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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 \(\dfrac{6.4 + 2.9}{5.1 - 1.8}\). Give your answer correct to 3 significant figures. [2 marks]

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    Model answer

    \(\dfrac{9.3}{3.3} = 2.818\ldots = 2.82\) to 3 significant figures.

    Mark scheme

    • \(9.3\) and \(3.3\), or \(2.818\ldots\) — M1
    • \(2.82\) — A1
  2. 2 Work out [3 marks]

    Jon invests \(\pounds 2400\) for 5 years at 2.5% per year compound interest. Work out the total value of his investment at the end of 5 years. Give your answer to the nearest penny. [3 marks]

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    Model answer

    \(2400 \times 1.025^5 = \pounds 2715.38\).

    Mark scheme

    • \(1.025^5\) — M1
    • \(2400 \times 1.025^5\) — M1
    • \(2715.38\) — A1
  3. 3 Work out [2 marks]

    Work out \((6.5 \times 10^4) \times (2.4 \times 10^{-2})\). Give your answer in standard form. [2 marks]

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    Model answer

    \(6.5 \times 10^4 \times 2.4 \times 10^{-2} = 1560 = 1.56 \times 10^3\).

    Mark scheme

    • \(1560\) — M1
    • \(1.56 \times 10^3\) — A1
  4. 4 Work out [3 marks]

    \(PQR\) is a right-angled triangle with the right angle at \(R\). \(PQ = 15\) cm and \(QR = 9\) cm. Work out the size of angle \(QPR\). Give your answer correct to 1 decimal place. [3 marks]

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    Model answer

    \(\sin QPR = \dfrac{9}{15}\), so angle \(QPR = \sin^{-1}\left(\dfrac{9}{15}\right) = 36.9^\circ\).

    Mark scheme

    • \(\sin QPR = \dfrac{9}{15}\) — M1
    • \(36.869\ldots\) — A1
    • \(36.9\) — A1
  5. 5 Work out [3 marks]

    Work out \(\sqrt{6.3^2 + 4.8^2}\). Give your answer correct to 3 significant figures. [3 marks]

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    Model answer

    \(6.3^2 + 4.8^2 = 39.69 + 23.04 = 62.73\) and \(\sqrt{62.73} = 7.920\ldots = 7.92\).

    Mark scheme

    • \(39.69 + 23.04 = 62.73\) — M1
    • \(7.920\ldots\) — A1
    • \(7.92\) — A1
  6. 6 Work out [3 marks]

    A train travels 215 km in 2 hours 36 minutes. Work out the average speed of the train in kilometres per hour. Give your answer correct to 1 decimal place. [3 marks]

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    Model answer

    2 hours 36 minutes is 2.6 hours. Average speed \(= \dfrac{215}{2.6} = 82.7\) km/h.

    Mark scheme

    • \(2.6\) hours — M1
    • \(\dfrac{215}{2.6}\) — M1
    • \(82.7\) — 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 \(215 \div 2.6 = 82.69\ldots\).