IGCSE · Additional Mathematics 0606 · Algebra

Quadratic functions: IGCSE Additional Mathematics questions with answers

Free Quadratic functions questions for IGCSE Additional Mathematics (0606), part of Algebra. Each question has the answer and the marking points an examiner would look for.

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Quadratic functions practice questions

Question 1Structured · 4 marksA* challenge

Find the set of values of m for which the line y = mx − 3 does not meet the curve y = x2 + 22.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
−10 < m < 10
x2 − mx + 25 = 0 M1
b2 − 4ac < 0 M1
critical values ±10 A1
−10 < m < 10 A1
4
Question 2Structured · 3 marks

Find the values of k for which the line y = kx + 5 is a tangent to the curve y = x2 + 6.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
k = ±2
x2 − kx + 1 = 0 M1
b2 − 4ac = 0: k2 = 4 M1
k = ±2 A1
3
Question 3Structured · 3 marks
(a)

Solve x2 + 4x − 5 > 0.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x < −5, x > 1
factorise / critical values M1
−5 and 1 A1
x < −5, x > 1 A1
3
Question 4Structured · 8 marks
(a)

Express 2x2 − 8x + 16 in the form a(x + b)2 + c.

[3]
(b)

Hence write down the minimum value of the expression and the value of x at which it occurs.

[2]
(c)

Find the set of values of k for which x2 + kx + 9 = 0 has no real roots.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)2(x − 2)2 + 8
a = 2 B1
b = −2 B1
c = 8 B1
3
(b)minimum 8 at x = 2
8 B1
x = 2 B1
2
(c)−6 < k < 6
k2 − 4(9) < 0 M1
critical values ±6 A1
−6 < k < 6 A1
3
Question 5Structured · 4 marksA* challenge

Find the set of values of m for which the line y = mx − 23 does not meet the curve y = x2 + 2.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
−10 < m < 10
x2 − mx + 25 = 0 M1
b2 − 4ac < 0 M1
critical values ±10 A1
−10 < m < 10 A1
4
Question 6Structured · 3 marks

Find the values of k for which the line y = kx + 3 is a tangent to the curve y = x2 + 12.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
k = ±6
x2 − kx + 9 = 0 M1
b2 − 4ac = 0: k2 = 36 M1
k = ±6 A1
3

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in