Exam questions · Maths · Number Without a Calculator
Place Value, Negatives and the Four Operations
- 7 exam questions
- 16 marks
- 9 quick checks
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1 Write down [1 mark]
Write down the value of the digit 6 in the number \(28.065\).
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Model answer
The 6 is in the second column after the decimal point, so it is worth 6 hundredths, which is \(0.06\).
Mark scheme
- 0.06 or six hundredths — B1
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2 Work out [2 marks]
Work out \(7123 - 4856\).
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Model answer
Subtracting column by column with exchanging gives \(7123 - 4856 = 2267\). Check: \(4856 + 2267 = 7123\).
Mark scheme
- A correct method for the subtraction, with an error in at most one column — M1
- 2267 — A1
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3 Work out [2 marks]
Work out \(3.7 \times 0.6\).
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Model answer
\(37 \times 6 = 222\). There are 2 decimal places in the question, so the answer is \(2.22\).
Mark scheme
- \(37 \times 6 = 222\) or \(3.7 \times 6 = 22.2\) — M1
- 2.22 — A1
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4 Work out [3 marks]
Work out \(1764 \div 12\). You must show your working.
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Model answer
\(12 \times 100 = 1200\), and \(1764 - 1200 = 564\). \(12 \times 47 = 564\), so \(1764 \div 12 = 100 + 47 = 147\).
Mark scheme
- A correct first step, such as a chunking multiple like \(12 \times 100\) or a first bus-stop line — M1
- A correct second stage — M1
- 147 — A1
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5 Work out [3 marks]
Work out \((-6 + 2) \times (3 - 8) - 7\).
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Model answer
Brackets first: \((-6 + 2) = -4\) and \((3 - 8) = -5\). Then \((-4) \times (-5) = 20\) and \(20 - 7 = 13\).
Mark scheme
- One bracket evaluated correctly — M1
- \((-4) \times (-5) = 20\) — M1
- 13 — A1
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6 Work out [3 marks]
A tank holds 1200 litres of water when it is full. Some water is poured in using a bucket that holds 7.5 litres. The bucket is used 40 times. How many more litres are needed to fill the tank?
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Model answer
\(40 \times 7.5 = 300\) litres poured in, so \(1200 - 300 = 900\) litres are still needed.
Mark scheme
- \(40 \times 7.5\) or \(7.5 \times 4\) with a power of 10 correct — M1
- \(1200 - 300\) — M1
- 900 — A1
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7 Work out [2 marks]
Jack says, ‘The answer to \(0.2 \times 0.4\) is \(0.8\).’ Is Jack correct? You must show how you decide.
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Model answer
No. \(2 \times 4 = 8\) and there are two decimal places in total, so \(0.2 \times 0.4 = 0.08\). Jack is wrong because he has put the decimal point in the wrong place.
Mark scheme
- Shows \(2 \times 4 = 8\) or \(0.08\) — M1
- No, supported by \(0.08\) — Q1
Quick check
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1
Estimate \(38 \times 21\) by rounding each number to 1 significant figure.
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D: 800
\(38 \approx 40\) and \(21 \approx 20\), so the estimate is \(40 \times 20 = 800\).
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2
Tickets cost £8.50 each. How many tickets can be bought with £60?
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A: 7
\(8.50 \times 7 = 59.50\), which fits, and \(8.50 \times 8 = 68\), which does not.
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3
What is the value of the digit 7 in the number 4.073?
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B: 7 hundredths
The 7 is in the second column after the decimal point, so it is worth 7 hundredths.
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4
Which of these decimals is the largest?
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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.
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5
What is 6.4 ÷ 100?
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A: 0.064
Dividing by 100 moves every digit two columns to the right, giving 0.064.
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6
Work out \(-3 - (-7)\).
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B: \(4\)
Subtracting a negative is the same as adding: \(-3 + 7 = 4\).
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7
Work out \((-6) \times 3 \div (-2)\).
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C: \(9\)
\((-6)\times 3 = -18\), then \(-18 \div (-2) = 9\) because the signs are the same.
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8
Work out \(2 + 3 \times 4^2\).
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C: \(50\)
Indices first: \(4^2 = 16\). Then multiply: \(3 \times 16 = 48\). Then add: \(2 + 48 = 50\).
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9
Work out \(0.3 \times 0.2\).
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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.