Calculator Skills (the Two Calculator Papers)

Four of the six OCR GCSE Mathematics (J560) papers allow a calculator — the two outer papers of each tier. On Foundation these are Paper 1 (J560/01) and Paper 3 (J560/03); on Higher they are Paper 4 (J560/04) and Paper 6 (J560/06). A calculator is a powerful tool, but only if you can drive it. The marks lost on calculator papers are rarely "I didn't know the maths" — they are "I typed it in wrongly", "I rounded too early", or "I didn't notice my answer was absurd". This lesson covers efficient, accurate calculator use: the key functions, entering fractions, powers and roots, the standard-form key, keeping full accuracy, and sanity-checking every result.

Calculator fluency is AO1 (carrying out standard techniques efficiently). But not rounding early protects accuracy across multi-step AO3 problems, and sanity-checking a result is an AO2/AO3 habit of interpreting whether an answer is sensible. A calculator never makes a question easier to understand — it only does the arithmetic faster — so the thinking is still yours; the machine simply removes the drudgery, provided you drive it accurately.

Key Reminder: Which Papers Are Calculator Papers?

Tier	Calculator papers	Non-calculator paper
Foundation	Paper 1 (J560/01) and Paper 3 (J560/03)	Paper 2
Higher	Paper 4 (J560/04) and Paper 6 (J560/06)	Paper 5

A calculator is permitted on the two outer papers of each tier, not the middle one. Bring a calculator you know well — ideally the exact model you have practised on all year. The exam is not the place to meet a new calculator. It is also worth checking, before the exam, that your calculator is on the list of models permitted in GCSE exams (a standard scientific calculator is fine; graphical or programmable models may be restricted) — your school can confirm this. And always have working batteries or a spare, since a dead calculator on a calculator paper is a needless disaster.

Know Your Function Keys

A scientific calculator does far more than $+$+, $-$−, $\times$×, $\div$÷. The keys below earn marks when used correctly. (Labels vary by model — find the equivalents on your calculator before the exam.)

Key / function	Use it for
Fraction key (often $\frac{a}{b}$ba​ or similar)	Entering and calculating with fractions exactly
Power key ($x^{\square}$x□ or $\wedge$∧)	Any power, e.g. $7^{4}$74
Square / cube ($x^{2}$x2, $x^{3}$x3)	Squaring and cubing quickly
Root keys ($\sqrt{\ }$ ​, $\sqrt[3]{\ }$3 ​, $\sqrt[\square]{\ }$□ ​)	Square, cube and other roots
Standard-form key (often labelled $\times 10^{x}$×10x or EXP)	Entering numbers in standard form
Brackets ( )	Controlling order of operations
$S{\Leftrightarrow}D$S⇔D (or equivalent)	Toggling between exact (surd/fraction) and decimal display
Memory / Ans	Reusing the previous answer without retyping (preserves full accuracy)
$\pi$π	Using $\pi$π to full precision

The single most valuable habit is using the Ans / memory key to carry a full-precision result into the next step instead of writing down a rounded number and retyping it.

A word of caution before the exam: spend time with your calculator's manual or a teacher to find where your model hides these functions, because labels and key sequences vary between makes. Some calculators require you to press "=" before a fraction displays; others need a "shift" or "2nd function" key to reach roots and inverse-trig. The exam is not the moment to discover that your calculator behaves differently from the one in the worked examples. The few minutes spent locating each key in advance pay back many times over in avoided fumbling and mis-keying during the paper.

Fractions, Powers and Roots

Entering fractions

Use the fraction key, not the $\div$÷ key, when you want an exact fraction. For $\dfrac{3}{8} + \dfrac{1}{6}$83​+61​, enter both as fractions and the calculator returns $\dfrac{13}{24}$2413​ exactly. If you instead type $3 \div 8 + 1 \div 6$3÷8+1÷6 you get the decimal $0.5416\ldots$0.5416…, which is fine only if a decimal is wanted — but you lose the exact form a "give your answer as a fraction" question demands.

Powers and roots

Work out $\sqrt{12.96}$12.96​. Use the root key: $\sqrt{12.96} = 3.6$12.96​=3.6 exactly. Answer: $3.6$3.6.

Work out $2.5^{4}$2.54. Use the power key: $2.5^{4} = 39.0625$2.54=39.0625. Answer: $39.0625$39.0625. (Do not approximate by hand — let the calculator do it precisely.)

Order of operations and brackets

Calculators follow the order of operations, so you must use brackets to group correctly. To compute $\dfrac{8.4 + 3.6}{2.5}$2.58.4+3.6​, type $(8.4 + 3.6) \div 2.5$(8.4+3.6)÷2.5. Without the brackets the calculator reads $8.4 + 3.6 \div 2.5 = 8.4 + 1.44 = 9.84$8.4+3.6÷2.5=8.4+1.44=9.84 — the wrong answer. With the brackets you get $12 \div 2.5 = 4.8$12÷2.5=4.8. Answer: $4.8$4.8.

The Standard-Form Key

The standard-form (or EXP / $\times 10^{x}$×10x) key enters powers of 10 cleanly and avoids mistakes.

Worked Example

Work out $(6.4 \times 10^{7}) \div (1.6 \times 10^{3})$(6.4×107)÷(1.6×103), giving your answer in standard form.

Enter $6.4$6.4, the standard-form key, $7$7; divide; $1.6$1.6, the standard-form key, $3$3. The calculator returns $40000$40000, i.e. $4 \times 10^{4}$4×104. Answer: $4 \times 10^{4}$4×104.

A warning: do not type the literal characters "$\times 10$×10" with the multiply and digit keys — type the exponent using the dedicated standard-form key. Typing it the long way risks errors and may not be read as a power. And remember the calculator may display the result as an ordinary number; you must still write it in standard form if the question asks for it.

Trigonometry and the Degree Mode

On the calculator papers, questions using $\sin$sin, $\cos$cos and $\tan$tan need the calculator set to degrees (look for a small "DEG" or "D" on the display). If it is in radian or gradian mode, every trig answer will be wrong — checking the mode is a five-second habit worth a lot of marks.

Worked Example: a trig calculation

A right-angled triangle has a hypotenuse of $12$12 cm and an angle of $35°$35°. Work out the length of the side opposite the $35°$35° angle, to 1 decimal place.

Opposite and hypotenuse means sine: $\sin 35° = \dfrac{\text{opp}}{12}$sin35°=12opp​, so $\text{opp} = 12 \times \sin 35°$opp=12×sin35°. With the calculator in degrees: $12 \times \sin 35° = 12 \times 0.5735\ldots = 6.882\ldots$12×sin35°=12×0.5735…=6.882…, which rounds to $6.9$6.9 cm. Answer: $6.9$6.9 cm. (Keep the full value of $\sin 35°$sin35° on the display — don't round it to $0.57$0.57 first.)

To find an angle from a ratio, use the inverse keys ($\sin^{-1}$sin−1, $\cos^{-1}$cos−1, $\tan^{-1}$tan−1), again in degrees. For example $\tan^{-1}(1) = 45°$tan−1(1)=45°. A quick check that your calculator is in the right mode: $\sin 30°$sin30° should give exactly $0.5$0.5. If it gives $-0.988\ldots$−0.988… you are in radian mode — switch to degrees before going any further, or every trig answer on the paper will be wrong.

Don't Round Early — Keep Full Accuracy

This is where the most marks quietly leak away on calculator papers. If you round an intermediate result and then carry on, your final answer can drift outside the accepted range.

Worked Example: the cost of early rounding

A circle has radius $4.7$4.7 cm. Work out its area, giving your answer to 1 decimal place. (Area $= \pi r^{2}$=πr2.)

Correct method — full accuracy throughout: $A = \pi \times 4.7^{2} = \pi \times 22.09 = 69.3977\ldots$A=π×4.72=π×22.09=69.3977…, which rounds to $69.4\text{ cm}^{2}$69.4 cm2. Answer: $69.4\text{ cm}^{2}$69.4 cm2.