IGCSE · Additional Mathematics 0606 · Algebra

Equations, inequalities & graphs: IGCSE Additional Mathematics questions with answers

Free Equations, inequalities & graphs 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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Equations, inequalities & graphs practice questions

Question 1Structured · 3 marks

Solve the equation x23 − 5x13 + 4 = 0.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = 1, x = 64
substitute y = x1/3 M1
y = 1, y = 4 A1
x = 1, x = 64 A1
3
Question 2Structured · 3 marks
(a)

Solve |3x − 7| = 10.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x = 173, x = −1
3x − 7 = 10 M1
x = 173 A1
x = −1 A1
3
Question 3Structured · 3 marks
(a)

State what is meant by the term , the non-negative value of f(x.

[1]
(b)

State what is meant by the term modulus function.

[1]
(c)

State what is meant by the term f(x.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a), the non-negative value of f(x)
, the non-negative value of f(x) B1
1
(b)
B1
1
(c)F(x)
F(x) B1
1
Question 4Structured · 3 marks

Solve the equation x23 − 4x13 + 3 = 0.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = 1, x = 27
substitute y = x1/3 M1
y = 1, y = 3 A1
x = 1, x = 27 A1
3
Question 5Structured · 3 marks
(a)

Solve |2x − 6| = 8.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x = 7, x = −1
2x − 6 = 8 M1
x = 7 A1
x = −1 A1
3
Question 6Structured · 3 marks
(a)

State what is meant by the term modulus function.

[1]
(b)

State what is meant by the term , the non-negative value of f(x.

[1]
(c)

State what is meant by the term f(x.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)
B1
1
(b), the non-negative value of f(x)
, the non-negative value of f(x) B1
1
(c)F(x)
F(x) B1
1

More Algebra questions

FunctionsQuadratic functionsFactors of polynomialsSimultaneous equationsLogarithmic & exponential functions

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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