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Cambridge IGCSE Maths: Number — Practice Questions & Answers
Topic 1 is the foundation of IGCSE Mathematics 0580. It covers the full number system from integers to surds: how to classify numbers, find HCF and LCM, work confidently with fractions, decimals and percentages, handle percentage change, simple and compound interest, share quantities in ratio, use direct and inverse proportion, apply the laws of indices, write very large and very small numbers in standard form, simplify surds, find upper and lower bounds, and read set notation. Mastering these skills earns easy marks across every paper and underpins nearly all later topics.
946 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Easy
What is the highest common factor (HCF) of $24$ and $36$?
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Why $24 = 2^{3}\times 3$ and $36 = 2^{2}\times 3^{2}$. The HCF takes the lowest power of each shared prime: $2^{2}\times 3 = 12$.
2
Multiple choice · Easy
Which of these numbers is a prime number?
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Why A prime has exactly two factors, $1$ and itself. $29$ has no factors other than $1$ and $29$, so it is prime.
3
Multiple choice · Easy
Write $\frac{3}{4}$ as a percentage.
$75\%$
$34\%$
$43\%$
$0.75\%$
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Why $\frac{3}{4} = 0.75$, and multiplying by $100$ gives $75\%$.
4
Multiple choice · Easy
Evaluate $2^{5}$.
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Why $2^{5} = 2\times 2\times 2\times 2\times 2 = 32$.
5
Multiple choice · Easy
Round $3.6471$ to $2$ decimal places.
$3.65$
$3.64$
$3.647$
$3.66$
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Why The third decimal digit is $7$, so the second decimal place $4$ rounds up to $5$, giving $3.65$.
6
Multiple choice · Easy
Write $0.0045$ in standard form.
$4.5\times 10^{-3}$
$4.5\times 10^{3}$
$45\times 10^{-4}$
$4.5\times 10^{-2}$
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Why Move the decimal point $3$ places to the right to get $4.5$, so the power is $-3$: $4.5\times 10^{-3}$.
7
Multiple choice · Easy
Increase $80$ by $25\%$.
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Why $25\%$ of $80$ is $20$, so the increased value is $80 + 20 = 100$.
8
Multiple choice · Easy
Share $\$60$ in the ratio $2:3$. What is the larger share?
$\$36$
$\$24$
$\$30$
$\$40$
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Why There are $2+3 = 5$ parts, so one part is $\$12$. The larger share is $3\times 12 = \$36$.
9
Multiple choice · Easy
Round $48\,627$ to $2$ significant figures.
$49\,000$
$48\,000$
$48\,600$
$50\,000$
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Why The first two significant figures are $4$ and $8$. The next digit is $6$, so $8$ rounds up to $9$, giving $49\,000$.
10
Multiple choice · Medium
Find the lowest common multiple (LCM) of $12$ and $18$.
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Why $12 = 2^{2}\times 3$ and $18 = 2\times 3^{2}$. The LCM takes the highest power of each prime: $2^{2}\times 3^{2} = 36$.
Key terms in Number
Natural number: A positive whole number used for counting, such as $1, 2, 3, \ldots$; some definitions include $0$.
Integer: Any whole number, positive, negative, or zero, with no fractional part, such as $-3, 0, 7$.
Rational number: A number that can be written as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$.
Irrational number: A number that cannot be written as an exact fraction, such as $\pi$ or $\sqrt{2}$; its decimal neither terminates nor repeats.
Real number: Any number that can be placed on the number line, including all rational and irrational numbers.
Prime number: A natural number greater than $1$ with exactly two factors, itself and $1$.
Composite number: A natural number greater than $1$ that has more than two factors.
Factor: A whole number that divides exactly into another number with no remainder.
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