Cambridge IGCSE Maths (0580) · Revision notes · Topic 1 of 9

Cambridge IGCSE Maths 0580 Number Notes

Revision notes for topic 1, Number, of the Cambridge IGCSE Mathematics (0580) syllabus for exams in 2025, 2026 and 2027. Each of the 18 sub-topics lists what the syllabus asks, marked Core or Extended, with a short explanation and a worked example. Cover the answer and try each example first.

18 sub-topics
16 Core and Extended
2 Extended only
5 with notes written for 0580

Core Core students (Papers 1 and 3) learn the Core statements. Extended Extended students (Papers 2 and 4) learn everything: the Core statements, the Extended additions and the Extended-only sub-topics. Papers 1 and 2 are non-calculator.

1.1 Types of number

Core C1.1 Extended E1.1

Natural numbers, integers (positive, zero and negative), prime numbers, square and cube numbers
Factors, multiples, common factors and common multiples, HCF and LCM
Rational and irrational numbers, reciprocals

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

‘Prime factor decomposition’ means writing a number as a product of prime numbers using powers.

Example: Express 120 as a product of its prime factors.

Answer: 120 = 2³ × 3 × 5.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 3 marks):

Here is a list of numbers: $4, \ 9, \ 11, \ 15, \ 27, \ 31, \ 36$

From the list, write down

(a) the prime numbers (b) the square numbers (c) a cube number.

Show the answer and mark scheme

B1 (a) 11 and 31
B1 (b) 4, 9 and 36
B1 (c) 27

Answer: (a) $11, 31$ (b) $4, 9, 36$ (c) $27$

Practice question (Core, calculator, 2 marks):

Find the highest common factor (HCF) of 28 and 42.

Show the answer and mark scheme

M1 lists factors or writes 28 = 2² × 7 and 42 = 2 × 3 × 7
A1 14

Answer: $14$

Edexcel 4MA1 notes: Prime Factor Decomposition
Practise (4MA1 questions, same mathematics): HCF, LCM and Prime Factors questions

1.2 Sets

Core C1.2 Extended E1.2

Set notation n(A), the universal set, the complement A′, union A ∪ B and intersection A ∩ B
Venn diagrams with two sets to describe sets and solve problems

Extended also: The symbols ∈, ∉, ∅, ⊆ and ⊈, and set-builder notation such as {(x, y): y = mx + c}; Venn diagrams with two or three sets.

Same mathematics as Edexcel 4MA1.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

ℰ $= \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$, $A = \{\text{multiples of } 2\}$ and $B = \{\text{multiples of } 3\}$.

List the members of

(a) $A \cap B$ (b) $A \cup B$

Show the answer and mark scheme

B1 (a) {6, 12}
B1 (b) {2, 3, 4, 6, 8, 9, 10, 12}

Answer: (a) $\{6, 12\}$ (b) $\{2, 3, 4, 6, 8, 9, 10, 12\}$

Practice question (Core, non-calculator, 2 marks):

ℰ $= \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$ and $A = \{\text{even numbers}\}$.

(a) Find $n(A)$.

(b) List the members of $A'$.

Show the answer and mark scheme

B1 (a) 6
B1 (b) {1, 3, 5, 7, 9, 11}

Answer: (a) $6$ (b) $\{1, 3, 5, 7, 9, 11\}$

Edexcel 4MA1 notes: Statistics and Probability (all notes)
Practise (4MA1 questions, same mathematics): Sets and Venn Diagrams questions

1.3 Powers and roots

Core C1.3 Extended E1.3

Squares, square roots, cubes, cube roots and other powers and roots of numbers

Same mathematics as Edexcel 4MA1.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 3 marks):

Work out

(a) $7^2$ (b) $\sqrt{81}$ (c) $4^3$

Show the answer and mark scheme

B1 (a) 49
B1 (b) 9
B1 (c) 64

Answer: (a) $49$ (b) $9$ (c) $64$

Practice question (Core, non-calculator, 2 marks):

Work out $\sqrt[3]{125} + \sqrt{36}$.

Show the answer and mark scheme

M1 5 or 6 seen
A1 11

Answer: $11$

Edexcel 4MA1 notes: Laws of Indices
Practise (4MA1 questions, same mathematics): HCF, LCM and Prime Factors questions · Indices and Standard Form questions

1.4 Fractions, decimals and percentages

Core C1.4 Extended E1.4

Equivalent fractions, decimals and percentages, and converting between them

Extended also: Convert recurring decimals to fractions.

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

Mixed numbers are whole + fraction (e.g. 1¾). Convert to improper fractions first when adding, subtracting, multiplying or dividing.

Example: Work out 1¾ + 2⅔ as a mixed number.

Answer: = 7/4 + 8/3 = 21/12 + 32/12 = 53/12 = 4 5/12.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Write $\frac{5}{8}$ as

(a) a decimal (b) a percentage.

Show the answer and mark scheme

B1 (a) 0.625
B1 (b) 62.5%

Answer: (a) $0.625$ (b) $62.5\%$

Practice question (Core, non-calculator, 2 marks):

Write $0.45$ as a fraction in its simplest form.

Show the answer and mark scheme

M1 45/100
A1 9/20

Answer: $\frac{9}{20}$

Edexcel 4MA1 notes: Fraction Arithmetic
Practise (4MA1 questions, same mathematics): Fractions and Decimals questions · Recurring Decimals questions

1.5 Ordering

Core C1.5 Extended E1.5

Order quantities by magnitude (integers, decimals, fractions, percentages)
Use the symbols =, ≠, >, <, ≥ and ≤

Partly in Edexcel 4MA1: No 4MA1 lesson on ordering mixed fractions, decimals and percentages; the symbols appear only inside inequalities.

Notes for 0580

To order numbers written in different forms, change them all to decimals (to enough places to tell them apart), put the decimals in order, then write the answer using the numbers as they were given.

With negative numbers, the further below zero, the smaller the number: −7 is less than −2. Read < as 'is less than', > as 'is greater than', ≤ and ≥ as 'less than or equal to' and 'greater than or equal to', and ≠ as 'is not equal to'.

Example (Core, non-calculator): Write these in order of size, smallest first: 0.65, 5/8, 63%, 2/3.

5/8 = 0.625
63% = 0.63
2/3 = 0.666…
In order: 0.625, 0.63, 0.65, 0.666…

Answer: 5/8, 63%, 0.65, 2/3

Example (Core, non-calculator): Write < or > between each pair: (a) −4 and −9 (b) 0.3 and 1/3.

(a) −4 is nearer to zero than −9, so it is larger.
(b) 1/3 = 0.333…, which is more than 0.3.

Answer: (a) −4 > −9 (b) 0.3 < 1/3

0580 practice questions

12 questions written for 0580 in the Number practice: 12 Core, all non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Write these numbers in order of size, starting with the smallest: $0.3, \quad \frac{1}{4}, \quad 28\%, \quad 0.27$

Show the answer and mark scheme

M1 converts all four to decimals (0.3, 0.25, 0.28, 0.27) or to percentages
A1 1/4, 0.27, 28%, 0.3 cao

Answer: $\frac{1}{4},\ 0.27,\ 28\%,\ 0.3$

Practice question (Core, non-calculator, 3 marks):

Write these numbers in order of size, starting with the smallest. Use the symbols $\lt$ and $=$ in your answer.

$\frac{3}{8}, \quad 0.4, \quad 35\%, \quad 0.37, \quad \frac{2}{5}$

Show the answer and mark scheme

M1 converts to a common form, e.g. 0.375, 0.4, 0.35, 0.37, 0.4
A1 $35\% \lt 0.37 \lt \frac{3}{8} \lt 0.4$ order correct
B1 shows 0.4 = 2/5

Answer: $35\% \lt 0.37 \lt \frac{3}{8} \lt 0.4 = \frac{2}{5}$

Practise the shared part (4MA1 questions): Fractions and Decimals questions · Inequalities questions

1.6 The four operations

Core C1.6 Extended E1.6

The four operations with integers, fractions and decimals, including the order of operations and brackets

Same mathematics as Edexcel 4MA1.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Work out $3 + 4 \times 5 - 6 \div 2$.

Show the answer and mark scheme

M1 20 and 3 seen
A1 20

Answer: $20$

Practice question (Core, non-calculator, 2 marks):

Work out $\frac{2}{3} + \frac{1}{4}$.

Show the answer and mark scheme

M1 8/12 + 3/12
A1 11/12

Answer: $\frac{11}{12}$

Edexcel 4MA1 notes: Fraction Arithmetic
Practise (4MA1 questions, same mathematics): Fractions and Decimals questions

1.7 Indices I

Core C1.7 Extended E1.7

Positive, zero and negative integer indices and the laws of indices

Extended also: Fractional indices.

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

Laws of indices tell you how to multiply, divide and raise powers to other powers.

Example: Simplify ((x⁴)³ × x⁻⁵) ÷ x².

Answer: = x¹² × x⁻⁵ ÷ x² = x⁷ ÷ x² = x⁵.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Work out

(a) $5^0$ (b) $2^{-3}$

Show the answer and mark scheme

B1 (a) 1
B1 (b) 1/8

Answer: (a) $1$ (b) $\frac{1}{8}$

Practice question (Core, non-calculator, 2 marks):

Write each answer as a single power.

(a) $3^4 \times 3^5$ (b) $7^8 \div 7^3$

Show the answer and mark scheme

B1 (a) 3⁹
B1 (b) 7⁵

Answer: (a) $3^9$ (b) $7^5$

Edexcel 4MA1 notes: Laws of Indices
Practise (4MA1 questions, same mathematics): Indices and Standard Form questions

1.8 Standard form

Core C1.8 Extended E1.8

Write numbers in standard form A × 10ⁿ (1 ≤ A < 10) and convert back
Calculate with numbers in standard form

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

Standard form writes a number as A × 10ⁿ where 1 ≤ A < 10.

Example: Write 0.00000384 in standard form.

Answer: = 3.84 × 10⁻⁶.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Write these numbers in standard form.

(a) $45\,000$ (b) $0.0062$

Show the answer and mark scheme

B1 (a) 4.5 × 10⁴
B1 (b) 6.2 × 10⁻³

Answer: (a) $4.5 \times 10^{4}$ (b) $6.2 \times 10^{-3}$

Practice question (Core, non-calculator, 2 marks):

Write these as ordinary numbers.

(a) $3.07 \times 10^{5}$ (b) $8 \times 10^{-4}$

Show the answer and mark scheme

B1 (a) 307 000
B1 (b) 0.0008

Answer: (a) $307\,000$ (b) $0.0008$

Edexcel 4MA1 notes: Standard Form
Practise (4MA1 questions, same mathematics): Indices and Standard Form questions

1.9 Estimation

Core C1.9 Extended E1.9

Round to a given number of decimal places or significant figures
Estimate calculations by rounding each number, and round answers sensibly in context

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

‘Significant figures’ (s.f.) count from the first non-zero digit. Rounding to 3 s.f. means keeping the three most important digits.

Example: Use your calculator to evaluate (4.72 × 18.9) ÷ (3.14 − 1.09). Round to 3 s.f.

Answer: Full answer 43.51..., so to 3 s.f. → 43.5.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Write $0.047362$ correct to

(a) 2 decimal places (b) 3 significant figures.

Show the answer and mark scheme

B1 (a) 0.05
B1 (b) 0.0474

Answer: (a) $0.05$ (b) $0.0474$

Practice question (Core, calculator, 2 marks):

Write $38\,452$ correct to

(a) the nearest hundred (b) 2 significant figures.

Show the answer and mark scheme

B1 (a) 38 500
B1 (b) 38 000

Answer: (a) $38\,500$ (b) $38\,000$

Edexcel 4MA1 notes: Rounding & Calculator Skills
Practise (4MA1 questions, same mathematics): Rounding and Bounds questions

1.10 Limits of accuracy

Core C1.10 Extended E1.10

Upper and lower bounds of values rounded to a given accuracy

Extended also: Upper and lower bounds of the results of calculations.

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

A rounded measurement has a lower and upper bound — the range of true values it could really be.

Example: A piece of wood is 2.4 m to the nearest cm. Find the bounds.

Answer: Lower 2.395 m · Upper 2.405 m.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

The length of a pencil is 12 cm, correct to the nearest centimetre. Write down the lower bound and the upper bound of the length.

Show the answer and mark scheme

B1 11.5
B1 12.5

Answer: lower bound $11.5$ cm, upper bound $12.5$ cm

Practice question (Core, non-calculator, 2 marks):

The mass of a bag is 3.4 kg, correct to 1 decimal place. Write down the lower bound and the upper bound of the mass.

Show the answer and mark scheme

B1 3.35
B1 3.45

Answer: lower bound $3.35$ kg, upper bound $3.45$ kg

Edexcel 4MA1 notes: Upper & Lower Bounds
Practise (4MA1 questions, same mathematics): Rounding and Bounds questions

1.11 Ratio and proportion

Core C1.11 Extended E1.11

Ratios in simplest form, dividing a quantity in a given ratio, proportional reasoning in context

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

A ratio shares a quantity into parts. To split £X in the ratio a:b:c, work out one part (£X ÷ (a+b+c)) then multiply.

Example: Divide £240 in the ratio 3:5:4.

Answer: 12 parts total → 1 part = £20 → £60 : £100 : £80.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Write each ratio in its simplest form.

(a) $24 : 36$ (b) $1.5\text{ kg} : 600\text{ g}$

Show the answer and mark scheme

B1 (a) 2 : 3
B1 (b) 5 : 2

Answer: (a) $2 : 3$ (b) $5 : 2$

Practice question (Core, non-calculator, 2 marks):

Share $\$45$ in the ratio $4 : 5$.

Show the answer and mark scheme

M1 45 ÷ 9 = 5
A1 20 and 25

Answer: $\$20$ and $\$25$

Edexcel 4MA1 notes: Ratio & Proportion
Practise (4MA1 questions, same mathematics): Ratio questions

1.12 Rates

Core C1.12 Extended E1.12

Common measures of rate, and other rates such as density, pressure and population density
Average speed

Extended also: Convert between units, including units of rate.

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

Compound measures combine two quantities: e.g. speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area.

Example: A cyclist travels at 18 km/h for 1 h 45 min. Distance?

Answer: 1.75 × 18 = 31.5 km.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

A car travels 150 km in 2.5 hours. Work out its average speed.

Show the answer and mark scheme

M1 150 ÷ 2.5
A1 60 km/h

Answer: $60$ km/h

Practice question (Core, non-calculator, 2 marks):

A metal block has a mass of 240 g and a volume of $30\text{ cm}^3$. Work out its density.

Show the answer and mark scheme

M1 240 ÷ 30
A1 8 g/cm³

Answer: $8\text{ g/cm}^3$

Edexcel 4MA1 notes: Compound Measures · Area & Volume Conversions
Practise (4MA1 questions, same mathematics): Units and Compound Measures questions

1.13 Percentages

Core C1.13 Extended E1.13

A percentage of a quantity; one quantity as a percentage of another
Percentage increase and decrease
Simple and compound interest

Extended also: Reverse percentages (finding the original amount).

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

A percentage multiplier turns ‘×20% increase’ into a single number (1.20). Compound interest uses the multiplier once per year.

Example: £4000 invested at 3.5% compound interest for 3 years — total value?

Answer: 4000 × 1.035³ = £4434.87.

0580 practice questions

6 questions written for 0580 in the Number practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Find $15\%$ of $\$60$.

Show the answer and mark scheme

M1 0.15 × 60 or 10% = 6 and 5% = 3
A1 9

Answer: $\$9$

Practice question (Core, non-calculator, 2 marks):

Write 18 as a percentage of 72.

Show the answer and mark scheme

M1 18/72 × 100
A1 25%

Answer: $25\%$

Edexcel 4MA1 notes: Percentages & Compound Measures
Practise (4MA1 questions, same mathematics): Percentages questions

1.14 Using a calculator

Core C1.14 Extended E1.14

Use a scientific calculator efficiently, enter values correctly and interpret the display

Partly in Edexcel 4MA1: 4MA1 practises calculator use only inside rounding; nothing on reading displays such as 3.2E-4 or entering nested fractions and roots.

Notes for 0580

Type a calculation exactly as it is written, putting brackets around every numerator, denominator and square root that holds more than one term (or use the fraction key and the root key, which keep them together).

Write down the full calculator display before you round, then round as the question asks: 3 significant figures unless it says otherwise. A display such as 4.7E−3 or 4.7 × 10⁻³ is standard form, so it means 0.0047. A quick estimate with rounded numbers catches most keying mistakes.

Example (Core, calculator): Use your calculator to work out √(13.6² − 6.4²) ÷ (2.5 × 1.8). Write down all the figures on your display, then give the answer to 3 significant figures.

13.6² − 6.4² = 184.96 − 40.96 = 144, so the square root is 12.
2.5 × 1.8 = 4.5
12 ÷ 4.5 = 2.666666667 on the display

Answer: 2.666666667, which is 2.67 to 3 significant figures

Example (Core, calculator): A calculator display shows 4.7E−3. Write this as an ordinary number.

4.7E−3 means 4.7 × 10⁻³: move the decimal point 3 places to the left.

Answer: 0.0047

0580 practice questions

12 questions written for 0580 in the Number practice: 12 Core, all calculator (Papers 3 and 4), each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, calculator, 2 marks):

Use your calculator to work out $3.7^2 + \sqrt{19.36}$.

Show the answer and mark scheme

M1 13.69 or 4.4 seen
A1 18.09 cao

Answer: $18.09$

Practice question (Core, calculator, 3 marks):

Mia wants to work out $\dfrac{24.6}{3.2 \times 1.5}$. She keys 24.6 ÷ 3.2 × 1.5 = into her calculator.

(a) Work out the correct value.

(b) Work out the value Mia's calculator gives, correct to 3 significant figures.

Show the answer and mark scheme

B1 (a) 5.125
B1 (b) 11.5 (11.53125)
B1 (c) brackets round 3.2 × 1.5, e.g. 24.6 ÷ (3.2 × 1.5), or 24.6 ÷ 3.2 ÷ 1.5

Answer: (a) $5.125$ (b) $11.5$ (c) $24.6 \div (3.2 \times 1.5)$

Edexcel 4MA1 notes: Rounding & Calculator Skills
Practise the shared part (4MA1 questions): Rounding and Bounds questions

1.15 Time

Core C1.15 Extended E1.15

Calculate with time: seconds, minutes, hours, days, weeks, months and years (1 year = 365 days)
12-hour and 24-hour clock times (24-hour times written as 15 15), clocks, timetables, time zones and time differences

New for 0580: not in Edexcel 4MA1: Not taught in 4MA1 Higher (time is assumed knowledge there).

Notes for 0580

There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and 365 days in a year. Cambridge writes 24-hour times as four digits with a space: 3.15 p.m. is 15 15 (not 15:15). The day runs from 00 00 (midnight) to 23 59.

From 1.00 p.m. to 11.59 p.m., add 12 to the hour (7.25 p.m. is 19 25). From 12.00 noon to 12.59 p.m., keep the hour (12.30 p.m. is 12 30). From midnight to 12.59 a.m., the hour is 00 (12.40 a.m. is 00 40). Other a.m. times just gain a leading zero (9.05 a.m. is 09 05).

To find how long something takes, count on in steps: up to the next whole hour, then the whole hours, then the minutes left. A decimal part of an hour is not a number of minutes: 0.4 hours is 0.4 × 60 = 24 minutes. For journeys across time zones, add or subtract the time difference to change a local time into the other place's local time.

Example (Core, non-calculator): A train leaves at 21 47 and arrives at 02 15 the next day. How long is the journey?

21 47 to 22 00 is 13 minutes.
22 00 to 02 00 is 4 hours.
02 00 to 02 15 is 15 minutes.
13 + 15 = 28 minutes.

Answer: 4 hours 28 minutes

Example (Core, non-calculator): Write 3.4 hours in hours and minutes.

0.4 hours = 0.4 × 60 = 24 minutes.

Answer: 3 hours 24 minutes

Example (Core, non-calculator): The first bus leaves at 07 50 and then one leaves every 25 minutes. Kim reaches the stop at 09 10. How long does she wait for the next bus?

Buses leave at 07 50, 08 15, 08 40, 09 05, 09 30, …
The first one after 09 10 is at 09 30.

Answer: 20 minutes

0580 practice questions

12 questions written for 0580 in the Number practice: 12 Core, 8 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 1 mark):

Write 7.45 pm as a time on the 24-hour clock.

Show the answer and mark scheme

B1 19 45 cao

Answer: 19 45

Practice question (Core, non-calculator, 4 marks):

Part of a train timetable is shown.

\[\begin{array}{l|ccc} & \text{Train 1} & \text{Train 2} & \text{Train 3} \\ \hline \text{Ashford} & 13\ 25 & 14\ 10 & 15\ 05 \\ \text{Beckton} & 13\ 52 & 14\ 37 & 15\ 32 \\ \text{Carlow} & 14\ 18 & 15\ 03 & 15\ 58 \\ \text{Denby} & 14\ 46 & 15\ 31 & 16\ 26 \end{array}\]

(a) How long does Train 2 take to travel from Ashford to Denby?

(b) Leah arrives at Beckton station at 14 20. She must be in Denby by 16 00. Which train should she catch, and how many minutes does she wait at Beckton?

Show the answer and mark scheme

M1 (a) 14 10 to 15 31
A1 (a) 1 hour 21 minutes
B1 (b) Train 2
B1 (b) 17 minutes

Answer: (a) 1 hour 21 minutes (b) Train 2, waiting 17 minutes

1.16 Money

Core C1.16 Extended E1.16

Calculate with money
Convert from one currency to another

Partly in Edexcel 4MA1: 4MA1 covers exchange rates and best buys; household money problems (bills, wages, profit) are not practised.

Notes for 0580

Work in one unit throughout (all in dollars, or all in cents) and write money to 2 decimal places: $4.50, not $4.5.

An exchange rate is a multiplier. If £1 = $1.27, change pounds to dollars by multiplying by 1.27 and dollars to pounds by dividing by 1.27. Check the answer is sensible: there should be more dollars than pounds.

Example (Core, calculator): £1 = $1.27. (a) Change £350 to dollars. (b) Change $500 to pounds, giving your answer to the nearest penny.

(a) 350 × 1.27 = 444.5
(b) 500 ÷ 1.27 = 393.700…

Answer: (a) $444.50 (b) £393.70

Example (Core, calculator): Sam is paid $14.80 an hour for the first 37.5 hours of a week and 1.5 times that rate for every hour after that. One week he works 42 hours. How much is he paid?

Normal pay: 37.5 × 14.80 = $555
Overtime: 42 − 37.5 = 4.5 hours at 1.5 × 14.80 = $22.20 an hour
4.5 × 22.20 = $99.90
555 + 99.90 = 654.90

Answer: $654.90

0580 practice questions

12 questions written for 0580 in the Number practice: 12 Core, 6 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Ravi buys 3 notebooks costing $\$2.45$ each and a pen costing $\$1.30$. He pays with a $\$10$ note. How much change does he get?

Show the answer and mark scheme

M1 3 × 2.45 + 1.30 (= 8.65)
A1 1.35 cao

Answer: $\$1.35$

Practice question (Core, non-calculator, 3 marks):

Priya changes $\$500$ into euros when $1$ euro $= \$1.25$. She spends 310 euros on holiday. She changes the euros she has left back into dollars when $1$ euro $= \$1.20$. How many dollars does she get back?

Show the answer and mark scheme

M1 500 ÷ 1.25 (= 400 euros)
M1 (their 400 − 310) × 1.20
A1 108 cao

Answer: $\$108$

Practise the shared part (4MA1 questions): Exchange Rates and Best Buys questions

1.17 Exponential growth and decay

Extended only E1.17

Extended: Exponential growth and decay in context, e.g. depreciation and population change, using the multiplier and repeated multiplication (knowledge of e is not required).

Partly in Edexcel 4MA1: 4MA1 practises compound interest and depreciation; growth and decay of populations, and finding when a value passes a limit, are not practised.

Notes for 0580

When a quantity grows by r% in each time period, multiply by (1 + r/100) once for each period; when it decays by r%, multiply by (1 − r/100). After n periods, amount = starting amount × multiplierⁿ.

To find when an amount first passes a target, work out the amount after 1, 2, 3, … periods (keep multiplying by the multiplier on your calculator) until it first passes the target.

Example (Extended, calculator): A town has a population of 12 000. It grows by 3% each year. Find the population after 5 years. Give your answer to the nearest whole number.

Multiplier = 1 + 3/100 = 1.03
12 000 × 1.03⁵ = 13 911.28…

Answer: 13 911 people

Example (Extended, calculator): A car is worth $18 000. It loses 15% of its value each year. (a) Find its value after 3 years. (b) After how many whole years is it first worth less than half of $18 000?

Multiplier = 1 − 0.15 = 0.85
(a) 18 000 × 0.85³ = 11 054.25
(b) Half of 18 000 is 9000. After 4 years: 18 000 × 0.85⁴ = 9396.11 (more than 9000). After 5 years: 18 000 × 0.85⁵ = 7986.70 (less than 9000).

Answer: (a) $11 054.25 (b) 5 years

0580 practice questions

14 questions written for 0580 in the Number practice: 14 Extended, 4 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Extended, non-calculator, 2 marks):

A population of bacteria doubles every hour. At first there are 300 bacteria. How many bacteria are there after 4 hours?

Show the answer and mark scheme

M1 300 × 2⁴ or 300 × 2 × 2 × 2 × 2
A1 4800 cao

Answer: $4800$

Practice question (Extended, calculator, 3 marks):

The population of a city $t$ years after 2020 is modelled by $P = 2400 \times 1.035^{t}$ (in thousands).

(a) Write down the percentage increase each year.

(b) Find the population when $t = 10$. Give your answer in thousands, correct to 3 significant figures.

Show the answer and mark scheme

B1 (a) 3.5%
M1 (b) 2400 × 1.035¹⁰
A1 (b) 3390 (3385.4…)

Answer: (a) $3.5\%$ (b) $3390$ thousand

Edexcel 4MA1 notes: Percentages & Compound Measures
Practise the shared part (4MA1 questions): Percentages questions

1.18 Surds

Extended only E1.18

Extended: Simplify expressions with surds and rationalise the denominator.

Same mathematics as Edexcel 4MA1.

Revise it

A surd is a root that can't simplify to an integer (e.g. √2). Rationalising means removing surds from a fraction's denominator.

Example: Simplify √48.

Answer: = √(16 × 3) = 4√3.

Edexcel 4MA1 notes: Surd Operations
Practise (4MA1 questions, same mathematics): Surds questions

Practise number

134 practice questions are written for 0580 on 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17. For the 13 sub-topics that are the same mathematics in Edexcel 4MA1, the practice also has our 4MA1 Higher questions, which are Extended level. Core students: use the Core filter on the practice page; every sub-topic with Core content has questions written for 0580 Core. Practice is part of the IGCSE plan, with a free preview; these notes are free.

Number practice for 0580: the 134 questions written for 0580, tagged Core or Extended and non-calculator or calculator, with the Edexcel 4MA1 Higher questions for the sub-topics that are the same mathematics
Student hub: the Edexcel 4MA1 units (Unit 1, Unit 2, Unit 3, Unit 4, Unit 6), each question marked
Cambridge IGCSE Maths 0580 past papers: the 2025 specimen papers and past papers, with a timer
IGCSE Maths questions by topic with worked answers