What does 'Applying Number' mean in the context of Edexcel IGCSE Mathematics?

'Applying Number' in Edexcel IGCSE Mathematics refers to the practical use of numerical skills to solve real-world problems. This includes understanding and manipulating numbers, performing calculations, and interpreting numerical data in various contexts such as finance, measurement, and statistics.

How can I improve my skills in applying number for the Edexcel IGCSE exam?

To improve your skills in applying number, practice solving a variety of problems that require numerical calculations. Focus on understanding the underlying concepts of arithmetic operations, percentages, ratios, and proportions. Utilize past exam papers and online resources to familiarize yourself with the types of questions that may appear in the exam.

What types of problems are included under 'Applying Number' in the IGCSE syllabus?

The 'Applying Number' section in the IGCSE syllabus includes problems related to arithmetic operations, percentages, ratios, proportions, and real-life applications such as currency conversion, budgeting, and interpreting data from charts and graphs. These problems test your ability to apply mathematical concepts to everyday situations.

Why is it important to learn about 'Applying Number' in Mathematics?

Learning about 'Applying Number' is crucial as it equips students with essential skills needed for everyday life. It helps in making informed decisions, managing finances, and solving practical problems efficiently. These skills are not only vital for academic success but also for personal and professional life.

What resources are available for practicing 'Applying Number' in Edexcel IGCSE Mathematics?

There are numerous resources available for practicing 'Applying Number' in Edexcel IGCSE Mathematics. These include textbooks specifically designed for the IGCSE curriculum, online platforms offering interactive exercises, past exam papers, and educational websites that provide practice questions and detailed solutions. Utilizing a mix of these resources can help reinforce your understanding and application of numerical concepts.

Why is "Forgetting to convert units (g vs kg, ml vs L, p vs £)" a common mistake in Applying Number?

Why it happens: Rushing. How to avoid it: Always check units BEFORE calculating. Convert to one consistent unit. Show '1.5 kg = 1500g' as a working step.

Why is "Treating time as base-10 (e.g. $1.5$ hours $= 1$ hour $50$ minutes)" a common mistake in Applying Number?

Why it happens: Decimal habits. How to avoid it: 1.5 hours = 1 hour 30 min (0.5 × 60 = 30). Time uses base 60.

Why is "Multiplying when you should divide for currency conversion" a common mistake in Applying Number?

Why it happens: Easy to confuse. How to avoid it: Test with one unit: '£1 = \1.25. So £10 should be more than \10. So multiply.' Reverse: \$10 → divide.

Why is "Charging the fixed rate AND the per-unit rate for the first unit (double counting)" a common mistake in Applying Number?

Why it happens: Misreading the question. How to avoid it: READ CAREFULLY. 'First km £3.50, additional km £1.20' means 3.50 FOR THAT FIRST km. Additional is 13 km, not 14. Source: 4MA1/2H May/Jun 2024 — examiner report Q3

Edexcel IGCSE Mathematics (4MA1)

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Short Notes - Applying Number

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Detailed Study Notes

Detailed notes on Numbers and the Number System for Edexcel IGCSE Mathematics, covering key concepts, explanations, examples, and exam-focused revision points.

Applying Number Study Notes — Edexcel IGCSE 4MA1 Higher Tier (2026 onwards)

Real-world number problems: money, time, units, rates and tariffs. Crucial for Paper 2H — and for life beyond exams.

At a glance

Tariffs: fixed charge + (rate × units).
Best buy: lowest unit price wins.
Currency: rate as multiplier; reverse with division.
Time: base 60 (not 100). $0.5$ h $= 30$ min.
Units: convert to consistent before calculating.
Speed-distance-time: $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ .

What you’ll learn

Mapped to the Pearson Edexcel IGCSE 4MA1 syllabus (2026 onwards).

1.12 — Solve real-life problems involving money, time, units and rates.
1.12 — Calculate best buys, taxi fares, currency conversions.
1.12 — Use speed-distance-time formula.

Tariffs and rates

Many bills follow: fixed charge + per-unit rate × units used.

Tariff structure.

Total cost = fixed charge + (rate × units used)

Examples:

Taxi: £ $3.50$ initial + £ $1.20$ /km. For $14$ km: $3.50 + 1.20 \times 13 = £19.10$ (note: $13$ additional, not $14$ ).
Electricity: £ $15$ standing charge + $20$ p/kWh. For $300$ kWh: $15 + 0.20 \times 300 = £75$ .
Gym: £ $25$ /month + £ $5$ /visit. For $8$ visits in a month: $25 + 5 \times 8 = £65$ .

Read carefully. Phrases like 'first $X$ included', 'additional $Y$ ' affect counting.

Worked qualitative. A water bill: £ $30$ standing charge + $0.20$ p/litre after the first $1000$ litres. Cost for $1500$ litres?

First $1000$ litres included in standing charge.
Additional $500$ litres at $0.20$ p each: $500 \times 0.20 = £100$ .
Total: $30 + 100 = £130$ .

Edexcel tip. Underline key numbers in the question. Identify: fixed cost, rate, units used. Compute step by step.

Total = fixed + rate × units.
Read 'first X' and 'additional Y' carefully.
Show working step by step.

Currency and units

Multiply for one direction, divide for the other. Always identify the direction.

Currency conversion.

If £ $1 = \$ 1.25$:

£ → $\$$: multiply by$ 1.25$.
$\$$ → £: divide by$ 1.25$.

Worked example. Convert £ $240$ to USD, then $\$$$ 400$ back to GBP.

£ $240 \times 1.25 = \$ 300$.
$\$$$ 400 / 1.25 = £320$.

Sense check. £ $1$ buys $\$ 1.25 $(more than$ 1 $). So £ →$ $$ should give a BIGGER number. Multiply confirms.

Unit conversions.

Memorise:

$1$ km = $1000$ m. $1$ m = $100$ cm. $1$ cm = $10$ mm.
$1$ kg = $1000$ g. $1$ g = $1000$ mg.
$1$ L = $1000$ ml = $1000$ cm³.
$1$ tonne = $1000$ kg.
$1$ hour = $60$ min = $3600$ s.
$1$ day = $24$ h.

Time arithmetic.

Time is BASE 60, NOT base 10.

$0.5$ hours = $30$ minutes (NOT $50$ ).
$1$ h $30$ min + $2$ h $45$ min = $3$ h $75$ min = $4$ h $15$ min.

Worked qualitative. A train leaves at $10{:}45$ and arrives at $14{:}20$ . Journey length?

Method 1 — split:

$10{:}45$ → $11{:}00$ = $15$ min.
$11{:}00$ → $14{:}00$ = $3$ h.
$14{:}00$ → $14{:}20$ = $20$ min.
Total: $3$ h $35$ min.

Method 2 — convert to minutes from start of day:

$14{:}20 = 14 \times 60 + 20 = 860$ min.
$10{:}45 = 10 \times 60 + 45 = 645$ min.
Difference: $215$ min $= 3$ h $35$ min.

Edexcel tip. Show the conversion explicitly. 'Converting both to minutes: ...' earns the M1 mark.

Currency: multiply or divide by rate.
Sense check the direction.
Memorise unit equivalents.
Time = base 60.

Best buys and unit prices

Find unit price for each option. Lowest wins.

Step 1. Pick a common unit (g, ml, item).

Step 2. Compute total cost ÷ quantity for each option.

Step 3. Compare. Lowest unit price = best buy.

Worked example. Brand A: $500$ g for £ $3.00$ . Brand B: $750$ g for £ $4.20$ .

A: $300$ p / $500$ g = $0.60$ p/g.
B: $420$ p / $750$ g = $0.56$ p/g.

B is cheaper.

Reduce each option to one common unit; the lowest unit price wins.

Bonus offers.

Sometimes packages have 'extra free'. Calculate the EFFECTIVE quantity.

Brand C: $750$ g + $20\%$ extra free for £ $4.20$ .

Effective quantity: $750 \times 1.2 = 900$ g.
Unit price: $420 / 900 = 0.467$ p/g.

Worked qualitative. Why are unit prices the universal yardstick?

They normalise for package size.
Easy to compare different brands.
Many countries require unit prices on shop labels by law.

Edexcel tip. State which is the best buy CLEARLY. 'Brand B at $0.56$ p/g, lower than Brand A at $0.60$ p/g.' Mark schemes credit the comparison reasoning.

Unit price = cost ÷ quantity.
Lowest wins.
Check for 'extra free' adjustments.
State the comparison clearly.

Speed, distance, time

$d = vt$ . Watch units and time conversions.

The triangle:

       D
      ---
      v|t

So:

$D = v \times t$ .
$v = D / t$ .
$t = D / v$ .

Cover the quantity you need: distance on top, speed and time multiply below.

Worked example. Car travels $135$ km in $2$ hours $15$ min. Find the average speed in km/h.

Convert time to hours: $2$ h $15$ min = $2.25$ h.
$v = 135 / 2.25 = 60$ km/h.

Worked example. A train travels at $90$ km/h for $40$ minutes. Distance?

Convert time to hours: $40/60 = 2/3$ h.
$D = 90 \times 2/3 = 60$ km.

Compound trips.

Often two parts at different speeds.

Example: $30$ km at $60$ km/h, then $20$ km at $40$ km/h. Average speed for the WHOLE trip?

Time for first leg: $30/60 = 0.5$ h.
Time for second leg: $20/40 = 0.5$ h.
Total distance: $50$ km. Total time: $1$ h.
Average speed: $50$ km/h. (NOT $50$ km/h average of speeds — that would be wrong!)

Worked qualitative. Why isn't average speed the same as average of speeds?

Speeds are weighted by TIME, not by speeds.
$60$ km/h for $0.5$ h covers more ground than $40$ km/h for $0.5$ h.
The 'simple average' of $60$ and $40$ is $50$ , but only correct if equal TIMES are spent at each speed.
For equal DISTANCES, use harmonic mean: $\dfrac{2}{1/60 + 1/40} = \dfrac{2}{0.0167 + 0.025} = 48$ .

Edexcel tip. Always convert time to consistent units (hours OR minutes — not mixed). Speed has units (km/h, m/s) — get them right.

$D = vt$ .
Convert time consistently.
Average speed = total distance / total time.
NOT simply the average of two speeds.

Quick recap

Tariffs: fixed + rate × units.
Currency: multiply or divide by rate.
Time: base 60.
Best buy: lowest unit price.
$D = vt$ for speed problems.
Always check + state units.

Memorise this

Verbatim phrases and definitions Edexcel mark schemes credit.

Tariff: total = fixed + rate × units.
Unit price = cost / quantity.
Currency: multiply (or divide) by exchange rate.
Time: $1$ h $= 60$ min, $1$ min $= 60$ s.
Speed: $D = vt$ .

How it’s examined

Applying number appears Paper 2H (4-6 marks): tariffs, best buys, currency, speed problems. Examiner reports flag (1) wrong direction in currency conversion, (2) treating time as base 10, (3) double-charging in two-part tariffs.

Sources: Pearson Edexcel International GCSE Mathematics A 4MA1 specification (2026 onwards); 4MA1 Examiner Reports — Jan and May/Jun 2022-2024 series; Past Papers — 4MA1/2H May/Jun 2024. Last reviewed 2026-05-07.

Take this whole topic with you

Step-by-step worked examples — Applying Number

Step-by-step solutions to past-paper-style questions on applying number, written exactly the way a tutor would explain them at the board.

1Convert units in a multi-step problem
Foundation• units, conversion
Question
A car uses $6.5$ litres of fuel per $100$ km. The fuel costs £ $1.40$ per litre. How much will it cost in fuel for a $250$ km journey?
Step-by-step solution
1. Step 1
  Fuel for $250$ km: $\dfrac{250}{100} \times 6.5 = 16.25$ litres.
2. Step 2
  Cost: $16.25 \times 1.40 = £22.75$ .
Answer
£ $22.75$
Examiner tip
Multi-step problems get partial credit if intermediate steps are clear. Always show working — even if final answer is wrong, method marks add up.
2Convert time and combine
Foundation• time
Question
A train leaves at $10{:}45$ and arrives at $14{:}20$ . How long is the journey?
Step-by-step solution
1. Step 1
  From $10{:}45$ to $14{:}45$ : $4$ hours.
2. Step 2
  But arrival is $14{:}20$ , which is $25$ minutes EARLIER than $14{:}45$ .
3. Step 3
  $4$ hours $- 25$ minutes $= 3$ hours $35$ minutes.
Answer
$3$ hours $35$ minutes
Examiner tip
Time arithmetic can be tricky. Convert to total minutes if confused: $14{:}20 = 14 \times 60 + 20 = 860$ min from start of day; $10{:}45 = 645$ min. Difference: $215$ min $= 3$ h $35$ min.
3Money calculation with rate
Foundation• Adapted from 4MA1/2H May/Jun 2024 Q3• money, rate
Question
A taxi charges £ $3.50$ for the first km and £ $1.20$ for each additional km. Calculate the cost of a $14$ km journey.
Step-by-step solution
1. Step 1
  First km: £ $3.50$ .
2. Step 2
  Additional km: $14 - 1 = 13$ km at £ $1.20$ each $= 13 \times 1.20 = £15.60$ .
3. Step 3
  Total: $3.50 + 15.60 = £19.10$ .
Answer
£ $19.10$
Examiner tip
Tariff problems use a fixed charge plus a per-unit rate. Always identify the structure first: 'fixed + (rate × units)'.
4Compare best buys with bonus offers
Higher• best buy
Question
Brand A: $500$ g at £ $3.00$ . Brand B: $750$ g at £ $4.20$ , but with $20\%$ extra free. Which is cheaper per gram?
Step-by-step solution
1. Step 1
  Brand A: cost per gram $= \dfrac{300\,p}{500\,\text{g}} = 0.6$ p per g.
2. Step 2
  Brand B: $20\%$ extra → $750 \times 1.2 = 900$ g. Cost per g $= \dfrac{420\,p}{900\,\text{g}} = 0.467$ p per g.
3. Step 3
  Brand B is cheaper.
Answer
Brand B (about $0.47$ p/g vs $0.60$ p/g for A).
Examiner tip
Always reduce to a unit price (per gram, per litre, per item). When 'extra free' is offered, calculate the EFFECTIVE quantity first.
5Currency conversion
Foundation• currency
Question
$£1 = \$ 1.25 $. Convert (a) £$ 320 $to USD, (b)$ $500$ to GBP.
Step-by-step solution
1. Step 1
  (a) £→ $\$$: multiply by$ 1.25$.
  $320 \times 1.25 = \$400$
2. Step 2
  (b) $\$ →£ $: divide by$ 1.25$.
  $\frac{500}{1.25} = £400$
Answer
(a) $\$ 400 $(b) £$ 400$
Examiner tip
Determine the rate's direction. £ $1 = \$ 1.25 $means: £→$ $ $multiply by$ 1.25 $.$ $→£ $divide by$ 1.25$.

Key Formulae — Applying Number

The formulae you need to memorise for applying number on the Pearson Edexcel IGCSE 4MA1 paper, with every variable defined in plain English and a note on when to use it.

Two-part tariff
$\text{Total} = \text{Fixed charge} + (\text{Rate} \times \text{Units used})$
$\text{Fixed charge}$
the standing/connection fee
$\text{Rate}$
cost per unit (per km, per kWh, per minute)
When to use
For utility bills, taxi fares, mobile-phone tariffs — anything with a fixed component plus per-unit cost.
Example
Taxi: £ $3.50$ + £ $1.20$ × km. For $14$ km: $3.50 + 1.20 \times 13 = £19.10$ .
Unit price
$\text{Unit price} = \dfrac{\text{Total cost}}{\text{Quantity}}$
$\text{Quantity}$
in consistent units (g, kg, L, items)
When to use
When comparing prices of different sizes/brands. Lowest unit price = best buy.
Example
$500$ g for £ $3.00$ : unit price $= 600$ p/ $500$ g $= 1.2$ p/g.

Key Definitions and Keywords — Applying Number

Definitions to memorise and the exact keywords mark schemes credit for applying number answers — sharpened from recent examiner reports for the 2026 Pearson Edexcel IGCSE 4MA1 sitting.

Rate
Examiner keyword
A ratio of two quantities with different units, expressing change per unit of one.
Example
$60$ km/h, £ $1.40$ /litre, $5$ litres/100 km.
Tariff
A pricing structure, often with a fixed charge plus a per-unit rate.
Example
Mobile phone: £ $10$ /month + $5$ p/minute over $100$ minutes.
Best buy
The product with the LOWEST unit price (cost per gram, per litre, per item).
Example
Compare unit prices: lowest wins.

Common Mistakes and Misconceptions — Applying Number

The traps other students keep falling into on applying number questions — taken from recent Pearson Edexcel IGCSE 4MA1 examiner reports and mark schemes — and how to avoid them.

✕Forgetting to convert units (g vs kg, ml vs L, p vs £)
Why it happens
Rushing.
How to avoid it
Always check units BEFORE calculating. Convert to one consistent unit. Show ' $1.5$ kg $= 1500$ g' as a working step.
✕Treating time as base-10 (e.g. $1.5$ hours $= 1$ hour $50$ minutes)
Why it happens
Decimal habits.
How to avoid it
$1.5$ hours $= 1$ hour $30$ min ( $0.5 \times 60 = 30$ ). Time uses base 60.
✕Multiplying when you should divide for currency conversion
Why it happens
Easy to confuse.
How to avoid it
Test with one unit: '£ $1 = \$ 1.25 $. So £$ 10 $should be more than \$ 10. So multiply.' Reverse: $ $10$ → divide.
✕Charging the fixed rate AND the per-unit rate for the first unit (double counting)
4MA1/2H May/Jun 2024 — examiner report Q3
Why it happens
Misreading the question.
How to avoid it
READ CAREFULLY. 'First km £ $3.50$ , additional km £ $1.20$ ' means $3.50$ FOR THAT FIRST km. Additional is $13$ km, not $14$ .

Applying Number — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Edexcel IGCSE Mathematics (4MA1)

Applying Number

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Short Notes - Applying Number

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Detailed Study Notes

Detailed notes on Numbers and the Number System for Edexcel IGCSE Mathematics, covering key concepts, explanations, examples, and exam-focused revision points.

Applying Number Study Notes — Edexcel IGCSE 4MA1 Higher Tier (2026 onwards)

Real-world number problems: money, time, units, rates and tariffs. Crucial for Paper 2H — and for life beyond exams.

At a glance

Tariffs: fixed charge + (rate × units).
Best buy: lowest unit price wins.
Currency: rate as multiplier; reverse with division.
Time: base 60 (not 100). $0.5$ h $= 30$ min.
Units: convert to consistent before calculating.
Speed-distance-time: $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ .

What you’ll learn

Mapped to the Pearson Edexcel IGCSE 4MA1 syllabus (2026 onwards).

1.12 — Solve real-life problems involving money, time, units and rates.
1.12 — Calculate best buys, taxi fares, currency conversions.
1.12 — Use speed-distance-time formula.

Tariffs and rates

Many bills follow: fixed charge + per-unit rate × units used.

Tariff structure.

Total cost = fixed charge + (rate × units used)

Examples:

Taxi: £ $3.50$ initial + £ $1.20$ /km. For $14$ km: $3.50 + 1.20 \times 13 = £19.10$ (note: $13$ additional, not $14$ ).
Electricity: £ $15$ standing charge + $20$ p/kWh. For $300$ kWh: $15 + 0.20 \times 300 = £75$ .
Gym: £ $25$ /month + £ $5$ /visit. For $8$ visits in a month: $25 + 5 \times 8 = £65$ .

Read carefully. Phrases like 'first $X$ included', 'additional $Y$ ' affect counting.

Worked qualitative. A water bill: £ $30$ standing charge + $0.20$ p/litre after the first $1000$ litres. Cost for $1500$ litres?

First $1000$ litres included in standing charge.
Additional $500$ litres at $0.20$ p each: $500 \times 0.20 = £100$ .
Total: $30 + 100 = £130$ .

Edexcel tip. Underline key numbers in the question. Identify: fixed cost, rate, units used. Compute step by step.

Total = fixed + rate × units.
Read 'first X' and 'additional Y' carefully.
Show working step by step.

Currency and units

Multiply for one direction, divide for the other. Always identify the direction.

Currency conversion.

If £ $1 = \$ 1.25$:

£ → $\$$: multiply by$ 1.25$.
$\$$ → £: divide by$ 1.25$.

Worked example. Convert £ $240$ to USD, then $\$$$ 400$ back to GBP.

£ $240 \times 1.25 = \$ 300$.
$\$$$ 400 / 1.25 = £320$.

Sense check. £ $1$ buys $\$ 1.25 $(more than$ 1 $). So £ →$ $$ should give a BIGGER number. Multiply confirms.

Unit conversions.

Memorise:

$1$ km = $1000$ m. $1$ m = $100$ cm. $1$ cm = $10$ mm.
$1$ kg = $1000$ g. $1$ g = $1000$ mg.
$1$ L = $1000$ ml = $1000$ cm³.
$1$ tonne = $1000$ kg.
$1$ hour = $60$ min = $3600$ s.
$1$ day = $24$ h.

Time arithmetic.

Time is BASE 60, NOT base 10.

$0.5$ hours = $30$ minutes (NOT $50$ ).
$1$ h $30$ min + $2$ h $45$ min = $3$ h $75$ min = $4$ h $15$ min.

Worked qualitative. A train leaves at $10{:}45$ and arrives at $14{:}20$ . Journey length?

Method 1 — split:

$10{:}45$ → $11{:}00$ = $15$ min.
$11{:}00$ → $14{:}00$ = $3$ h.
$14{:}00$ → $14{:}20$ = $20$ min.
Total: $3$ h $35$ min.

Method 2 — convert to minutes from start of day:

$14{:}20 = 14 \times 60 + 20 = 860$ min.
$10{:}45 = 10 \times 60 + 45 = 645$ min.
Difference: $215$ min $= 3$ h $35$ min.

Edexcel tip. Show the conversion explicitly. 'Converting both to minutes: ...' earns the M1 mark.

Currency: multiply or divide by rate.
Sense check the direction.
Memorise unit equivalents.
Time = base 60.

Best buys and unit prices

Find unit price for each option. Lowest wins.

Step 1. Pick a common unit (g, ml, item).

Step 2. Compute total cost ÷ quantity for each option.

Step 3. Compare. Lowest unit price = best buy.

Worked example. Brand A: $500$ g for £ $3.00$ . Brand B: $750$ g for £ $4.20$ .

A: $300$ p / $500$ g = $0.60$ p/g.
B: $420$ p / $750$ g = $0.56$ p/g.

B is cheaper.

Reduce each option to one common unit; the lowest unit price wins.

Bonus offers.

Sometimes packages have 'extra free'. Calculate the EFFECTIVE quantity.

Brand C: $750$ g + $20\%$ extra free for £ $4.20$ .

Effective quantity: $750 \times 1.2 = 900$ g.
Unit price: $420 / 900 = 0.467$ p/g.

Worked qualitative. Why are unit prices the universal yardstick?

They normalise for package size.
Easy to compare different brands.
Many countries require unit prices on shop labels by law.

Edexcel tip. State which is the best buy CLEARLY. 'Brand B at $0.56$ p/g, lower than Brand A at $0.60$ p/g.' Mark schemes credit the comparison reasoning.

Unit price = cost ÷ quantity.
Lowest wins.
Check for 'extra free' adjustments.
State the comparison clearly.

Speed, distance, time

$d = vt$ . Watch units and time conversions.

The triangle:

       D
      ---
      v|t

So:

$D = v \times t$ .
$v = D / t$ .
$t = D / v$ .

Cover the quantity you need: distance on top, speed and time multiply below.

Worked example. Car travels $135$ km in $2$ hours $15$ min. Find the average speed in km/h.

Convert time to hours: $2$ h $15$ min = $2.25$ h.
$v = 135 / 2.25 = 60$ km/h.

Worked example. A train travels at $90$ km/h for $40$ minutes. Distance?

Convert time to hours: $40/60 = 2/3$ h.
$D = 90 \times 2/3 = 60$ km.

Compound trips.

Often two parts at different speeds.

Example: $30$ km at $60$ km/h, then $20$ km at $40$ km/h. Average speed for the WHOLE trip?

Time for first leg: $30/60 = 0.5$ h.
Time for second leg: $20/40 = 0.5$ h.
Total distance: $50$ km. Total time: $1$ h.
Average speed: $50$ km/h. (NOT $50$ km/h average of speeds — that would be wrong!)

Worked qualitative. Why isn't average speed the same as average of speeds?

Speeds are weighted by TIME, not by speeds.
$60$ km/h for $0.5$ h covers more ground than $40$ km/h for $0.5$ h.
The 'simple average' of $60$ and $40$ is $50$ , but only correct if equal TIMES are spent at each speed.
For equal DISTANCES, use harmonic mean: $\dfrac{2}{1/60 + 1/40} = \dfrac{2}{0.0167 + 0.025} = 48$ .

Edexcel tip. Always convert time to consistent units (hours OR minutes — not mixed). Speed has units (km/h, m/s) — get them right.

$D = vt$ .
Convert time consistently.
Average speed = total distance / total time.
NOT simply the average of two speeds.

Quick recap

Tariffs: fixed + rate × units.
Currency: multiply or divide by rate.
Time: base 60.
Best buy: lowest unit price.
$D = vt$ for speed problems.
Always check + state units.

Memorise this

Verbatim phrases and definitions Edexcel mark schemes credit.

Tariff: total = fixed + rate × units.
Unit price = cost / quantity.
Currency: multiply (or divide) by exchange rate.
Time: $1$ h $= 60$ min, $1$ min $= 60$ s.
Speed: $D = vt$ .

How it’s examined

Take this whole topic with you

Step-by-step worked examples — Applying Number

Step-by-step solutions to past-paper-style questions on applying number, written exactly the way a tutor would explain them at the board.

1Convert units in a multi-step problem
Foundation• units, conversion
Question
A car uses $6.5$ litres of fuel per $100$ km. The fuel costs £ $1.40$ per litre. How much will it cost in fuel for a $250$ km journey?
Step-by-step solution
1. Step 1
  Fuel for $250$ km: $\dfrac{250}{100} \times 6.5 = 16.25$ litres.
2. Step 2
  Cost: $16.25 \times 1.40 = £22.75$ .
Answer
£ $22.75$
Examiner tip
Multi-step problems get partial credit if intermediate steps are clear. Always show working — even if final answer is wrong, method marks add up.
2Convert time and combine
Foundation• time
Question
A train leaves at $10{:}45$ and arrives at $14{:}20$ . How long is the journey?
Step-by-step solution
1. Step 1
  From $10{:}45$ to $14{:}45$ : $4$ hours.
2. Step 2
  But arrival is $14{:}20$ , which is $25$ minutes EARLIER than $14{:}45$ .
3. Step 3
  $4$ hours $- 25$ minutes $= 3$ hours $35$ minutes.
Answer
$3$ hours $35$ minutes
Examiner tip
Time arithmetic can be tricky. Convert to total minutes if confused: $14{:}20 = 14 \times 60 + 20 = 860$ min from start of day; $10{:}45 = 645$ min. Difference: $215$ min $= 3$ h $35$ min.
3Money calculation with rate
Foundation• Adapted from 4MA1/2H May/Jun 2024 Q3• money, rate
Question
A taxi charges £ $3.50$ for the first km and £ $1.20$ for each additional km. Calculate the cost of a $14$ km journey.
Step-by-step solution
1. Step 1
  First km: £ $3.50$ .
2. Step 2
  Additional km: $14 - 1 = 13$ km at £ $1.20$ each $= 13 \times 1.20 = £15.60$ .
3. Step 3
  Total: $3.50 + 15.60 = £19.10$ .
Answer
£ $19.10$
Examiner tip
Tariff problems use a fixed charge plus a per-unit rate. Always identify the structure first: 'fixed + (rate × units)'.
4Compare best buys with bonus offers
Higher• best buy
Question
Brand A: $500$ g at £ $3.00$ . Brand B: $750$ g at £ $4.20$ , but with $20\%$ extra free. Which is cheaper per gram?
Step-by-step solution
1. Step 1
  Brand A: cost per gram $= \dfrac{300\,p}{500\,\text{g}} = 0.6$ p per g.
2. Step 2
  Brand B: $20\%$ extra → $750 \times 1.2 = 900$ g. Cost per g $= \dfrac{420\,p}{900\,\text{g}} = 0.467$ p per g.
3. Step 3
  Brand B is cheaper.
Answer
Brand B (about $0.47$ p/g vs $0.60$ p/g for A).
Examiner tip
Always reduce to a unit price (per gram, per litre, per item). When 'extra free' is offered, calculate the EFFECTIVE quantity first.
5Currency conversion
Foundation• currency
Question
$£1 = \$ 1.25 $. Convert (a) £$ 320 $to USD, (b)$ $500$ to GBP.
Step-by-step solution
1. Step 1
  (a) £→ $\$$: multiply by$ 1.25$.
  $320 \times 1.25 = \$400$
2. Step 2
  (b) $\$ →£ $: divide by$ 1.25$.
  $\frac{500}{1.25} = £400$
Answer
(a) $\$ 400 $(b) £$ 400$
Examiner tip
Determine the rate's direction. £ $1 = \$ 1.25 $means: £→$ $ $multiply by$ 1.25 $.$ $→£ $divide by$ 1.25$.

Key Formulae — Applying Number

The formulae you need to memorise for applying number on the Pearson Edexcel IGCSE 4MA1 paper, with every variable defined in plain English and a note on when to use it.

Two-part tariff
$\text{Total} = \text{Fixed charge} + (\text{Rate} \times \text{Units used})$
$\text{Fixed charge}$
the standing/connection fee
$\text{Rate}$
cost per unit (per km, per kWh, per minute)
When to use
For utility bills, taxi fares, mobile-phone tariffs — anything with a fixed component plus per-unit cost.
Example
Taxi: £ $3.50$ + £ $1.20$ × km. For $14$ km: $3.50 + 1.20 \times 13 = £19.10$ .
Unit price
$\text{Unit price} = \dfrac{\text{Total cost}}{\text{Quantity}}$
$\text{Quantity}$
in consistent units (g, kg, L, items)
When to use
When comparing prices of different sizes/brands. Lowest unit price = best buy.
Example
$500$ g for £ $3.00$ : unit price $= 600$ p/ $500$ g $= 1.2$ p/g.

Key Definitions and Keywords — Applying Number

Definitions to memorise and the exact keywords mark schemes credit for applying number answers — sharpened from recent examiner reports for the 2026 Pearson Edexcel IGCSE 4MA1 sitting.

Rate
Examiner keyword
A ratio of two quantities with different units, expressing change per unit of one.
Example
$60$ km/h, £ $1.40$ /litre, $5$ litres/100 km.
Tariff
A pricing structure, often with a fixed charge plus a per-unit rate.
Example
Mobile phone: £ $10$ /month + $5$ p/minute over $100$ minutes.
Best buy
The product with the LOWEST unit price (cost per gram, per litre, per item).
Example
Compare unit prices: lowest wins.

Common Mistakes and Misconceptions — Applying Number

The traps other students keep falling into on applying number questions — taken from recent Pearson Edexcel IGCSE 4MA1 examiner reports and mark schemes — and how to avoid them.

✕Forgetting to convert units (g vs kg, ml vs L, p vs £)
Why it happens
Rushing.
How to avoid it
Always check units BEFORE calculating. Convert to one consistent unit. Show ' $1.5$ kg $= 1500$ g' as a working step.
✕Treating time as base-10 (e.g. $1.5$ hours $= 1$ hour $50$ minutes)
Why it happens
Decimal habits.
How to avoid it
$1.5$ hours $= 1$ hour $30$ min ( $0.5 \times 60 = 30$ ). Time uses base 60.
✕Multiplying when you should divide for currency conversion
Why it happens
Easy to confuse.
How to avoid it
Test with one unit: '£ $1 = \$ 1.25 $. So £$ 10 $should be more than \$ 10. So multiply.' Reverse: $ $10$ → divide.
✕Charging the fixed rate AND the per-unit rate for the first unit (double counting)
4MA1/2H May/Jun 2024 — examiner report Q3
Why it happens
Misreading the question.
How to avoid it
READ CAREFULLY. 'First km £ $3.50$ , additional km £ $1.20$ ' means $3.50$ FOR THAT FIRST km. Additional is $13$ km, not $14$ .

Applying Number — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Applying Number

Short Notes - Applying Number

Detailed Study Notes

At a glance

What you’ll learn

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Convert units in a multi-step problem

2Convert time and combine

3Money calculation with rate

4Compare best buys with bonus offers

5Currency conversion

Two-part tariff

Unit price

Rate

Tariff

Best buy

✕Forgetting to convert units (g vs kg, ml vs L, p vs £)

✕Treating time as base-10 (e.g. 1.51.51.5 hours =1= 1=1 hour 505050 minutes)

✕Multiplying when you should divide for currency conversion

✕Charging the fixed rate AND the per-unit rate for the first unit (double counting)

Applying Number — frequently asked questions

Applying Number

Short Notes - Applying Number

Detailed Study Notes

At a glance

What you’ll learn

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Convert units in a multi-step problem

2Convert time and combine

3Money calculation with rate

4Compare best buys with bonus offers

5Currency conversion

Two-part tariff

Unit price

Rate

Tariff

Best buy

✕Forgetting to convert units (g vs kg, ml vs L, p vs £)

✕Treating time as base-10 (e.g. 1.51.51.5 hours =1= 1=1 hour 505050 minutes)

✕Multiplying when you should divide for currency conversion

✕Charging the fixed rate AND the per-unit rate for the first unit (double counting)

Applying Number — frequently asked questions

✕Treating time as base-10 (e.g. $1.5$ hours $= 1$ hour $50$ minutes)

✕Treating time as base-10 (e.g. $1.5$ hours $= 1$ hour $50$ minutes)