Pearson Edexcel International GCSE Mathematics A 4MA1: Applying number and electronic calculators – Study Guide

This study guide teaches sections 1.10 (Applying number) and 1.11 (Electronic calculators) of topic 1, Numbers and the number system, in the Pearson Edexcel International GCSE Mathematics A (4MA1) specification, Issue 2 (November 2017), first assessed in June 2018 with papers available in January and June. Both sections are Foundation Tier content. The Higher Tier content for 1.10 and 1.11 simply says “See Foundation Tier”, so everything here applies to both tiers and nothing is Higher tier only.

Each tier sits two 2-hour papers of 100 marks (1F and 2F, or 1H and 2H), each worth 50% of the qualification. A calculator may be used on every paper, and the specification says questions are set in SI units.

See also the revision notes, the practice questions, the Edexcel IGCSE Mathematics hub, the printable 4MA1 checklist and the free 10-minute diagnostics. For the rest of topic 1 (fractions, percentages, ratio, bounds, standard form), use the Numbers and the number system study guide.

What this unit covers

Section	What you must be able to do	Tier
1.10 A	Use and apply number in everyday personal, domestic or community life	Both tiers
1.10 B	Carry out calculations using standard units of mass, length, area, volume and capacity (metric units only)	Both tiers
1.10 C	Understand and carry out calculations using time; carry out calculations using money, including converting between currencies	Both tiers
1.11 A	Use a scientific electronic calculator to determine numerical results	Both tiers

The note against 1.10 B in the specification says “Metric units only”. You will not be asked to convert miles, pounds (weight) or gallons.

1.10 B: Metric units

Length, mass and capacity

All metric units are built from a base unit and a prefix. Learn these conversions:

Quantity	Conversions
Length	10 mm = 1 cm, 100 cm = 1 m, 1000 mm = 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

To a smaller unit, multiply; to a larger unit, divide. 2.7 km = 2700 m; 450 g = 0.45 kg.

Area and volume units

This is where most unit marks are lost. An area unit is a length unit squared, so the conversion factor is squared too. A volume unit is cubed, so the factor is cubed.

1 m = 100 cm      ->  1 m² = 100 × 100 = 10 000 cm²
                  ->  1 m³ = 100 × 100 × 100 = 1 000 000 cm³
1 cm = 10 mm      ->  1 cm² = 100 mm²,  1 cm³ = 1000 mm³

Volume and capacity are linked:

1 cm³ = 1 ml      1000 cm³ = 1 litre      1 m³ = 1000 litres

The safest method is to convert lengths first, then calculate the area or volume in the unit you want.

Worked example 1 (volume to capacity). A fish tank is a cuboid with internal measurements 80 cm long, 45 cm wide and 50 cm high. It is filled with water to 4 cm below the top. How many litres of water are in the tank?

depth of water = 50 − 4 = 46 cm
volume = 80 × 45 × 46 = 165 600 cm³
165 600 cm³ ÷ 1000 = 165.6 litres

Worked example 2 (area and cost). A rectangular room measures 450 cm by 380 cm. Carpet costs £18.50 per m². Find the cost of carpeting the room.

Convert to metres first: 4.5 m and 3.8 m.

area = 4.5 × 3.8 = 17.1 m²
cost = 17.1 × 18.50 = £316.35

If you multiply 450 × 380 = 171 000 cm² and then divide by 100, you get 1710 “m²”, which is wrong by a factor of 100. Divide cm² by 10 000 to get m².

Worked example 3 (mass). A lift can carry at most 630 kg. A worker of mass 75 kg wants to take boxes of mass 18.5 kg each. What is the greatest number of boxes he can take in one trip?

mass available = 630 − 75 = 555 kg
555 ÷ 18.5 = 30

He can take 30 boxes. Had the division given 30.4, the answer would still be 30: in everyday problems, round up or down from the context.

1.10 C: Time

12-hour and 24-hour clocks

3:25 pm is 15:25. 12:10 am is 00:10. Always write 24-hour times with four digits.

Time intervals

Count up in steps: to the next whole hour, then whole hours, then the remaining minutes. Do not subtract times as if they were decimals.

Worked example 4. A train leaves at 22:47 and arrives at 01:18 the next day. How long is the journey?

22:47 -> 23:00    13 min
23:00 -> 01:00    2 h
01:00 -> 01:18    18 min
total             2 h 31 min

Decimal hours

There are 60 minutes in an hour, not 100. To change between hours and minutes:

hours -> minutes: multiply the decimal part by 60
3.35 h = 3 h + 0.35 × 60 min = 3 h 21 min
minutes -> hours: divide by 60
2 h 45 min = 2 + 45/60 = 2.75 h

A calculator showing 3.35 for a time does not mean 3 hours 35 minutes.

Worked example 5 (pay). Amir is paid £12.40 per hour. He works 7 hours 45 minutes. How much is he paid?

7 h 45 min = 7.75 h
7.75 × 12.40 = £96.10

1.10 C: Money

Bills, wages and value for money

Money answers are given to the nearest penny (2 decimal places) unless the question says otherwise. If a calculator shows 96.1, write £96.10.

Convert pence to pounds before you add.

Worked example 6 (a bill). An electricity bill has a standing charge of 48p per day for 92 days, plus 1240 units at 26.5p per unit. VAT at 5% is added to the total. Find the amount to pay.

standing charge = 92 × 0.48 = £44.16
units           = 1240 × 0.265 = £328.60
subtotal        = £372.76
with VAT        = 372.76 × 1.05 = 391.398 -> £391.40

Worked example 7 (best buy). Rice is sold in a 750 g bag for £2.85 and a 1.2 kg bag for £4.40. Which is better value?

Compare the cost of 100 g:

750 g:  2.85 ÷ 7.5 = £0.38 per 100 g
1.2 kg = 1200 g:  4.40 ÷ 12 = £0.3667 per 100 g

The 1.2 kg bag is better value. You must show both unit costs and then state the conclusion; a conclusion on its own scores nothing.

Converting between currencies

An exchange rate such as £1 = €1.16 is a multiplier.

pounds -> euros: multiply by 1.16
euros  -> pounds: divide by 1.16

Check the direction: at this rate the number of euros should be bigger than the number of pounds.

Worked example 8. The rate is £1 = €1.16.

(a) Change £350 into euros: 350 × 1.16 = €406.

(b) Change €95 into pounds: 95 ÷ 1.16 = 81.896… = £81.90.

(c) A jacket costs €129 in Paris and £108 in London. Where is it cheaper, and by how much?

€129 = 129 ÷ 1.16 = £111.21 (2 d.p.)
£111.21 − £108 = £3.21

It is cheaper in London by £3.21. Convert to one currency before comparing.

1.10 A: Everyday problems

Section 1.10 A asks you to use and apply number in “personal, domestic or community life”: multi-step problems such as tariffs, budgets, timetables and ordering materials, where you choose the operations yourself. The method:

1. Write down what the question wants as a final answer, with its unit.
2. Convert all quantities to consistent units.
3. Do each step on its own line with a short label (“area of floor =”, “packs needed =”).
4. Decide whether to round up or down from the context (you buy whole packs; you fit whole boxes).
5. Answer the question in words if it asks “which” or “is it enough”.

Tariff questions often ask when two options cost the same. Set the totals equal, or find the difference in fixed cost and divide by the difference in rate. You can see this in practice question 9.

1.11: Using a scientific calculator

What the specification expects

Section 1.11 A is one line: use a scientific electronic calculator to determine numerical results. Page 42 of the specification lists the minimum functions. For both tiers these include the four operations, squares, powers and roots, memory, brackets, Σx and Σfx, and sine, cosine, tangent and their inverses. The Higher Tier list also includes standard form. Calculators with databanks, retrieval of text or formulae, QWERTY keyboards, built-in symbolic algebra, or symbolic differentiation or integration are prohibited in all examinations.

Order of operations on a calculator

A scientific calculator follows the hierarchy of operations (brackets, then powers and roots, then multiplication and division, then addition and subtraction). That is why you must add brackets the calculator cannot see.

Worked example 9. Work out (2.7 + 5.85) / (1.9 × 0.4).

Correct key sequence: ( 2.7 + 5.85 ) ÷ ( 1.9 × 0.4 ) = gives 11.25.

Typing 2.7 + 5.85 ÷ 1.9 × 0.4 = gives 3.9315…, because the calculator divides only 5.85 by 1.9. Alternatively, use the fraction template so the whole numerator and denominator sit in their own boxes.

Negative numbers and powers

(−4)² = 16, but −4² = −16 on a calculator, because the square is applied before the minus sign. Always put a negative number in brackets before squaring it.

Write down the full display, then round

Worked example 10. Work out √(15.2² − 6.8²) / (3.4 × 0.75). Write down all the figures on your calculator display, then give your answer to 3 significant figures.

15.2² − 6.8² = 184.8, √184.8 = 13.594116...
3.4 × 0.75 = 2.55
13.594116... ÷ 2.55 = 5.331026029...

All figures: 5.331026029. To 3 s.f.: 5.33.

Use the square-root template over the whole of 15.2² − 6.8², or press = and then √Ans.

Good habits

• Round only at the end. Rounding 13.594 to 13.6 before dividing gives 5.333…, which is wrong at 4 s.f. (the true value is 5.331).
• Estimate (section 1.8 D) so you notice a wrong key press: √(15.2² − 6.8²) is a bit less than 15, and 3.4 × 0.75 is about 2.5, so the answer should be a bit under 6. 5.33 fits.
• Interpret the display in context: 96.1 for money means £96.10; 3.35 for time means 3 h 21 min; 31.104 bags means you need 32.

Common errors

• Dividing cm² by 100 (instead of 10 000) to get m², or cm³ by 1000 (instead of 1 000 000) to get m³.
• Reading 2.5 hours as 2 h 50 min, or writing 1 h 45 min as 1.45 h.
• Subtracting clock times like decimals across the hour (14:15 − 09:38 is 4 h 37 min, not “4.77”).
• Multiplying when you should divide in a currency conversion.
• Comparing prices in two currencies without converting one of them.
• Rounding to the nearest whole when the context needs rounding up (packs, bags, coaches).
• Missing brackets around a numerator or denominator, or squaring a negative without brackets.

Next steps

Use the revision notes for quick recall, then test yourself with the practice questions. For percentages, ratio and bounds questions, try the Numbers and the number system practice and revision notes.

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.