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Exam questions · Maths · Number Without a Calculator

Place Value, Negatives and the Four Operations

  • 7 exam questions
  • 21 marks
  • 9 quick checks
  1. 1 Write [2 marks]

    Write these numbers in order of size. Start with the smallest. \(0.45\) \(0.405\) \(0.54\) \(0.045\)

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    Model answer

    \(0.045,\ 0.405,\ 0.45,\ 0.54\). Writing every number to three decimal places (0.450, 0.405, 0.540, 0.045) makes the comparison easy.

    Mark scheme

    • At least three of the numbers in the correct order, or all four written to 3 decimal places — M1
    • \(0.045, 0.405, 0.45, 0.54\) — A1
  2. 2 Work out [3 marks]

    Work out \(346 \times 27\). You must show all your working.

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    Model answer

    \(346 \times 20 = 6920\) and \(346 \times 7 = 2422\), so \(346 \times 27 = 6920 + 2422 = 9342\).

    Mark scheme

    • A complete method with at most one arithmetic error, such as \(346\times20\) and \(346\times7\), or a grid — M1
    • Adds their partial products — M1
    • 9342 — A1
  3. 3 Work out [2 marks]

    Work out \(8.4 \div 0.07\).

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    Model answer

    Multiply both numbers by 100 so the divisor is a whole number: \(840 \div 7 = 120\).

    Mark scheme

    • Converts to a whole-number division such as \(840 \div 7\) — M1
    • 120 — A1
  4. 4 Work out [3 marks]

    At midnight the temperature in Oslo was \(-7^\circ\text{C}\). By noon the temperature had risen by 12 degrees. (a) Work out the temperature at noon. (1 mark) At 6 pm the temperature had fallen by 11 degrees from its value at noon. (b) Work out the temperature at 6 pm. (2 marks)

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    Model answer

    (a) \(-7 + 12 = 5^\circ\text{C}\). (b) \(5 - 11 = -6^\circ\text{C}\).

    Mark scheme

    • (a) \(5^\circ\text{C}\) — B1
    • (b) Subtracts 11 from their noon temperature — M1
    • \(-6^\circ\text{C}\) — A1 (follow through from (a))
  5. 5 Work out [3 marks]

    Work out \((-3)^2 - 4 \times (-2) + 6 \div (-3)\).

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    Model answer

    \((-3)^2 = 9\), \(-4 \times (-2) = +8\) and \(6 \div (-3) = -2\), so the total is \(9 + 8 - 2 = 15\).

    Mark scheme

    • \((-3)^2 = 9\) — M1
    • At least one of \(-4 \times (-2) = 8\) or \(6 \div (-3) = -2\) — M1
    • 15 — A1
  6. 6 Show that [3 marks]

    Show that \(4.5 \times 0.8 + 2.4 \div 0.6 = 7.6\)

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    Model answer

    \(4.5 \times 0.8 = 3.6\) because \(45 \times 8 = 360\) with two decimal places. \(2.4 \div 0.6 = 24 \div 6 = 4\). Then \(3.6 + 4 = 7.6\), as required.

    Mark scheme

    • \(4.5 \times 0.8 = 3.6\) — M1
    • \(2.4 \div 0.6 = 4\) — M1
    • \(3.6 + 4 = 7.6\) with the conclusion stated — C1
  7. 7 Work out [5 marks]

    Hassan buys 15 boxes of pencils. Each box contains 24 pencils and costs \(\pounds 4.80\). (a) Work out the total number of pencils. (2 marks) (b) Work out the total cost of the 15 boxes. (3 marks)

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    Model answer

    (a) \(15 \times 24 = 360\) pencils. (b) \(15 \times 4.80 = 10 \times 4.80 + 5 \times 4.80 = 48 + 24 = \pounds 72\).

    Mark scheme

    • (a) \(15 \times 24\) or equivalent — M1
    • (a) 360 — A1
    • (b) A complete method, such as \(10 \times 4.80\) and \(5 \times 4.80\), or \(15 \times 480\) — M1
    • (b) Evaluates and gives a consistent decimal point — M1
    • (b) \(\pounds 72\) — 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.