IGCSE · Mathematics 0580 · Algebra & graphs

Indices II: IGCSE Mathematics questions with answers

Free Indices II 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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Indices II practice questions

Question 1Structured · 3 marksA* challenge

Solve 4x − 1 = 8x × 2.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = −3
both sides as powers of 2 M1
2(x − 1) = 3(x) + 1 M1
−3 A1
3
Question 2Structured · 5 marks
(a)

Simplify x5 × x6.

[1]
(b)

Simplify (2y5)2.

[2]
(c)

Find the value of 1252/3.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x11
x11 B1
1
(b)4y10
4y10 B2
B1 for one part correct
2
(c)25
∛125 = 5 seen M1
25 A1
2
Question 3Structured · 3 marksA* challenge

Solve 27x − 2 = 9x + 3 × 3−1.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = 11
both sides as powers of 3 M1
3(x − 2) = 2(x + 3) − 1 M1
11 A1
3
Question 4Structured · 5 marks
(a)

Simplify x2 × x5.

[1]
(b)

Simplify (5y2)3.

[2]
(c)

Find the value of 1252/3.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x7
x7 B1
1
(b)125y6
125y6 B2
B1 for one part correct
2
(c)25
∛125 = 5 seen M1
25 A1
2
Question 5Structured · 3 marksA* challenge

Solve 27x − 3 = 3x + 2 × 3.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = 6
both sides as powers of 3 M1
3(x − 3) = x + 2 + 1 M1
6 A1
3
Question 6Structured · 5 marks
(a)

Simplify x5 × x2.

[1]
(b)

Simplify (5y5)3.

[2]
(c)

Find the value of 1252/3.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x7
x7 B1
1
(b)125y15
125y15 B2
B1 for one part correct
2
(c)25
∛125 = 5 seen M1
25 A1
2

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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