MathematicsExam code: 0580
Using a Calculator
Number
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