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Exam questions · Maths · Calculator Skills

Using Your Calculator

  • 6 exam questions
  • 16 marks
  • 9 quick checks
  1. 1 Work out [2 marks]

    Work out \(\dfrac{5.6 + 3.2}{4.1 - 1.7}\). Give your answer correct to 3 significant figures. (2 marks)

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    Model answer

    \(\dfrac{8.8}{2.4} = 3.666\ldots = 3.67\) to 3 significant figures.

    Mark scheme

    • \(8.8\) and \(2.4\), or \(3.666\ldots\) — M1
    • \(3.67\) — A1
  2. 2 Work out [3 marks]

    Hana invests \(\pounds 1500\) for 4 years at 3% per year compound interest. Work out the total value of her investment at the end of 4 years. (3 marks)

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    Model answer

    \(1500 \times 1.03^4 = \pounds 1688.26\) to the nearest penny.

    Mark scheme

    • \(1.03^4\) or \(1500 \times 1.03\) repeated — M1
    • \(1500 \times 1.03^4\) — M1
    • \(1688.26\) — A1
  3. 3 Work out [2 marks]

    Work out \((3.2 \times 10^5) \times (4.5 \times 10^{-3})\). Give your answer in standard form. (2 marks)

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    Model answer

    \(3.2 \times 10^5 \times 4.5 \times 10^{-3} = 1440 = 1.44 \times 10^3\).

    Mark scheme

    • \(1440\) — M1
    • \(1.44 \times 10^3\) — A1
  4. 4 Work out [3 marks]

    \(ABC\) is a right-angled triangle with the right angle at \(B\). \(AB = 12\) cm and \(BC = 7\) cm. Work out the size of angle \(BAC\). Give your answer correct to 1 decimal place. (3 marks)

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    Model answer

    \(\tan BAC = \dfrac{7}{12}\), so angle \(BAC = \tan^{-1}\left(\dfrac{7}{12}\right) = 30.3^\circ\).

    Mark scheme

    • \(\tan BAC = \dfrac{7}{12}\) — M1
    • \(30.256\ldots\) — A1
    • \(30.3\) — A1
  5. 5 Work out [3 marks]

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

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    Model answer

    \(8.4^2 + 5.1^2 = 70.56 + 26.01 = 96.57\) and \(\sqrt{96.57} = 9.827\ldots = 9.83\).

    Mark scheme

    • \(70.56 + 26.01 = 96.57\) — M1
    • \(9.827\ldots\) — A1
    • \(9.83\) — A1
  6. 6 Work out [3 marks]

    A car travels 148 miles in 2 hours 45 minutes. Work out the average speed of the car in miles per hour. Give your answer correct to 1 decimal place. (3 marks)

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    Model answer

    2 hours 45 minutes is 2.75 hours. Average speed \(= \dfrac{148}{2.75} = 53.8\) mph.

    Mark scheme

    • \(2.75\) hours — M1
    • \(\dfrac{148}{2.75}\) — M1
    • \(53.8\) — A1

Quick check

  1. 1

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

    1. ARadians
    2. BDegrees
    3. CGradians
    4. DFractions
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    B: Degrees

    GCSE angles are measured in degrees.

  2. 2

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

    1. AEXP
    2. BThe subtract key
    3. CThe square root key
    4. DAns
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    A: EXP

    EXP enters the times ten to a power part.

  3. 3

    What does the Ans key do?

    1. AClears the calculator
    2. BFinds an angle
    3. CAdds brackets
    4. DRecalls the last answer
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    D: Recalls the last answer

    Ans holds the previous result.

  4. 4

    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\((5.6 + 3.2) \div (4.1 - 1.7)\)
    4. D\(5.6 + (3.2 \div 4.1) - 1.7\)
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    C: \((5.6 + 3.2) \div (4.1 - 1.7)\)

    Brackets are needed round both the top and the bottom.

  5. 5

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

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

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

  6. 6

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

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

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

  7. 7

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

    1. A13.5
    2. B9.82
    3. C96.6
    4. D9.83
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    D: 9.83

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

  8. 8

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

    1. ACalculators cannot round
    2. BIt uses more time
    3. CIt makes the final answer less accurate
    4. DIt is not allowed
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    C: It makes the final answer less accurate

    Rounding early builds up errors.

  9. 9

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

    1. A82.6 km/h
    2. B82.7 km/h
    3. C83.1 km/h
    4. D82.0 km/h
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    B: 82.7 km/h

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