Using a Calculator

Key a fraction into your calculator with brackets round the top and the bottom, write down every figure on the display, then round it if the question asks.

In the exam for Cambridge IGCSE Maths 0580, Edexcel IGCSE Maths 4MA1, Cambridge O Level Maths 4024 · 46 real past-paper questions below

اقرأ هذا الدرس مشروحاً بالعربي ←

What the Question Asks

The 2-mark question: use your calculator to work out a value, then write down all the figures on the display.

Your calculator does exactly what you type. On paper a fraction bar holds the whole top together and the whole bottom together. The ÷ key does not.

Rule

Put brackets round the whole top and the whole bottom. $\frac{a + b}{c - d}$ is keyed as $(a + b) \div (c - d)$ .

Key idea

Copy every figure on the screen. Do not round unless the question asks you to.

Key idea

Type $0.7734$ into a calculator with blocky digits, then turn it upside down. It says hELLO! Your calculator does exactly what you type, and sometimes it is even polite about it.

A Fraction Plus Another Term

The 2-mark question you see most: a fraction, then + or − another number, often a square.

Worked example

1
$\frac{6.5}{4.3 - 1.9} + 2. 4^{2}$ — The question. A fraction, with a square added on the end.
2
$6.5 \div (4.3 - 1.9)$ — Key the fraction. The bottom goes in brackets, because the fraction bar keeps 4.3 − 1.9 together.
3
$= 2.708333333$ — Press = to get the fraction on its own. Leave it on the screen and do not round it.
4
$2. 4^{2} = 5.76$ — Now the square. Use the square key: it means 2.4 × 2.4, not 2.4 × 2.
5
$Ans + 5.76 = 8.468333333$ — Add the square to the full value on the screen. Write every figure: this is the answer mark.

Common mistake

Typing 6.5 ÷ 4.3 − 1.9 + 2.4² with no brackets. The calculator divides by 4.3 only, and you get 5.371627907.

One Fraction, Sums on Top and Bottom

The 2-mark question: a single fraction with + or − on the top, the bottom, or both.

Worked example

1
$\frac{7.3 + 4.6}{6.1 - 2.8}$ — The question. A sum on the top and a subtraction on the bottom.
2
$(7.3 + 4.6) \div (6.1 - 2.8)$ — Key it with the top and the bottom each in brackets, because the fraction bar groups each one.
3
$7.3 + 4.6 = 11.9$ — The brackets make the calculator add the top first.
4
$6.1 - 2.8 = 3.3$ — Then it works out the bottom on its own.
5
$11.9 \div 3.3 = 3.606060606$ — Only then does it divide top by bottom. Write all the figures.

Common mistake

No brackets: 7.3 + 4.6 ÷ 6.1 − 2.8 gives 5.254098361. The calculator divides 4.6 alone, so it is a different sum.

Squares and Square Roots Inside

The 2-mark question: a fraction with a square or a square root on the top or the bottom.

Worked example

1
$\frac{9.8 - 1. 6 ^{2}}{4.1 + 5.3}$ — The question. Work out the top, then the bottom, then divide.
2
$1. 6^{2} = 2.56$ — Top: square first, because powers come before take away.
3
$9.8 - 2.56 = 7.24$ — Finish the top by taking the square away from 9.8.
4
$5.3 = 2.302172887$ — Bottom: the root covers 5.3 only, so close the root bracket straight after 5.3.
5
$4.1 + 2.302172887 = 6.402172887$ — Finish the bottom. Keep every figure, so nothing is lost.
6
$7.24 \div 6.402172887 = 1.130866056$ — Divide top by bottom. Write all the figures.

Common mistake

Typing 1.6 × 2 for 1.6². Squaring means 1.6 × 1.6. Use the square key.

Key idea

The √ key opens a bracket on most calculators. Close it straight after 5.3.

A Root Over a Whole Sum

Sometimes the root sign stretches over a whole sum. Then the root bracket closes at the end of the sum, not after the first number.

Worked example

1
$\frac{6.2 + 3. 5 ^{2}}{2.7 \times 0.8}$ — The question. The root's roof covers all of 6.2 + 3.5², so the whole sum goes under it.
2
$3. 5^{2} = 12.25$ — Under the root, square first, because powers come before +.
3
$6.2 + 12.25 = 18.45$ — Finish the sum under the root.
4
$18.45 = 4.295346319$ — Only now take the root. On the calculator, this is where the root bracket closes.
5
$2.7 \times 0.8 = 2.16$ — The bottom. It goes in brackets too, because it is the whole bottom.
6
$4.295346319 \div 2.16 = 1.988586259$ — Divide top by bottom. Write all the figures.

Rule

Key it as $(6.2 + 3. 5^{2}) \div (2.7 \times 0.8)$ . Check the screen: the root sign must cover the whole sum.

Common mistake

Typing ÷ 2.7 × 0.8 with no brackets. The calculator divides by 2.7, then multiplies by 0.8, and you get 1.272695206.

Cubes and Other Powers

Exams also use cubes and higher powers, like $2. 3^{3}$ or $2. 5^{4}$ . Use the power key, marked $x^{□}$ or ^.

Worked example

1
$\frac{2. 3 ^{3} - 4.7}{1.9}$ — The question. A cube on the top and a root on the bottom.
2
$2. 3^{3} = 12.167$ — Type 2.3, the power key, then 3. Cubing means 2.3 × 2.3 × 2.3, not 2.3 × 3.
3
$12.167 - 4.7 = 7.467$ — Finish the top by taking away 4.7.
4
$1.9 = 1.378404875$ — The bottom. Keep every figure.
5
$7.467 \div 1.378404875 = 5.41713116$ — Divide top by bottom. Write all the figures.

The bottom can come out negative. That is fine: keep the minus all the way.

Worked example

1
$\frac{12}{0. 3 ^{2} - 0.5}$ — The question.
2
$0. 3^{2} = 0.09$ — Square first.
3
$0.09 - 0.5 = - 0.41$ — The bottom is negative, because 0.5 is bigger than 0.09.
4
$12 \div (- 0.41) = - 29.26829268$ — A positive divided by a negative is negative. Leave out the minus and the answer is wrong.

Common mistake

Typing −3² when you mean $(- 3)^{2}$ . The calculator squares 3 first, then puts the minus in front, so it shows −9. Type $(- 3)^{2}$ to get 9.

Give Your Answer as a Decimal

Many calculators show a fraction answer. When the question says “give your answer as a decimal”, you must switch it.

Worked example

1
$\frac{2.9 + 4.6}{11.2} + \frac{6.3}{5 \times 2.8}$ — The question. Two fractions added together.
2
$(2.9 + 4.6) \div 11.2 = 0.6696428571$ — Work out the first fraction. Write it down: it can earn a mark on its own.
3
$6.3 \div (5 \times 2.8) = 0.45$ — Then the second fraction. The bottom 5 × 2.8 goes in brackets, because it is the whole bottom.
4
$0.6696428571 + 0.45 = \frac{627}{560}$ — Add them. Keyed in one go, many calculators show the answer as a fraction. The question wants a decimal.
5
$\frac{627}{560} = 1.119642857$ — Press the S⇔D key (or ≈) to turn it into a decimal. Write all the figures.

Key idea

Write down the value of each part, or of the top and the bottom, before the final answer. If the last keying goes wrong, that working still earns 1 of the 2 marks. A bare wrong answer earns nothing.

Common mistake

Writing 1.12 when the question asks for all the figures. A rounded answer loses the answer mark. Round only when the question tells you to.

Write It All, Then Round

The next part often says: give your answer to 3 significant figures, or to 1 decimal place. Write the full display first.

Worked example

1
$8.468333333$ — Write the full display first. It earns its mark even if the rounding slips.
2
$8.46 8333333$ — 3 significant figures: keep 8, 4 and 6. The 4th figure, 8, decides which way to round.
3
$\approx 8.47$ — 8 is 5 or more, so the 6 goes up to 7.
4
$8.4 68333333$ — 1 decimal place: keep one figure after the point. The 2nd decimal, 6, decides.
5
$\approx 8.5$ — 6 is 5 or more, so 8.4 goes up to 8.5.

Rule

Round once, at the very end. Never round a middle step and type it back in.

Read the Display in Context

In a money or real-life question, the display is not always the answer. Read it, then decide what makes sense.

Worked example

1
$40 \div 6.85 = 5.839416058$ — Mia has $40 and a book costs $6.85. Divide to see how many books fit into $40.
2
$5 books$ — Round down. She cannot buy part of a book, and 6 books cost $41.10, which is more than $40.
3
$5 \times 6.85 = 34.25$ — The cost of the 5 books she can buy.
4
$40 - 34.25 = 5.75$ — Take it from $40 to find her change: $5.75.

Rule

Round down for how many you can buy or make. Round up for how many you need: 130 students and 50 seats per bus gives 2.6, so you need 3 buses.

Key idea

Money has 2 decimal places. If 3 × 2.1 shows 6.3, write $6.30.

Which Method? Read the Question

Look at the words and at what sits on the top and bottom of the fraction.

You see	You do
Write down all the figures	copy every digit on the screen
+ or − on the top or bottom	brackets round the top and the bottom
A square or a root	square key; close the root bracket
A root over a whole sum	close the root bracket after the whole sum
A cube or a higher power	the power key, not × 3
Give your answer as a decimal	press S⇔D if a fraction shows
Money, or how many you can buy	$ to 2 decimal places; round down
No calculator: which part first?	Order of Operations
Give it to 3 significant figures	Significant Figures
Give it to 1 decimal place	Rounding to Decimal Places

Key idea

Check with a rough estimate. If the display is far from it, you keyed it wrong.

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