IGCSE · Mathematics 0580 · Algebra & graphs

Algebraic fractions: IGCSE Mathematics questions with answers

Free Algebraic fractions questions for IGCSE Mathematics (0580), Extended tier (Supplement content), part of Algebra & graphs. Each question has the answer and the marking points an examiner would look for.

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Algebraic fractions practice questions

Question 1Structured · 8 marksA* challenge
(a)

Solve the equation 3x − 1 + 2x + 1 = 2.

[5]
(b)

Simplify fully x2 − 93x2 − 6x − 9.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x = 3 or x = −12
multiply by (x − 1)(x + 1) M1
3(x + 1) + 2(x − 1) = 2(x2 − 1) A1
rearrange to a quadratic = 0 M1
factorise / formula M1
3, −12 A1
5
(b)x + 33(x + 1)
(x − 3)(x + 3) B1
3(x − 3)(x + 1) B1
x + 33(x + 1) B1
3
Question 2Structured · 5 marksA* challenge

Solve the equation
4x + 1 + 3x + 4 = 1.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = −3 or x = 5
4(x + 4) + 3(x + 1) = 1(x + 1)(x + 4) M1
correct expansion M1
x2 − 2x − 15 = 0 A1
correct factorisation or formula M1
−3, 5 A1
5
Question 3Structured · 3 marks

Simplify x2 + 2x − 3x2 − 9.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x − 1x − 3
(x + 3)(x − 1) M1
(x + 3)(x − 3) M1
x − 1x − 3 A1
3
Question 4Structured · 4 marksA* challenge

Simplify fully
x2 + 11x + 302x2 + 11x − 6.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x + 52x − 1
(x + 5)(x + 6) B1
(2x − 1)(x + 6) B2
x + 52x − 1 B1
4
Question 5Structured · 8 marksA* challenge
(a)

Solve the equation 3x − 1 + 3x + 1 = 4.

[5]
(b)

Simplify fully x2 − 43x2 − 3x − 6.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x = 2 or x = −12
multiply by (x − 1)(x + 1) M1
3(x + 1) + 3(x − 1) = 4(x2 − 1) A1
rearrange to a quadratic = 0 M1
factorise / formula M1
2, −12 A1
5
(b)x + 23(x + 1)
(x − 2)(x + 2) B1
3(x − 2)(x + 1) B1
x + 23(x + 1) B1
3
Question 6Structured · 5 marksA* challenge

Solve the equation
3x − 3 + 4x + 2 = 1.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = 0 or x = 8
3(x + 2) + 4(x − 3) = 1(x − 3)(x + 2) M1
correct expansion M1
x2 − 8x = 0 A1
correct factorisation or formula M1
0, 8 A1
5

More Algebra & graphs questions

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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