IGCSE · Mathematics 0580 · Number

Indices I: IGCSE Mathematics questions with answers

Free Indices I questions for IGCSE Mathematics (0580), part of Number. Each question has the answer and the marking points an examiner would look for.

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Indices I practice questions

Question 1Structured · 9 marksA* challenge

Do not use a calculator in this question.

(a)

Find the last two digits of 72026.

[5]
(b)

Find the last two digits of 32026 + 72026.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)49
72 = 49, 74 = 2401 M1
74 ends in 01, so 74k ends in 01 M1
2026 = 4 × 506 + 2 M1
72026 = (74)506 × 49 M1
last two digits 49 A1
5
(b)78
finds a power of 3 ending in 01 (320) M1
2026 = 20 × 101 + 6 M1
32026 ends in 29 (36 = 729) A1
29 + 49 = 78 A1
4
Question 2Structured · 3 marksA* challenge

Solve 4x + 1 = 2x + 2 × 22.

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

Simplify x3 × x2.

[1]
(b)

Simplify (5y3)3.

[2]
(c)

Find the value of 27−1/3.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x5
x5 B1
1
(b)125y9
125y9 B2
B1 for one part correct
2
(c)13
∛27 = 3 seen M1
13 A1
2
Question 4Structured · 3 marksA* challenge

Solve 3x + 2 = 9x + 3 × 33.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = −7
both sides as powers of 3 M1
1(x + 2) = 2(x + 3) + 3 M1
−7 A1
3
Question 5Structured · 5 marks
(a)

Simplify x3 × x5.

[1]
(b)

Simplify (2y3)2.

[2]
(c)

Find the value of 64−2/3.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)x8
x8 B1
1
(b)4y6
4y6 B2
B1 for one part correct
2
(c)116
∛64 = 4 seen M1
116 A1
2
Question 6Structured · 3 marksA* challenge

Solve 27x = 3x − 1 × 3−1.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x = −1
both sides as powers of 3 M1
3(x) = x − 1 − 1 M1
−1 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