Pearson Edexcel International GCSE Mathematics A 4MA1: Applying number and electronic calculators – Revision Notes

For full explanations and worked examples, use the Applying number and electronic calculators study guide.

These notes cover sections 1.10 (Applying number) and 1.11 (Electronic calculators) of topic 1 in the Pearson Edexcel International GCSE Mathematics A (4MA1) specification, Issue 2 (November 2017), first assessed in June 2018 with papers in January and June. Both sections are Foundation Tier content, and the Higher Tier lists them as “See Foundation Tier”, so they apply in full to both tiers. Nothing here is Higher tier only. A calculator may be used on all four papers (1F, 2F, 1H, 2H).

Links: practice questions · Edexcel IGCSE Mathematics hub · printable 4MA1 checklist · free 10-minute diagnostics · topic-level Numbers and the number system revision notes (percentages, ratio, bounds, standard form).

The specification in four lines

Ref	Outcome	Tier
1.10 A	Use and apply number in everyday personal, domestic or community life	Both
1.10 B	Calculations using standard units of mass, length, area, volume and capacity (metric only)	Both
1.10 C	Calculations using time; calculations using money, including converting between currencies	Both
1.11 A	Use a scientific electronic calculator to determine numerical results	Both

1.10 B: Metric conversions

Core facts

Quantity	Facts to know
Length	10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km
Mass	1000 mg = 1 g; 1000 g = 1 kg; 1000 kg = 1 tonne
Capacity	1000 ml = 1 litre; 100 cl = 1 litre
Area	1 cm² = 100 mm²; 1 m² = 10 000 cm²; 1 km² = 1 000 000 m²
Volume	1 cm³ = 1000 mm³; 1 m³ = 1 000 000 cm³
Volume ↔ capacity	1 cm³ = 1 ml; 1000 cm³ = 1 litre; 1 m³ = 1000 litres

Method in steps: any unit question

1. Decide the unit the answer must be in.
2. Convert every LENGTH into a matching unit first.
3. Then work out the area or volume.
4. Smaller unit -> multiply; larger unit -> divide.
5. Sense-check: a room is about 10-30 m², a bath holds about 100-200 litres.

Quick reminder. A box 30 cm × 20 cm × 15 cm has volume 9000 cm³ = 9 litres. A garden 12 m × 8 m has area 96 m² = 960 000 cm².

Must-know distinction: length factor vs area factor vs volume factor

From → to	Length	Area	Volume
m → cm	× 100	× 10 000	× 1 000 000
cm → mm	× 10	× 100	× 1000
km → m	× 1000	× 1 000 000	not needed

The factor is squared for area and cubed for volume.

1.10 C: Time

Facts

• 60 seconds = 1 minute; 60 minutes = 1 hour; 24 hours = 1 day.
• 24-hour times use four digits: 7:05 pm = 19:05; 12:30 am = 00:30.

Method in steps: time between two clock times

1. Count on to the next whole hour.
2. Count whole hours.
3. Count the leftover minutes.
4. Add the pieces. Cross midnight by counting to 00:00 (or 24:00).

Decimal hours

decimal hours -> h and min: multiply the decimal part by 60
minutes -> decimal hours:   divide by 60

Minutes	6	12	15	20	30	45
Hours	0.1	0.2	0.25	0.3̇	0.5	0.75

Must-know distinction: 1.5 h is 1 h 30 min, not 1 h 50 min. 1 h 50 min is 1.83 h (to 2 d.p.).

Use decimal hours for any multiplication (pay rates, flow rates, costs per hour). Use hours and minutes for clock answers.

1.10 C: Money

Rules

• Money answers to 2 d.p. (the nearest penny) unless told otherwise: £7.2 → £7.20.
• Convert pence to pounds before mixing: 45p = £0.45.
• Do not round in the middle of a money calculation; round the final total.

Best buy (value for money)

1. Find the cost of ONE common amount (per 100 g, per litre, per item),
   or the amount per £1.
2. Show both values.
3. State which is better value.

Without the comparison values, a correct choice earns no marks.

Bills and wages

Type	How to calculate
Hourly pay	hours (as a decimal) × rate
Overtime “time-and-a-half”	overtime hours × rate × 1.5
Standing charge	number of days × daily charge
Units used	number of units × price per unit
Adding VAT at r%	subtotal × (1 + r/100)

Currency conversion

For a rate “£1 = k units of currency X”:

pounds -> X:  multiply by k
X -> pounds:  divide by k
X -> Y via pounds:  divide by k_X, then multiply by k_Y

Sense-check: if £1 buys more than 1 unit of X, the X amount must be bigger than the pound amount.

Comparing prices in two countries: convert one price into the other currency, then subtract. Say clearly where it is cheaper and by how much.

1.10 A: Everyday problems

• Read the final sentence first: what is the answer and its unit?
• Label every line of working (“cost of paint =”, “tins needed =”).
• Round up when you must have enough (tins, packs, buses, bags).
• Round down when you can only fit or afford whole items (boxes in a lift, tickets with a budget).
• For “which option is cheaper” questions, work out both totals and state the difference.
• For “when do two tariffs cost the same”, divide the difference in fixed charges by the difference in rates.

1.11: Calculator essentials

The specification lists minimum calculator functions on page 42: for both tiers, the four operations, squares, powers and roots, memory, brackets, Σx, Σfx, and sine, cosine, tangent and their inverses; the Higher Tier list adds standard form. Calculators with databanks, text or formula retrieval, QWERTY keyboards, symbolic algebra, or symbolic differentiation or integration are prohibited.

Method in steps: a “use your calculator” question

1. Put brackets round every numerator and denominator
   (or use the fraction template).
2. Put brackets round negative numbers before powers: (−3)² = 9, −3² = −9.
3. Use the √ template over the WHOLE expression under the root.
4. Write down ALL the figures on the display.
5. Then round as asked (s.f. or d.p.).
6. Quick estimate: does the size look right?

Interpreting the display

Display	Context	Write
14.7	money	£14.70
2.25	hours	2 h 15 min
31.104	bags needed	32 bags
7.98	coaches of 50 for 399 people	8 coaches
4.6E+05 or 4.6 × 10⁵	standard form	4.6 × 10⁵ (not 4.6⁵)

Quick self-test

1. Change 3.6 m² into cm².
2. Change 2 500 000 cm³ into m³.
3. How many cm³ are in 4.5 litres?
4. Write 0.85 hours in minutes.
5. Find the time from 09:38 to 14:15.
6. Write 2 hours 12 minutes in hours as a decimal.
7. £1 = €1.15. Change €230 into pounds.
8. Pens cost £2.94 for 6 or £4.75 for 10. Which is better value? Show why.
9. Work out (3.8 + 4.6) / (2.1 × 0.5).
10. Work out √(7.2² + 9.6²).
11. A calculator shows 14.7 as a price in pounds. How should you write it?
12. Hana works a 38-hour week at £11.20 per hour, plus 5 hours of overtime at time-and-a-half. Find her pay for the week.

Answers

1. 3.6 × 10 000 = 36 000 cm².
2. 2 500 000 ÷ 1 000 000 = 2.5 m³.
3. 4.5 × 1000 = 4500 cm³.
4. 0.85 × 60 = 51 minutes.
5. 22 min to 10:00, 4 h to 14:00, 15 min more: 4 h 37 min.
6. 2 + 12/60 = 2.2 hours.
7. 230 ÷ 1.15 = £200.
8. 6-pack: 294 ÷ 6 = 49p each. 10-pack: 475 ÷ 10 = 47.5p each. The 10-pack is better value.
9. 8.4 ÷ 1.05 = 8.
10. √(51.84 + 92.16) = √144 = 12.
11. £14.70.
12. 38 × 11.20 = £425.60; 5 × 11.20 × 1.5 = £84.00; total £509.60.

Where marks are usually lost

• Dividing by 100 instead of 10 000 to change cm² to m², or by 1000 instead of 1 000 000 to change cm³ to m³.
• Working out an area in cm² and a cost per m² without converting, giving an answer 10 000 times too big.
• Writing 3 h 20 min as 3.2 h in a pay calculation (it is 3.3̇ h).
• Counting time across midnight or across the hour as if it were a decimal subtraction.
• Multiplying by the exchange rate when converting back into pounds.
• Comparing prices in two currencies without converting first.
• Giving a best-buy answer with no unit costs shown.
• Rounding 7.98 coaches to 7 or 31.1 bags to 31 when the context needs rounding up.
• Leaving out brackets around a denominator, so the calculator divides by only the first number.
• Rounding a value part-way through a calculation and losing the final accuracy mark.

Next steps

Try the practice questions, then revisit the study guide for any answer you got wrong. For wider topic 1 practice, use the Numbers and the number system practice.

Official syllabus

Pearson Edexcel International GCSE in Mathematics (Specification A) (4MA1), Specification Issue 2, November 2017, Pearson Education Limited. Topic 1, Numbers and the number system: 1.10 Applying number and 1.11 Electronic calculators (Foundation Tier content; the Higher Tier refers to the Foundation Tier for both sections). Calculator requirements: “Calculators”, page 42.