IGCSE · Mathematics 0580 · Topic

Number: IGCSE Mathematics questions and answers

10 free IGCSE Mathematics Number questions written in the style of Cambridge Mathematics papers, each with its answer and mark scheme. 4 of them are A* challenge questions, built to catch the mistakes strong students still make.

This topic covers Types of number, Sets, Powers & roots, Fractions, decimals & percentages, The four operations, Indices I, Standard form, Estimation, Limits of accuracy, Ratio & proportion, Rates, Percentages, Time, Money, Exponential growth & decay, Surds. Work through the questions below, then generate a full Number paper with a fresh set every time.

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Number sub-topics

Types of numberSetsPowers & rootsFractions, decimals & percentagesThe four operationsIndices IStandard formEstimationLimits of accuracyRatio & proportionRatesPercentagesTimeMoneyExponential growth & decaySurds

Number practice questions

Question 1Structured · 3 marksA* challenge

Solve 9x = 3x + 1 × 3−2.

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

After a 6% increase, a population is 6480. Find the population before the increase.

[2]
(b)

The population continues to grow by 6% each year. Find the number of years until it first exceeds 12960.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)6113.2
6480 ÷ 1.06 M1
6113.2 A1
2
(b)12
method M1
12 A1
2
Question 3Structured · 7 marksA* challenge

The price of a bicycle is increased by 10% and then the new price is reduced by 20% in a sale. The sale price is $440.

(a)

Find the original price.

[3]
(b)

Find the single percentage change from the original price to the sale price.

[2]
(c)

After the sale, the shop wants to return to the original price of $500. Find the percentage increase needed, correct to 1 decimal place.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$500
overall multiplier 1.1 × 0.8 = 0.8800000000000001 M1
440 ÷ 0.88 M1
500 A1
3
(b)12% decrease
multiplier − 1 M1
12% decrease A1
2
(c)13.6%
(500 − 440) ÷ 440 M1
13.6 A1
2
Question 4Structured · 3 marksA* challenge

Tap A can fill a tank in 15 hours. Tap B can fill the same tank in 60 hours.
Both taps are turned on together to fill the empty tank.
How long does it take to fill the tank? Give your answer in hours and minutes.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
12 hours
115 + 160 per hour M1
= 75900 so time = 90075 h A1
12 hours A1
3
Question 5Structured · 3 marks

Without using a calculator, work out 223 ÷ 313.
Show all your working and give your answer as a mixed number in its simplest form.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
45
83 and 103 seen B1
83 × 310 M1
45 A1
3
Question 6Structured · 4 marks
(a)

Work out 32.

[1]
(b)

Write down the value of √169.

[1]
(c)

Write down the value of ∛216.

[1]
(d)

Find the value of 4−3.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)9
9 B1
1
(b)13
13 B1
1
(c)6
6 B1
1
(d)164
164 B1
1
Question 7Structured · 2 marks

By rounding each number to 1 significant figure, estimate the value of
20.8 × 4.830.483
Show your working.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
200
20 × 5 ÷ 0.5 seen M1
200 A1
2
Question 8Structured · 3 marks
(a)

The length of a rectangle is 21 cm, correct to the nearest centimetre. Write down the lower bound of the length.

[1]
(b)

The width is 5 cm, correct to the nearest centimetre. Calculate the upper bound of the area.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)20.5 cm
20.5 B1
1
(b)118.25 cm²
21.5 × 5.5 M1
118.25 A1
2
Question 9Structured · 3 marks

In a sale, all prices are reduced by 24%.
A jacket costs $243.20 in the sale.
Calculate the original price.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
$320.00
243.20 ÷ 0.76 M2
M1 for 243.20 as 76%
320.00 A1
3
Question 10Structured · 3 marks

A small jar of coffee costs $2.59 for 500 g. A large jar costs $4.30 for 1000 g. Which jar is better value? Show your working.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
large jar
price per 100 g (or grams per $) for one jar M1
both values correct A1
large jar is better value A1
3

Other IGCSE Mathematics topics

Algebra & graphsCoordinate geometryGeometryMensurationTrigonometryTransformations & vectorsProbabilityStatistics

Frequently asked questions

What is in IGCSE Mathematics Number?

In the 0580 syllabus, Number covers Types of number, Sets, Powers & roots, Fractions, decimals & percentages, The four operations, Indices I, Standard form, Estimation, Limits of accuracy, Ratio & proportion, Rates, Percentages, Time, Money, Exponential growth & decay, Surds.

Where can I get Number questions with mark schemes?

This page has 10 Number questions with answers. For more, the free generator on mentorriyaz.in builds a new Number paper with a full mark scheme each time you click.

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Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

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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