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Exam questions · Maths · Number Without a Calculator

Place Value, Negatives and the Four Operations

  • 7 exam questions
  • 20 marks
  • 9 quick checks
  1. 1 Put [2 marks]

    Put these numbers in order, smallest first. \(0.3\) \(0.29\) \(0.302\) \(0.0399\)

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    Model answer

    Writing each number to four decimal places gives \(0.3000\), \(0.2900\), \(0.3020\) and \(0.0399\). The order is \(0.0399,\ 0.29,\ 0.3,\ 0.302\).

    Mark scheme

    • At least three numbers in the correct relative order, or all written to the same number of decimal places — M1
    • \(0.0399, 0.29, 0.3, 0.302\) — A1
  2. 2 Work out [3 marks]

    Work out \(408 \times 53\).

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    Model answer

    \(408 \times 50 = 20\,400\) and \(408 \times 3 = 1224\). Adding gives \(20\,400 + 1224 = 21\,624\).

    Mark scheme

    • A complete method, such as \(408\times50\) and \(408\times3\), or a grid or column method, with at most one error — M1
    • Adds their partial products — M1
    • 21624 — A1
  3. 3 Work out [3 marks]

    (a) Work out \(15.6 \div 0.4\). [2 marks] (b) Work out \(0.2 \times 0.03\). [1 mark]

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    Model answer

    (a) Multiply both numbers by 10: \(156 \div 4 = 39\). (b) \(2 \times 3 = 6\), and there are 3 decimal places in total, so \(0.006\).

    Mark scheme

    • (a) \(156 \div 4\) or equivalent — M1
    • (a) 39 — A1
    • (b) 0.006 — B1
  4. 4 Work out [3 marks]

    Source: Lowest temperature: Aberdeen \(-5^\circ\text{C}\), Bath \(3^\circ\text{C}\), Cardiff \(-12^\circ\text{C}\), Derby \(0^\circ\text{C}\). The table shows the lowest temperature in four towns one night. (a) Write the four temperatures in order, starting with the lowest. [1 mark] (b) Work out the difference between the highest and the lowest of the temperatures. [1 mark] The temperature in Bath then falls by \(8^\circ\text{C}\). (c) Work out the new temperature in Bath. [1 mark]

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    Model answer

    (a) \(-12,\ -5,\ 0,\ 3\). (b) \(3 - (-12) = 15^\circ\text{C}\). (c) \(3 - 8 = -5^\circ\text{C}\).

    Mark scheme

    • (a) \(-12, -5, 0, 3\) in this order — B1
    • (b) \(15^\circ\text{C}\) — B1
    • (c) \(-5^\circ\text{C}\) — B1
  5. 5 Work out [3 marks]

    Work out \(2 \times (-3)^2 - 18 \div (-3)\).

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    Model answer

    \((-3)^2 = 9\), so \(2 \times 9 = 18\). \(18 \div (-3) = -6\), so \(18 - (-6) = 18 + 6 = 24\).

    Mark scheme

    • \((-3)^2 = 9\) or \(2 \times 9 = 18\) — M1
    • \(18 \div (-3) = -6\) — M1
    • 24 — A1
  6. 6 Show that [3 marks]

    Show that \(6 + 4 \times 2.5 \div 0.5 = 26\).

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    Model answer

    Multiplication and division come before addition, working from left to right: \(4 \times 2.5 = 10\), then \(10 \div 0.5 = 20\), then \(6 + 20 = 26\).

    Mark scheme

    • \(4 \times 2.5 = 10\) — M1
    • \(10 \div 0.5 = 20\) — M1
    • \(6 + 20 = 26\) with the conclusion shown — A1
  7. 7 Work out [3 marks]

    A school hall has 24 rows of 32 chairs. In every row, 3 chairs are reserved for teachers. How many chairs are not reserved?

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    Model answer

    Each row has \(32 - 3 = 29\) chairs that are not reserved. So the total is \(24 \times 29 = 24 \times 30 - 24 = 720 - 24 = 696\).

    Mark scheme

    • \(32 - 3 = 29\) or \(24 \times 3 = 72\) — M1
    • \(24 \times 29\) or \(24 \times 32 = 768\) — M1
    • 696 — A1

Quick check

  1. 1

    Estimate \(38 \times 21\) by rounding each number to 1 significant figure.

    1. A600
    2. B80
    3. C1000
    4. D800
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    D: 800

    \(38 \approx 40\) and \(21 \approx 20\), so the estimate is \(40 \times 20 = 800\).

  2. 2

    Tickets cost £8.50 each. How many tickets can be bought with £60?

    1. A7
    2. B8
    3. C6
    4. D70
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    A: 7

    \(8.50 \times 7 = 59.50\), which fits, and \(8.50 \times 8 = 68\), which does not.

  3. 3

    What is the value of the digit 7 in the number 4.073?

    1. A70
    2. B7 hundredths
    3. C7 tenths
    4. D7 thousandths
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    B: 7 hundredths

    The 7 is in the second column after the decimal point, so it is worth 7 hundredths.

  4. 4

    Which of these decimals is the largest?

    1. A0.75
    2. B0.809
    3. C0.098
    4. D0.8
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    B: 0.809

    Writing each to 3 decimal places gives 0.800, 0.750, 0.809 and 0.098, so 0.809 is largest.

  5. 5

    What is 6.4 ÷ 100?

    1. A0.064
    2. B0.64
    3. C0.0064
    4. D640
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    A: 0.064

    Dividing by 100 moves every digit two columns to the right, giving 0.064.

  6. 6

    Work out \(-3 - (-7)\).

    1. A\(10\)
    2. B\(4\)
    3. C\(-10\)
    4. D\(-4\)
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    B: \(4\)

    Subtracting a negative is the same as adding: \(-3 + 7 = 4\).

  7. 7

    Work out \((-6) \times 3 \div (-2)\).

    1. A\(-36\)
    2. B\(-9\)
    3. C\(9\)
    4. D\(36\)
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    C: \(9\)

    \((-6)\times 3 = -18\), then \(-18 \div (-2) = 9\) because the signs are the same.

  8. 8

    Work out \(2 + 3 \times 4^2\).

    1. A\(196\)
    2. B\(22\)
    3. C\(50\)
    4. D\(80\)
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    C: \(50\)

    Indices first: \(4^2 = 16\). Then multiply: \(3 \times 16 = 48\). Then add: \(2 + 48 = 50\).

  9. 9

    Work out \(0.3 \times 0.2\).

    1. A0.06
    2. B0.006
    3. C0.5
    4. D0.6
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    A: 0.06

    \(3 \times 2 = 6\) and there are 2 decimal places in total, so the answer is 0.06.