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Maths · Calculator Skills

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Using Your Calculator

Setting the calculator up, entering calculations in the right order, and using the power, standard form and inverse trigonometry keys.

  • 9 key terms
  • All boards

Learning Objectives

  1. 1Check the calculator is set up correctly before an exam.
  2. 2Use brackets, powers, roots and fractions keys to enter calculations in the right order.
  3. 3Enter numbers in standard form and use the inverse trigonometric functions.
  4. 4Round only at the end, and keep full calculator values in between.

A tool you need to use well

On a calculator paper, a calculator saves time but it does not do the thinking. Most lost marks are caused by entering a calculation in the wrong order, by rounding too early, or by having the calculator in the wrong mode. A few minutes learning how your own model works is a good use of revision time. The keys named here are on every scientific calculator allowed in GCSE exams, but the labels can differ slightly, so check yours with the examples.

Before you start

Two checks save marks.

  • Angle mode

    The calculator must be in degrees for trigonometry. A small D or DEG shows on the screen.

  • Clear it

    Clear any memory or old answers, so that Ans does not carry something unexpected into a new question.

  • Fresh batteries

    Check that the display is clear and that the calculator is not in a strange mode, such as fractions where you expected decimals.

  • Know your model

    Using the same calculator in the exam as in revision avoids surprises.

Order of working and brackets

The calculator follows the order of operations, but only if you enter the calculation correctly.

  • Fractions

    For \(\dfrac{5.6 + 3.2}{4.1 - 1.7}\), put brackets round the top and the bottom: \((5.6 + 3.2) \div (4.1 - 1.7)\).

  • Powers

    \(1500 \times 1.03^4\) works out the power first, then multiplies.

  • Roots

    Use the root key with the whole expression inside the brackets, such as \(\sqrt{(8.4^2 + 5.1^2)}\).

  • Check

    Estimate the answer first, so that a slip is spotted.

A calculation with brackets

Work out \(\dfrac{5.6 + 3.2}{4.1 - 1.7}\). Give your answer to 3 significant figures.

Show the solutionHide the solution
  1. 1 Top \(5.6 + 3.2 = 8.8\).
  2. 2 Bottom \(4.1 - 1.7 = 2.4\).
  3. 3 Divide \(8.8 \div 2.4 = 3.666\ldots\).
  4. 4 Round 3.67 to 3 significant figures.

Answer3.67

Powers, standard form and trigonometry

These need particular keys, and are the usual places to go wrong.

  • Compound interest

    \(1500 \times 1.03^4 = 1688.26\ldots\), so the total value is \(\pounds 1688.26\).

  • Standard form

    Use EXP: \(3.2\) EXP \(5\) enters \(3.2 \times 10^5\). Do not type \(\times 10\) then the power separately.

  • Finding an angle

    If \(\tan\theta = \dfrac{7}{12}\), use SHIFT then tan: \(\theta = \tan^{-1}\left(\dfrac{7}{12}\right) = 30.3^\circ\).

  • Finding a side

    If \(\sin 40^\circ = \dfrac{x}{9}\), then \(x = 9\sin 40^\circ = 5.78\ldots\).

Standard form and an angle

(a) Work out \((3.2 \times 10^5) \times (4.5 \times 10^{-3})\), giving your answer in standard form. (b) In a right-angled triangle the side opposite angle \(\theta\) is 7 cm and the adjacent side is 12 cm. Work out \(\theta\) to 1 decimal place.

Show the solutionHide the solution
  1. 1 Standard form The calculator gives 1440, which is \(1.44 \times 10^3\).
  2. 2 Choose the ratio Opposite and adjacent, so use tangent: \(\tan\theta = \dfrac{7}{12}\).
  3. 3 Inverse \(\theta = \tan^{-1}\left(\dfrac{7}{12}\right) = 30.256\ldots\).
  4. 4 Round \(30.3^\circ\) to 1 decimal place.

Answer(a) \(1.44 \times 10^3\). (b) \(30.3^\circ\)

Test yourself

  1. 1

    What mode must the calculator be in for trigonometry?

    Show answerHide answer

    Degrees.

  2. 2

    Which key enters a number in standard form?

    Show answerHide answer

    EXP, or the times ten to a power key.

  3. 3

    Why do you use brackets on a fraction?

    Show answerHide answer

    So the top and bottom are each worked out before dividing.

  4. 4

    When should you round?

    Show answerHide answer

    At the end, not between steps.

  5. 5

    What does Ans do?

    Show answerHide answer

    Recalls the previous answer.

Exam technique: calculator papers

Show your working as well as the answer.

  • Write the calculation

    Write down what you entered, such as \(1500 \times 1.03^4\), so that you can earn method marks even if you slip.

  • Do not round early

    Keep the full display, or use Ans, and round only the final answer.

  • Check sense

    Does the answer make sense, for example is a length shorter than the hypotenuse?

  • Give the accuracy asked

    Write the answer to the number of decimal places or significant figures that the question asks for.

Summary and exam focus

  • Check the calculator is in degree mode and that it is cleared.
  • Use brackets, the power key and the fraction key carefully.
  • Use EXP for standard form, and SHIFT with sin, cos or tan to find angles.
  • Write your working and round only at the end.

Exam focus

Work out \(\sqrt{8.4^2 + 5.1^2}\). Give your answer correct to 3 significant figures. (2 marks) (2 marks)

\(8.4^2 + 5.1^2 = 70.56 + 26.01 = 96.57\), and \(\sqrt{96.57} = 9.827\ldots\), which is 9.83 to 3 significant figures. Write the unrounded value first.

Key terms

The words this lesson expects you to use. Each one is linked from the first place it appears above.

Calculator mode
The setting that decides how the calculator works, such as degrees.
Brackets
Symbols that show which part of a calculation is worked out first.
Standard form
A way to write numbers as \(a \times 10^n\) with \(1 \le a < 10\).
Inverse function
A function that reverses another, such as \(\tan^{-1}\).
Significant figures
The digits of a number that carry meaning, counted from the first non-zero digit.
Decimal places
The digits after the decimal point.
Compound interest
Interest that is added to the amount, so that it also earns interest.
Estimate
An approximate answer, found by rounding.
Display
The screen of the calculator.

Questions and answers

15 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question Calculate 2 marks Easier

Calculate \(\dfrac{8.3 + 4.7}{3.9 - 0.6}\). Give your answer correct to 3 significant figures. [2 marks]

Mark scheme — 2 marks available

  • \(13\) and \(3.3\), or \(3.939\ldots\) — M1
  • \(3.94\) — A1

Model answer

\(\dfrac{13}{3.3} = 3.939\ldots = 3.94\) to 3 significant figures.

2. Exam question Calculate 3 marks Core

Mia invests \(\pounds 3200\) for 6 years at 1.8% per year compound interest. Calculate the total value of her investment at the end of 6 years. Give your answer to the nearest penny. [3 marks]

Mark scheme — 3 marks available

  • \(1.018^6\) — M1
  • \(3200 \times 1.018^6\) — M1
  • \(3561.53\) — A1

Model answer

\(3200 \times 1.018^6 = \pounds 3561.53\).

3. Exam question Calculate 2 marks Core

Calculate \((8.1 \times 10^{-3}) \times (5 \times 10^6)\). Give your answer in standard form. [2 marks]

Mark scheme — 2 marks available

  • \(40\,500\) — M1
  • \(4.05 \times 10^4\) — A1

Model answer

\(8.1 \times 10^{-3} \times 5 \times 10^6 = 40\,500 = 4.05 \times 10^4\).

4. Exam question Calculate 3 marks Core

\(XYZ\) is a right-angled triangle with the right angle at \(Z\). \(XY = 13\) cm and \(XZ = 8\) cm. Calculate the size of angle \(YXZ\). Give your answer correct to 1 decimal place. [3 marks]

Mark scheme — 3 marks available

  • \(\cos YXZ = \dfrac{8}{13}\) — M1
  • \(52.020\ldots\) — A1
  • \(52.0\) — A1

Model answer

\(\cos YXZ = \dfrac{8}{13}\), so angle \(YXZ = \cos^{-1}\left(\dfrac{8}{13}\right) = 52.0^\circ\).

5. Exam question Calculate 3 marks Stretch

Calculate \(\sqrt{9.2^2 - 5.5^2}\). Give your answer correct to 3 significant figures. [3 marks]

Mark scheme — 3 marks available

  • \(84.64 - 30.25 = 54.39\) — M1
  • \(7.374\ldots\) — A1
  • \(7.37\) — A1

Model answer

\(9.2^2 - 5.5^2 = 84.64 - 30.25 = 54.39\) and \(\sqrt{54.39} = 7.374\ldots = 7.37\).

6. Exam question Calculate 3 marks Stretch

A cyclist rides 126 miles in 2 hours 40 minutes. Calculate the average speed in miles per hour. Give your answer correct to 1 decimal place. [3 marks]

Mark scheme — 3 marks available

  • \(2\dfrac{2}{3}\) hours or \(2.666\ldots\) — M1
  • \(\dfrac{126}{2.666\ldots}\) — M1
  • \(47.3\) — A1

Model answer

2 hours 40 minutes is \(2\dfrac{2}{3}\) hours. Average speed \(= \dfrac{126}{2\frac{2}{3}} = 47.25 = 47.3\) mph.

7. Multiple choice 1 mark Easier

Which mode must a calculator be in to find angles in a GCSE trigonometry question?

  1. A Radians
  2. B Degrees Correct
  3. C Gradians
  4. D Fractions

Why: GCSE angles are measured in degrees.

8. Multiple choice 1 mark Easier

Which key do you use to enter \(3.2 \times 10^5\)?

  1. A EXP Correct
  2. B The subtract key
  3. C The square root key
  4. D Ans

Why: EXP enters the times ten to a power part.

9. Multiple choice 1 mark Easier

What does the Ans key do?

  1. A Clears the calculator
  2. B Finds an angle
  3. C Adds brackets
  4. D Recalls the last answer Correct

Why: Ans holds the previous result.

10. Multiple choice 1 mark Core

What should you type to work out \(\dfrac{5.6 + 3.2}{4.1 - 1.7}\)?

  1. A \(5.6 + 3.2 \div 4.1 - 1.7\)
  2. B \((5.6 + 3.2) \div 4.1 - 1.7\)
  3. C \((5.6 + 3.2) \div (4.1 - 1.7)\) Correct
  4. D \(5.6 + (3.2 \div 4.1) - 1.7\)

Why: Brackets are needed round both the top and the bottom.

11. Multiple choice 1 mark Core

What is \(1500 \times 1.03^4\) to the nearest penny?

  1. A \(\pounds 1680.00\)
  2. B \(\pounds 1688.26\) Correct
  3. C \(\pounds 1688.00\)
  4. D \(\pounds 1695.75\)

Why: \(1.03^4 = 1.1255\ldots\), and \(1500 \times 1.1255\ldots = 1688.26\ldots\).

12. Multiple choice 1 mark Core

\(\tan\theta = \dfrac{7}{12}\). What is \(\theta\) to 1 decimal place?

  1. A \(30.3^\circ\) Correct
  2. B \(0.6^\circ\)
  3. C \(59.7^\circ\)
  4. D \(35.0^\circ\)

Why: \(\theta = \tan^{-1}\left(\dfrac{7}{12}\right) = 30.256\ldots\).

13. Multiple choice 1 mark Core

What is \(\sqrt{8.4^2 + 5.1^2}\) to 3 significant figures?

  1. A 13.5
  2. B 9.82
  3. C 96.6
  4. D 9.83 Correct

Why: \(8.4^2 + 5.1^2 = 96.57\) and \(\sqrt{96.57} = 9.827\ldots\).

14. Multiple choice 1 mark Stretch

Why should you avoid rounding in the middle of a calculation?

  1. A Calculators cannot round
  2. B It uses more time
  3. C It makes the final answer less accurate Correct
  4. D It is not allowed

Why: Rounding early builds up errors.

15. Multiple choice 1 mark Stretch

A train travels 215 km in 2 hours 36 minutes. What is its average speed to 1 decimal place?

  1. A 82.6 km/h
  2. B 82.7 km/h Correct
  3. C 83.1 km/h
  4. D 82.0 km/h

Why: 2 hours 36 minutes is 2.6 hours, and \(215 \div 2.6 = 82.69\ldots\).