1. Where a calculator is allowed
One paper with a calculator, one without
- Each candidate sits two papers of equal weight, one where calculators are not allowed and one where a scientific calculator is required: Paper 2 and Paper 4 on the Extended tier, Paper 1 and Paper 3 on the Core tier
- Half the assessment therefore rewards calculator fluency and half rewards written methods
- Any scientific model carries the functions needed, though the key sequences differ between makes, so the one taken into the exam should be the one practised on
- Older models sometimes take the number before the function rather than after it, which is worth confirming well before the exam
2. Settings to check
Before starting
- The angle unit must be set to degrees, since this specification works in degrees throughout
- Most calculators show a small D on the display when degrees are selected
- A mode that displays fractions and roots in their exact form is preferable, because it keeps answers exact until the moment a decimal is wanted
- A key marked S⇔D, or similar, switches a displayed answer between its exact and decimal forms
- Resetting the calculator before the exam restores every default and clears any setting changed for another subject
3. Entering values correctly
Converting before entering
- Quantities that are not decimal must be converted before they are typed in
- Time is the usual case, because minutes are sixtieths rather than hundredths
- 2 hours 30 minutes is entered as 2.5 hours
- 3 hours 20 minutes is entered as 3 ⅓ hours, since 20 minutes is a third of an hour
- Many calculators also have a degrees-minutes-seconds key, which allows hours and minutes to be entered directly
Using brackets
- Brackets are needed wherever the written layout does its own grouping
- A fraction line groups the whole numerator and the whole denominator, and a root sign groups everything beneath it
- (7 + 5) ÷ (9 − 3) must be typed with both brackets, or the calculator works out 7 + 5 ÷ 9 − 3, dividing only the 5 and only by the 9
- Negative numbers being squared need brackets, since without them the calculator squares first and applies the sign afterwards
Worked example
Evaluating a printed fraction to 3 significant figures
Work out the value of the fraction whose top line is √(14.6 − 2.3²) + 5.1 and whose bottom line is 2.7³ − 8.4, where the root sign covers only 14.6 − 2.3². Give your answer correct to 3 significant figures.
Solution:
- The fraction bar groups each line, so type the whole top and the whole bottom in brackets: (√(14.6 − 2.3²) + 5.1) ÷ (2.7³ − 8.4)
- Close the root's bracket where the root sign ends, straight after 2.3², so the + 5.1 stays outside the root
- As a check, the top is √9.31 + 5.1 = 3.0512… + 5.1 = 8.1512…, and the bottom is 19.683 − 8.4 = 11.283
- The calculator shows 0.722 434…
- The fourth significant figure is 4, so the third stays as it is: 0.722
- Without the brackets round the bottom line, the calculator works out 8.1512… ÷ 2.7³ − 8.4 = −7.99 (to 3 significant figures), nowhere near
Exam tip
Write the full display before you round
When a calculation asks for a stated accuracy, copy the full display onto your working line, then round. A wrong rounding still keeps one of the two marks if the correct longer value is written down, and even a mis-keyed value, written in full and rounded correctly, can earn a mark. A rounded answer on its own scores both marks or nothing.
Keys that save time
- The Ans key holds the previous result, so a calculation in stages continues without the last figure being retyped, and therefore without it being rounded
- The memory keys hold a value for use much later in the same question, which is what keeps full accuracy through a long chain of working
- The table function evaluates one expression at a whole list of x values at once, which fills in a table of values for a graph far faster than entering each substitution separately
- The π key keeps full accuracy, and a calculator with an exact display shows a multiple of π as it stands, so a result asked for in terms of π need not be turned into a decimal
4. Reading the display
The display is not always the answer
- A displayed figure has to be interpreted in the context the question set
- In money, a display of 7.5 means £7.50, because currency is written to two decimal places
- In time, a display of 1.75 means 1 hour 45 minutes, because 0.75 of an hour is 45 minutes
- Reading 1.75 as "1 hour 75 minutes" is the error this warns against
- A display in standard form, shown with a small exponent, must be written out properly rather than copied with the calculator's own notation
5. Rounding and accuracy
Round once, at the end
- Values are never rounded partway through a calculation: the full display is carried forward and only the final answer is rounded
- Rounding early shifts the final figure, and the more steps that follow, the larger the shift
- Where a value is needed again later, recall it from the calculator's memory rather than retyping a rounded version
Worked example
The cost of rounding too early
Work out 2/3 of 285, first exactly and then using 0.67 in place of the fraction. Compare the results.
Solution:
- Keeping the fraction exact: 285 × 2 ÷ 3 = 190
- Replacing 2/3 with the rounded 0.67: 285 × 0.67 = 190.95
- The rounded version is out by almost a whole unit, from a rounding that looked harmless
- Entering the fraction itself, rather than a decimal approximation of it, avoids this entirely
Worked example
Showing a value is correct to a given accuracy
£1600 is invested at 1.8% per year compound interest. Show that its value after 7 years is £1813, correct to the nearest pound.
Solution:
- A 1.8% increase each year is a multiplier of 1.018
- The value after 7 years is 1600 × 1.018⁷ = 1812.818…
- Write the value to more figures than the printed one: £1812.82, which is £1813 to the nearest pound
- Writing only £1813 would show nothing, because that is the value you were given
- Rounding 1.018⁷ = 1.1330… to 1.13 first gives 1600 × 1.13 = £1808, which does not round to £1813, so carry the full display
- If a later part needs this value, start from the printed £1813