Every other maths page on this site is deliberately non-calculator, because Paper 2 is non-calculator and Paper 2 is half your grade. That was the right call, and it left exactly one sub-topic on the whole Extended syllabus with nothing behind it: E1.14 — use a calculator efficiently, apply appropriate checks of accuracy. This page is that sub-topic and nothing else.
It is Paper 4 insurance. Paper 4 gives you a calculator, and a calculator does not make the paper easier — it makes it possible to be wrong very quickly and very confidently. Nearly every mark lost to a calculator is lost in one of four ways: a missing bracket, the wrong angle mode, an intermediate value rounded too early, or an answer nobody stopped to look at. All four are below.
That is the standard school scientific calculator: the fx-83GT (battery) and the fx-85GT (solar) are the same machine. The GT PLUS, GT X and CW versions all do everything on this page, and the Casio fx-991 behaves the same way too.
If yours is a different model — a Sharp, a Texas Instruments, an older Casio — the mathematics on this page is identical and only the labels move. So wherever a key matters, I have said what the key does as well as what it is called, and you can find your equivalent in about ten seconds by trying it.
One real difference worth knowing. On the newest ClassWiz CW models the single S⇔D key has been folded into a FORMAT menu instead, and the setup screen is reached through a SETTINGS menu rather than SHIFT SETUP. Same two jobs, one extra keypress. If a keystroke below does not exist on your machine, that is why — look for the menu instead.
| Key | What it actually does | Where it costs marks |
|---|---|---|
| ( ) | Forces the calculator to do that bit first | Denominators, anything under a root, anything inside sin/cos/tan |
| a b/c or the stacked-fraction key | Enters an exact fraction | Stops rounding drift dead |
| S⇔D | Swaps the display between exact form and decimal | The exam usually wants the decimal, to 3 s.f. |
| Ans | The previous answer, to full internal accuracy | The single biggest defence against early rounding |
| STO / RCL | Parks a value in a letter and gets it back | Multi-part questions that reuse one number |
| ×10x (older: EXP) | Builds a standard-form number as one piece | Standard form arithmetic |
| (−) | A negative sign, not a subtraction | Negative indices, negative coordinates, cos of an obtuse angle |
| x−1 | One divided by whatever is in front of it | Inverse proportion, 1/x tables |
(−)3 x² and you get 9. Type
−3 x² and you get −9, because the calculator squares the 3 first and
then makes it negative — which is correct order of operations, and almost never what you meant.A scientific calculator obeys BIDMAS exactly. It never guesses what you meant. Everything in this section is the same one mistake: you wrote a formula with a fraction bar or a root sign or a function, and those three all act as invisible brackets on paper — but the keyboard has no invisible brackets, so you have to type them.
sin 30 + 40 =
sin ( 30 + 40 ) =
√9 + 16 gives 19.
√(9 + 16) gives 5. Those are not near-misses; they are unrelated numbers.On paper you write a fraction bar and the whole bottom is underneath it. On the keyboard, division only applies to the very next thing.
12 ÷ 3 × 4 =
12 ÷ ( 3 × 4 ) =
7 + √25 ÷ 2 × 2 gives 7 + (5÷2)×2 = 12. You would write down
12 instead of 3, with no warning of any kind, because 12 is a perfectly reasonable-looking number.
This is why the estimate in section 7 exists.| Typed | Calculator gives | Why |
|---|---|---|
−4 x² | −16 | Powers before the sign. It squares 4, then negates. |
( (−)4 ) x² | 16 | The bracket ties the sign to the 4 before squaring. |
(−)4 x² | −16 on most models | Do not rely on this. Use the bracket every time. |
12 ÷ 3 × 4 =. What does it show?sin 30 + 40 = display?−4 x², typed exactly like that?√9 + 16 = give? (No bracket after the root.)Your calculator has two ways of holding a number: exactly (as a fraction, a surd, or a multiple of π) and as a decimal. Exact never loses anything. A decimal on the screen has already been cut off at ten digits, and every time you write one down and retype it, you cut it off again. Stay exact until the very last line.
The rubric on the front of Paper 4 tells you to give non-exact answers correct to three significant figures, and angles in degrees to one decimal place. It says nothing about the middle of your working — because you are not supposed to round in the middle at all.
Method marks survive a rounded intermediate. The accuracy mark does not, because the accuracy mark is for the final number, and a final number built out of rounded pieces is a different number.
| Method | How | Use it when |
|---|---|---|
| Ans | Just press Ans where the number should go, or start the next line with an operation and the calculator inserts Ans for you | The very next calculation. Simplest and safest. |
| STO | SHIFT STO then a letter, for example A. The value is parked in A. | You will need the number again two or three parts later. |
| RCL | RCL then the letter, or just press ALPHA A inside a calculation | Getting a parked value back, to full accuracy. |
… × A and it is exact. Write down the 3 s.f. value for the answer line, and use
the stored one for the arithmetic. Those are two different jobs.A scientific calculator can measure angles in three different units. Only one of them is on the 0580 syllabus. If the mode is wrong, every trigonometry answer on the paper is wrong, the working looks perfect, and you lose the accuracy marks on all of them.
| Mode | Display shows | What sin 30 gives | Meaning |
|---|---|---|---|
| Degrees | D | 0.5 | The one you want. Always. |
| Radians | R | −0.9880316241 | It read 30 radians, which is nearly five whole turns. |
| Gradians | G | 0.4539904997 | 400 to a full turn. Nobody uses these. |
sin 30 =. If it says 0.5, you are in degrees and you can forget about it for two
hours. If it says anything else, fix the mode now. This is the cheapest mark-protection on the
whole paper.tan 90 is undefined and the calculator says
Math ERROR. In radians it happily returns −1.9952, because 90 radians is not a right angle.
So tan 90 is a second, even faster mode check — an error message is the correct
result.sin 30 = and the screen shows −0.988. Ignore the mode for a moment: what should the answer have been?| You want | Press | Watch out for |
|---|---|---|
| 5² | 5 x² | — |
| 5³ | 5 x³ | — |
| 57 | 5 ^ 7 | Press → to come back down out of the exponent before typing anything else |
| 5−2 | 5 ^ (−) 2 | The sign key, not the subtract key |
| √40 | √ 40 | Bracket it if there is a sum underneath |
| 3√40 | SHIFT √ 40 | Different key from the square root |
| 5√40 | 5 SHIFT ^ 40 | The index goes first on this one |
| 1⁄8 | 8 x−1 | Faster than typing 1 ÷ 8, and it chains |
| 3.6 × 107 | 3.6 ×10x 7 | Not 3.6 × 10 ^ 7 unless you bracket it |
| 3.6 × 10−7 | 3.6 ×10x (−) 7 | Sign key again |
× 10 ^ n instead, the × and the ÷ around it
fight for precedence and you get the wrong answer — see the worked example below. Use the key. If
you ever do use ^, bracket the entire number.When a number is too big or too small for the screen, the calculator switches to its own shorthand. That shorthand is not an acceptable way to write an answer.
| Screen shows | The number is | Write it as |
|---|---|---|
3.2×10−5 or 3.2−05 or 3.2E−05 | 0.000032 | 3.2 × 10−5 |
1.44×1012 | 1 440 000 000 000 | 1.44 × 1012 |
3.2E−5 or 3.2−05 on the answer
line. That is calculator notation, not mathematics, and it scores nothing. Copy it out properly as
3.2 × 10−5. Also check the front: standard form means
1 ≤ a < 10, so 32 × 10−6 is the right value written the wrong way and
still loses the mark.E1.14 is not only use a calculator. It is use a calculator and apply appropriate checks of accuracy. Cambridge sets whole questions on this, and it is also the only defence you have against a mistyped keystroke, because a calculator will never tell you that your answer is absurd.
Round each number to 1 significant figure, work out the easy version by hand, and compare. You are not checking the digits — you are checking that the answer is roughly the right size. If the estimate says about 1 and the calculator says 12, you have found a missing bracket.
Do the estimate before you use the calculator, not after. Afterwards you already believe the answer, and the estimate stops being independent.
| Ask | Because |
|---|---|
| Is it the right size? | Compare against your 1 s.f. estimate. Out by a factor of 10, 100 or 1000 nearly always means a bracket or a power. |
| Is the sign right? | Lengths, areas, volumes, times and probabilities are never negative. A negative one of those means a sign error, and sign errors are your recurring mistake. |
| Is it possible in the story? | A probability above 1. An angle in a triangle above 180°. A percentage decrease over 100%. A hypotenuse shorter than a leg. A fraction of a bag over a whole bag. |
| Does it fit the picture? | On a diagram, the largest side is opposite the largest angle. If your answer contradicts the sketch, believe the sketch. |
Give non-exact answers correct to three significant figures, unless the question says otherwise. Give angles in degrees to one decimal place. For π, use the calculator value or 3.142 — never 3.14, and never 22/7 unless a question hands it to you.
That rubric is on every paper and almost nobody reads it. Two marks a paper live there.
| Situation | Give | Example |
|---|---|---|
| Ordinary non-exact answer | 3 significant figures | 15.8533… → 15.9 |
| An angle in degrees | 1 decimal place | 60.2551… → 60.3° |
| Money | 2 decimal places | $3159.2484 → $3159.25 |
| The question specifies | Whatever it says, always | “to the nearest metre” means the nearest metre |
| An exact answer is possible | Leave it exact | “in terms of π”, “in surd form”, a whole number, a fraction |
| Anywhere in the middle | Do not round at all | Use Ans or STO |
Start counting from the first non-zero digit. Zeros before that are placeholders and do not count. Zeros after it do.
| Number | To 3 s.f. | Why |
|---|---|---|
| 0.004056 | 0.00406 | Counting starts at the 4. The 5 rounds the 5 up to 6. |
| 2.7481 | 2.75 | Third figure is the 4; the 8 after it rounds it up. |
| 15 962 | 16 000 | The trailing zeros are placeholders. 160 would be a different number. |
| 0.09996 | 0.100 | Rounding up carries all the way. Keep both zeros — they show the accuracy. |
The display only shows a decimal. When the answer is a time or money, you have to turn that decimal into the form the answer line wants.
| display | it means | write |
|---|---|---|
| 3.25 (hours) | 3 hours + 0.25 × 60 minutes | 3 h 15 min |
| 2.35 (hours) | 2 hours + 0.35 × 60 = 21 minutes | 2 h 21 min |
| 0.75 (hours) | 0.75 × 60 = 45 minutes | 45 min |
| 4.8 (dollars) | four dollars and eighty cents | $4.80 |
| 12.5 (dollars) | twelve dollars and fifty cents | $12.50 |
Ten Paper 4 style questions, deliberately not labelled by section. Every one of them can be got wrong by a calculator on its own. For each: estimate first, then type it, then check the size of what came back. Answers to 3 significant figures unless the question says otherwise.
Paper 2 is two hours, 100 marks, non-calculator, and 50% of your final grade. Everything on this page is worth nothing in that room. Not less — nothing.
So be clear about what this page is. It is insurance on Paper 4: it stops you throwing away marks you had already earned, through a missing bracket or a wrong mode or a value rounded one line too early. It is not a way of getting better at maths, and it cannot substitute for a single one of the other pages in this section.
There is also a quieter risk. A calculator is very good at letting you do a question without ever understanding it — the keys give you a number, the number goes on the line, and nothing was learned. That is fine for Paper 4 and fatal for Paper 2, where the same topic comes back and you have to do it by hand. If you find yourself reaching for the calculator during ordinary practice, that is the signal to put it down, not a sign you need it.
| Paper 2 | Paper 4 | |
|---|---|---|
| Calculator | Not allowed | Scientific calculator |
| Time | 2 hours | 2 hours |
| Marks | 100 | 100 |
| Share of the grade | 50% | 50% |
| What this page is worth | Nothing | Several marks |