IGCSE · Mathematics 0580 · Algebra & graphs

Linear equations: IGCSE Mathematics questions with answers

Free Linear equations questions for IGCSE Mathematics (0580), part of Algebra & graphs. Each question has the answer and the marking points an examiner would look for.

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Linear equations practice questions

Question 1Structured · 3 marksA* challenge

The angles of a quadrilateral are (x + 14)°, (2x − 1)°, (3x + 5)° and 114°.
Find the size of the largest angle.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
119°
sum of angles = 360 M1
6x + 132 = 360, x = 38 A1
119 A1
3
Question 2Structured · 3 marks

Solve x + 10 = 6x − 50.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = 12
−5x = −60 M2
M1 for collecting x terms or number terms correctly
12 A1
3
Question 3Structured · 3 marksA* challenge

The angles of a quadrilateral are (x + 28)°, (2x + 16)°, (3x − 1)° and 77°.
Find the size of the largest angle.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
119°
sum of angles = 360 M1
6x + 120 = 360, x = 40 A1
119 A1
3
Question 4Structured · 3 marks

Solve 3x − 9 = −x − 33.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = −6
4x = −24 M2
M1 for collecting x terms or number terms correctly
−6 A1
3
Question 5Structured · 3 marksA* challenge

The angles of a quadrilateral are (x + 7)°, (2x + 1)°, (3x + 8)° and 116°.
Find the size of the largest angle.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
122°
sum of angles = 360 M1
6x + 132 = 360, x = 38 A1
122 A1
3
Question 6Structured · 3 marks

Solve 3x + 4 = 6x − 29.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = 11
−3x = −33 M2
M1 for collecting x terms or number terms correctly
11 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