/June · Paper 12 · Q5 (a, b)9 marksDiscriminant / tangency · Line-curve intersection
  • 2022 May/June · Paper 13 · Q5 (a)4 marksDisguised quadratic
  • 2022 May/June · Paper 13 · Q6 (a)2 marksCompleting the square
  • 2022 May/June · Paper 13 · Q11 (a)6 marksDiscriminant / tangency

References only, not question text. Open Official paper ↗ where Cambridge publishes the paper, or see the official Cambridge past-papers page; for other papers, ask your school. “Paper 42” means Paper 4, variant 2.

Practice questions

Original questions written by HomiLabs in the style of the exam, with answers and mark schemes. They are not Cambridge past paper questions and have not been reviewed by Cambridge. Try each one before opening the answer.

Q1Discriminant / tangency · Core · Paper 1 style · 3 marks
  1. (a) Find the values of the constant k for which the equation 2x² + kx + 18 = 0 has two equal roots. [3]
Show answer
  1. (a) k = 12 or k = −12
    Equal roots: b² − 4ac = 0 (M1). k² − 4(2)(18) = 0 so k² = 144 (A1). k = ±12 (A1).
Q2Discriminant / tangency · Core · Paper 1 style · 4 marks
  1. (a) Show that the equation 3x² − 5x + 4 = 0 has no real roots. [2]
  2. (b) Find the set of values of the constant p for which the equation x² + 6x + p = 0 has two distinct real roots. [2]
Show answer
  1. (a) Discriminant = −23 < 0, so no real roots
    b² − 4ac = 25 − 48 = −23 (M1). Negative, so no real roots (A1).
  2. (b) p < 9
    36 − 4p > 0 (M1). p < 9 (A1).
Q3Discriminant / tangency · Core · Paper 1 style · 4 marks
  1. (a) The line y = 2x + c is a tangent to the curve y = x² − 4x + 7. Find the value of c and the coordinates of the point where the line touches the curve. [4]
Show answer
  1. (a) c = −2; point of contact (3, 4)
    x² − 4x + 7 = 2x + c gives x² − 6x + (7 − c) = 0 (M1). Tangent: 36 − 4(7 − c) = 0 (M1), c = −2 (A1). Then x² − 6x + 9 = 0, x = 3, y = 4 (A1).
Q4Discriminant / tangency · Standard · Paper 1 style · 4 marks
  1. (a) The equation kx² + (k + 3)x + 1 = 0 is a quadratic equation in x, where k is a non-zero constant. Show that its discriminant is k² + 2k + 9. [2]
  2. (b) By completing the square, show that the equation has two distinct real roots for every non-zero value of k. [2]
Show answer
  1. (a) (k + 3)² − 4k = k² + 2k + 9
    b² − 4ac = (k + 3)² − 4(k)(1) (M1) = k² + 6k + 9 − 4k = k² + 2k + 9 (A1).
  2. (b) k² + 2k + 9 = (k + 1)² + 8 ≥ 8 > 0
    (k + 1)² + 8 (M1). A square is never negative, so the discriminant is at least 8 > 0: two distinct real roots for every k ≠ 0 (A1).
Q5Discriminant / tangency · Standard · Paper 1 style · 4 marks
  1. (a) Find the set of values of the constant m for which the line y = mx − 1 does not meet the curve y = x² + 3x + 3. [4]
Show answer
  1. (a) −1 < m < 7
    x² + 3x + 3 = mx − 1 gives x² + (3 − m)x + 4 = 0 (M1). No intersection: (3 − m)² − 16 < 0 (M1). Critical values 3 − m = ±4, m = −1, 7 (A1). −1 < m < 7 (A1).
Q6Discriminant / tangency · Standard · Paper 1 style · 4 marks
  1. (a) The curve y = x² − 2kx + 3k + 4 lies completely above the x-axis. Find the set of possible values of the constant k. [4]
Show answer
  1. (a) −1 < k < 4
    No real roots of x² − 2kx + 3k + 4 = 0: 4k² − 4(3k + 4) < 0 (M1). k² − 3k − 4 < 0 (A1). (k − 4)(k + 1) < 0, critical values −1, 4 (M1). −1 < k < 4 (A1).
Q7Discriminant / tangency · Challenge · Paper 1 style · 7 marks
  1. (a) The line y = mx + 5 is a tangent to the curve y = 2x² − 3x + 7. Find the two possible values of m. [4]
  2. (b) For each value of m, find the coordinates of the point of contact. [3]
Show answer
  1. (a) m = 1 or m = −7
    2x² − 3x + 7 = mx + 5 gives 2x² − (3 + m)x + 2 = 0 (M1). (3 + m)² − 16 = 0 (M1). 3 + m = ±4 (A1). m = 1 or −7 (A1).
  2. (b) m = 1: (1, 6); m = −7: (−1, 12)
    m = 1: 2x² − 4x + 2 = 0, x = 1, y = 6 (M1 A1). m = −7: 2x² + 4x + 2 = 0, x = −1, y = 12 (A1).
Q8Discriminant / tangency · Challenge · Paper 1 style · 7 marks
  1. (a) The equation kx² + 6x + (k − 8) = 0, where k ≠ 0, has two distinct real roots. Find the set of possible values of k. [4]
  2. (b) Find the value of k for which the equation has equal roots and that root is positive. State the root. [3]
Show answer
  1. (a) −1 < k < 9, k ≠ 0
    36 − 4k(k − 8) > 0 (M1). k² − 8k − 9 < 0 (A1). (k − 9)(k + 1) < 0 (M1). −1 < k < 9 with k ≠ 0 (A1).
  2. (b) k = −1, root x = 3
    Equal roots when k = −1 or 9 (B1). k = −1: −x² + 6x − 9 = 0, x = 3 (positive) (M1). k = 9: 9x² + 6x + 1 = 0, x = −1/3 (negative), so k = −1, root 3 (A1).
Q9Discriminant / tangency · Challenge · Paper 1 style · 6 marks
  1. (a) The line x + 2y = c is a tangent to the curve y = 4/x. Find the possible values of c, giving your answers in exact form. [4]
  2. (b) Find the coordinates of the point of contact for the positive value of c. [2]
Show answer
  1. (a) c = 4√2 or c = −4√2
    y = (c − x)/2, so (c − x)/2 = 4/x (M1). x² − cx + 8 = 0 (A1). Tangent: c² − 32 = 0 (M1). c = ±√32 = ±4√2 (A1).
  2. (b) (2√2, √2)
    x = c/2 = 2√2 (M1). y = 4/(2√2) = √2 (A1).
Q10Completing the square · Core · Paper 1 style · 4 marks
  1. (a) Express 2x² − 12x + 23 in the form a(x + b)² + c, where a, b and c are constants. [3]
  2. (b) Hence state the minimum value of 2x² − 12x + 23 and the value of x at which it occurs. [1]
Show answer
  1. (a) 2(x − 3)² + 5
    a = 2 (B1), b = −3 (B1), c = 23 − 18 = 5 (B1).
  2. (b) Minimum 5 when x = 3
    B1 for both.
Q11Completing the square · Core · Paper 1 style · 3 marks
  1. (a) Express 7 + 8x − x² in the form a − (x − b)². [2]
  2. (b) State the coordinates of the maximum point of the curve y = 7 + 8x − x². [1]
Show answer
  1. (a) 23 − (x − 4)²
    b = 4 (B1). a = 7 + 16 = 23 (B1).
  2. (b) (4, 23)
    B1 follow through.
Q12Completing the square · Core · Paper 1 style · 4 marks
  1. (a) Express x² + 5x + 1 in the form (x + p)² + q. [2]
  2. (b) Hence solve the equation x² + 5x + 1 = 0, giving your answers in exact form. [2]
Show answer
  1. (a) (x + 5/2)² − 21/4
    p = 5/2 (B1), q = 1 − 25/4 = −21/4 (B1).
  2. (b) x = (−5 ± √21)/2
    (x + 5/2)² = 21/4 (M1). x = −5/2 ± √21/2 (A1).
Q13Completing the square · Standard · Paper 1 style · 5 marks

The function f is defined by f(x) = 3x² + 18x + 20 for x ≥ k, where k is a constant.

  1. (a) Express f(x) in the form a(x + b)² + c. [3]
  2. (b) State the smallest value of k for which f is a one-one function. [1]
  3. (c) For this value of k, state the range of f. [1]
Show answer
  1. (a) 3(x + 3)² − 7
    a = 3 (B1), b = 3 (B1), c = 20 − 27 = −7 (B1).
  2. (b) k = −3
    B1: the vertex is at x = −3.
  3. (c) f(x) ≥ −7
    B1.
Q14Completing the square · Standard · Paper 1 style · 6 marks

The function g is defined for all real x by g(x) = 4x² − 12x + 13.

  1. (a) Express g(x) in the form (ax + b)² + c, where a > 0. [3]
  2. (b) Hence explain why g(x) > 0 for all x, and find the range of the function h(x) = 1/g(x). [3]
Show answer
  1. (a) (2x − 3)² + 4
    a = 2 (B1), b = −3 (B1), c = 13 − 9 = 4 (B1).
  2. (b) g(x) ≥ 4 > 0; range of h: 0 < h(x) ≤ 1/4
    (2x − 3)² ≥ 0 so g(x) ≥ 4 (B1). Largest value of h is 1/4 at x = 3/2 (M1). h(x) > 0 and tends to 0 as |x| grows: 0 < h(x) ≤ 1/4 (A1).
Q15Completing the square · Standard · Paper 1 style · 5 marks

A farmer near Sahiwal has 60 m of fencing. She uses it for three sides of a rectangular goat pen; the fourth side is an existing brick wall. The two sides perpendicular to the wall each have length x m.

  1. (a) Show that the area A m² of the pen is given by A = 60x − 2x². [1]
  2. (b) Express A in the form p − q(x − r)² and hence find the greatest possible area and the value of x that gives it. [4]
Show answer
  1. (a) A = x(60 − 2x) = 60x − 2x²
    Side parallel to wall = 60 − 2x, so A = x(60 − 2x) (B1).
  2. (b) A = 450 − 2(x − 15)²; greatest area 450 m² when x = 15
    −2(x² − 30x) = −2[(x − 15)² − 225] (M1) = 450 − 2(x − 15)² (A1 A1). Maximum 450 m² at x = 15 (A1).
Q16Completing the square · Challenge · Paper 1 style · 8 marks

The function f is defined for all real x by f(x) = −2x² + 8x + c, where c is a constant.

  1. (a) Express f(x) in the form a(x + b)² + d, giving d in terms of c. [3]
  2. (b) The line y = 3 is a tangent to the curve y = f(x). Find the value of c. [2]
  3. (c) For this value of c, find the set of values of x for which f(x) > −15. [3]
Show answer
  1. (a) −2(x − 2)² + 8 + c
    a = −2 (B1), b = −2 (B1), d = 8 + c (B1).
  2. (b) c = −5
    The maximum value 8 + c equals 3 (M1), c = −5 (A1).
  3. (c) −1 < x < 5
    3 − 2(x − 2)² > −15 so (x − 2)² < 9 (M1 A1). −1 < x < 5 (A1).
Q17Completing the square · Challenge · Paper 1 style · 6 marks

The function f is defined by f(x) = 2x² − 8x + 1 for x ≤ 1.

  1. (a) Express f(x) in the form a(x + b)² + c. [2]
  2. (b) State the range of f. [1]
  3. (c) Find an expression for f⁻¹(x) and state its domain. [3]
Show answer
  1. (a) 2(x − 2)² − 7
    b = −2 (B1); a = 2 and c = −7 (B1).
  2. (b) f(x) ≥ −5
    f is decreasing for x ≤ 1, f(1) = −5 (B1).
  3. (c) f⁻¹(x) = 2 − √((x + 7)/2), for x ≥ −5
    y = 2(x − 2)² − 7 so (x − 2)² = (y + 7)/2 (M1). x ≤ 1 so take the negative root: x = 2 − √((y + 7)/2) (A1). Domain x ≥ −5 (B1).
Q18Disguised quadratic · Core · Paper 1 style · 3 marks
  1. (a) Solve the equation x⁴ − 13x² + 36 = 0. [3]
Show answer
  1. (a) x = −3, −2, 2, 3
    Let u = x²: u² − 13u + 36 = 0 (M1). (u − 4)(u − 9) = 0, u = 4 or 9 (A1). x = ±2, ±3 (A1).
Q19Disguised quadratic · Core · Paper 1 style · 3 marks
  1. (a) Solve the equation 2x − 7√x + 3 = 0. [3]
Show answer
  1. (a) x = 9 or x = 1/4
    Let u = √x: 2u² − 7u + 3 = 0 (M1). (2u − 1)(u − 3) = 0, u = 1/2 or 3 (A1). x = 1/4 or 9 (A1).
Q20Disguised quadratic · Standard · Paper 1 style · 3 marks
  1. (a) Solve the equation x^(2/3) − 5x^(1/3) + 4 = 0. [3]
Show answer
  1. (a) x = 1 or x = 64
    Let u = x^(1/3): u² − 5u + 4 = 0 (M1). u = 1 or 4 (A1). x = 1³ = 1 or 4³ = 64 (A1).
Q21Disguised quadratic · Standard · Paper 1 style · 4 marks
  1. (a) Find the exact real solutions of the equation 3x² + 4 = 20/x². [4]
Show answer
  1. (a) x = √2 or x = −√2
    Multiply by x²: 3x⁴ + 4x² − 20 = 0 (M1). (3x² + 10)(x² − 2) = 0 (M1 A1). x² = −10/3 has no real solution; x = ±√2 (A1).
Q22Disguised quadratic · Challenge · Paper 1 style · 5 marks
  1. (a) Solve the equation (x² − 3x)² − 2(x² − 3x) − 8 = 0. [5]
Show answer
  1. (a) x = −1, 1, 2, 4
    Let u = x² − 3x: u² − 2u − 8 = 0 (M1), u = 4 or −2 (A1). x² − 3x − 4 = 0 gives x = 4 or −1 (A1). x² − 3x + 2 = 0 gives x = 1 or 2 (M1 A1).
Q23Disguised quadratic · Challenge · Paper 1 style · 6 marks
  1. (a) Find the set of values of the constant k for which the equation x − 4√x + k = 0 has two distinct real roots. [4]
  2. (b) Solve the equation when k = 3. [2]
Show answer
  1. (a) 0 ≤ k < 4
    Let u = √x (u ≥ 0): u² − 4u + k = 0 needs two distinct non-negative roots u (M1). Discriminant 16 − 4k > 0 gives k < 4 (A1). Sum of roots 4 > 0 and product k ≥ 0 (k = 0 gives u = 0 or 4, i.e. x = 0 or 16) (M1). 0 ≤ k < 4 (A1).
  2. (b) x = 1 or x = 9
    u² − 4u + 3 = 0, u = 1 or 3 (M1). x = 1 or 9 (A1).
Q24Line-curve intersection · Core · Paper 1 style · 4 marks
  1. (a) Find the coordinates of the points where the line y = x + 1 meets the curve y = x² − 3x + 4. [4]
Show answer
  1. (a) (1, 2) and (3, 4)
    x² − 3x + 4 = x + 1 (M1). x² − 4x + 3 = 0 (A1). x = 1 or 3 (A1). Points (1, 2), (3, 4) (A1).
Q25Line-curve intersection · Standard · Paper 1 style · 6 marks

The line 2x + y = 9 meets the curve x² + xy = 8 at the points A and B.

  1. (a) Find the coordinates of A and B. [4]
  2. (b) Find the exact length of AB. [2]
Show answer
  1. (a) (1, 7) and (8, −7)
    y = 9 − 2x so x² + x(9 − 2x) = 8 (M1). x² − 9x + 8 = 0 (A1). x = 1 or 8 (A1). (1, 7) and (8, −7) (A1).
  2. (b) 7√5
    AB² = 7² + 14² = 245 (M1). AB = √245 = 7√5 (A1).
Q26Line-curve intersection · Standard · Paper 1 style · 6 marks

The curve y = 2x² − 5x + 3 and the line y = 3 − x meet at the points P and Q.

  1. (a) Find the coordinates of P and Q. [3]
  2. (b) Find the equation of the perpendicular bisector of PQ. [3]
Show answer
  1. (a) (0, 3) and (2, 1)
    2x² − 5x + 3 = 3 − x gives 2x² − 4x = 0 (M1). x = 0 or 2 (A1). (0, 3), (2, 1) (A1).
  2. (b) y = x + 1
    Midpoint (1, 2) (B1). Gradient PQ = −1 so perpendicular gradient 1 (M1). y − 2 = x − 1, y = x + 1 (A1).
Q27Line-curve intersection · Challenge · Paper 1 style · 6 marks

The line y = kx − 2 meets the curve y = x² + 2 at two points. The x-coordinate of one point is four times the x-coordinate of the other.

  1. (a) Show that the x-coordinates satisfy x² − kx + 4 = 0. [1]
  2. (b) Find the two possible values of k. [3]
  3. (c) For the positive value of k, find the coordinates of the two points. [2]
Show answer
  1. (a) x² + 2 = kx − 2 gives x² − kx + 4 = 0
    B1.
  2. (b) k = 5 or k = −5
    Roots r and 4r: product 4r² = 4 so r = ±1 (M1 A1). Sum 5r = k, k = ±5 (A1).
  3. (c) (1, 3) and (4, 18)
    x² − 5x + 4 = 0, x = 1 or 4 (M1). (1, 3), (4, 18) (A1).
Q28Line-curve intersection · Challenge · Paper 1 style · 6 marks

The curve C has equation xy = 12.

  1. (a) Find the coordinates of the points where the line x + 2y = 10 meets C. [3]
  2. (b) Find the set of values of the constant c for which the line x + 2y = c meets C at two distinct points. [3]
Show answer
  1. (a) (4, 3) and (6, 2)
    x(10 − x)/2 = 12 (M1). x² − 10x + 24 = 0 (A1). x = 4, y = 3; x = 6, y = 2 (A1).
  2. (b) c < −4√6 or c > 4√6
    x² − cx + 24 = 0 (M1). c² − 96 > 0 (M1). c < −4√6 or c > 4√6 (A1).
Q29Sketching quadratics · Core · Paper 1 style · 5 marks

The curve C has equation y = x² − 2x − 8.

  1. (a) Find the coordinates of the points where C crosses the axes and the coordinates of its vertex. Describe the shape of C. [4]
  2. (b) Hence solve the inequality x² − 2x − 8 < 0. [1]
Show answer
  1. (a) x-axis (−2, 0) and (4, 0); y-axis (0, −8); vertex (1, −9); U-shaped (minimum) parabola
    (x − 4)(x + 2) = 0 (M1), (−2, 0), (4, 0) (A1). (0, −8) (B1). (x − 1)² − 9 gives vertex (1, −9), U-shape since coefficient of x² positive (B1).
  2. (b) −2 < x < 4
    B1: the curve is below the x-axis between the roots.
Q30Sketching quadratics · Standard · Paper 1 style · 6 marks

The curve C has equation y = (3 − x)(x + 1).

  1. (a) Describe a sketch of C, giving the coordinates of the points where it meets the axes and of its turning point. [3]
  2. (b) State the number of real solutions of the equation (3 − x)(x + 1) = k when (i) k = 5, (ii) k = 4, (iii) k = 0. [3]
Show answer
  1. (a) ∩-shaped parabola; meets x-axis at (−1, 0) and (3, 0), y-axis at (0, 3); maximum point (1, 4)
    Roots −1 and 3 and y-intercept 3 (B1). Coefficient of x² is −1 so ∩-shape (B1). Vertex at x = 1, y = 2 × 2 = 4 (B1).
  2. (b) (i) 0 (ii) 1 (iii) 2
    Maximum value 4: line y = 5 above the curve, none (B1); y = 4 touches at the vertex, one (B1); y = 0 cuts twice (B1).

Similar questions

Questions that test the same subtopic in different years, grouped so you can work on one skill at a time.

References only: find each question in its paper (official link where available, otherwise through your school).

Discriminant / tangency Banker18 questions · 9/9 sessions
Completing the square Banker20 questions · 9/9 sessions
Disguised quadratic Banker12 questions · 8/9 sessions
Line-curve intersection 8 questions · 4/9 sessions
Sketching quadratics Rare2 questions · 2/9 sessions

Subtopics

Our analysis of how often each subtopic was examined and how many marks it carried, 2022 to May/June 2026.

SubtopicMarks indexedSessions
Discriminant / tangency Banker719/9
Completing the square Banker589/9
Disguised quadratic Banker408/9
Line-curve intersection 364/9
Sketching quadratics Rare52/9

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