OpenRevise

Exam questions · Maths

Calculator Skills

  • 6 exam questions
  • 16 marks
  • 9 quick checks

Using Your Calculator

Just this lesson
  1. 1 Calculate [2 marks]

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

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    Model answer

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

    Mark scheme

    • \(13\) and \(3.3\), or \(3.939\ldots\) — M1
    • \(3.94\) — A1
  2. 2 Calculate [3 marks]

    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]

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    Model answer

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

    Mark scheme

    • \(1.018^6\) — M1
    • \(3200 \times 1.018^6\) — M1
    • \(3561.53\) — A1
  3. 3 Calculate [2 marks]

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

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    Model answer

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

    Mark scheme

    • \(40\,500\) — M1
    • \(4.05 \times 10^4\) — A1
  4. 4 Calculate [3 marks]

    \(XYZ\) 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]

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    Model answer

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

    Mark scheme

    • \(\cos YXZ = \dfrac{8}{13}\) — M1
    • \(52.020\ldots\) — A1
    • \(52.0\) — A1
  5. 5 Calculate [3 marks]

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

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    Model answer

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

    Mark scheme

    • \(84.64 - 30.25 = 54.39\) — M1
    • \(7.374\ldots\) — A1
    • \(7.37\) — A1
  6. 6 Calculate [3 marks]

    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]

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    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.

    Mark scheme

    • \(2\dfrac{2}{3}\) hours or \(2.666\ldots\) — M1
    • \(\dfrac{126}{2.666\ldots}\) — M1
    • \(47.3\) — 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 \(215 \div 2.6 = 82.69\ldots\).