mr barton maths

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KS2 2017 Mathematics Paper 1 – Interactive Practice

KS2 2017 Mathematics Paper 1 Interactive Practice

Mark Scheme Legend

  • 1m = 1 mark awarded for correct answer
  • 2m = Up to 2 marks awarded (method marks available)
  • Do not accept = Specific incorrect answers penalised
  • Accept = Allowable alternative formats

Table of Contents

Question 1 (1 mark)

Calculate:

\[ 40 + 1,000 = \]

Worked Solution

Step 1: Understanding the Operation

We are adding 40 to 1,000. This is a place value question. We add 40 to the tens column.

✏ Working:

   1000
 +   40
 ──────
   1040

Final Answer:

1,040

✓ (1m)

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Question 2 (1 mark)

Calculate:

\[ 707 + 1,818 = \]

Worked Solution

Step 1: Column Addition

Align the digits correctly by place value (units under units) and add from right to left.

✏ Working:

   1818
 +  707
 ──────
   2525
    11

Check:

8 + 7 = 15 (write 5, carry 1)
1 + 0 + 1 (carried) = 2
8 + 7 = 15 (write 5, carry 1)
1 + 1 (carried) = 2

Final Answer:

2,525

✓ (1m)

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Question 3 (1 mark)

Calculate:

\[ \frac{4}{6} + \frac{3}{6} = \]

Worked Solution

Step 1: Add the Numerators

The denominators are the same (6), so we just add the numerators.

✏ Working:

\[ \frac{4 + 3}{6} = \frac{7}{6} \]

Step 2: Convert to Mixed Number (Optional)

The answer \(\frac{7}{6}\) is an improper fraction. We can convert it to a mixed number.

\(7 \div 6 = 1\) remainder \(1\).

\[ \frac{7}{6} = 1\frac{1}{6} \]

Final Answer:

\(1\frac{1}{6}\) or \(\frac{7}{6}\)

✓ (1m)

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Question 4 (1 mark)

Calculate:

\[ 505 \div 1 = \]

Worked Solution

Step 1: Understanding Division by 1

Any number divided by 1 stays the same.

\[ 505 \div 1 = 505 \]

Final Answer:

505

✓ (1m)

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Question 5 (1 mark)

Calculate:

\[ 345 – 60 = \]

Worked Solution

Step 1: Column Subtraction

Align the digits. We need to borrow from the hundreds column because we can’t do \(4 – 6\) in the tens column.

✏ Working:

   23145
 -    60
 ───────
     285

Detail:
Units: \(5 – 0 = 5\)
Tens: \(4 – 6\) (can’t do). Borrow from 3 hundreds. 3 becomes 2. 4 becomes 14.
\(14 – 6 = 8\).
Hundreds: \(2 – 0 = 2\).

Final Answer:

285

✓ (1m)

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Question 6 (1 mark)

Calculate:

\[ 2.7 + 3.014 = \]

Worked Solution

Step 1: Align Decimal Points

It is crucial to line up the decimal points. You can add placeholder zeros to make it easier to see.

\(2.7\) becomes \(2.700\).

✏ Working:

   2.700
 + 3.014
 ───────
   5.714

Final Answer:

5.714

✓ (1m)

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Question 7 (1 mark)

Fill in the missing number:

\[ \Box = 4,500 + 600 \]

Worked Solution

Step 1: Addition

Add the two numbers together. You can do this mentally or using a column method.

\(45 + 6 = 51\), so \(4500 + 600 = 5100\).

✏ Working:

   4500
 +  600
 ──────
   5100
    1

Final Answer:

5,100

✓ (1m)

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Question 8 (1 mark)

Calculate:

\[ 8 \times 33 = \]

Worked Solution

Step 1: Multiplication

We can multiply 33 by 8 using short multiplication.

✏ Working:

    33
 ×   8
 ─────
   264
    2

\(8 \times 3 = 24\) (write 4, carry 2)
\(8 \times 3 = 24\). Add the carry: \(24 + 2 = 26\).

Final Answer:

264

✓ (1m)

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Question 9 (1 mark)

Calculate:

\[ 72 \div 9 = \]

Worked Solution

Step 1: Times Tables Knowledge

This relies on knowledge of the 9 times table.

We know that \(8 \times 9 = 72\).

\[ 72 \div 9 = 8 \]

Final Answer:

8

✓ (1m)

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Question 10 (1 mark)

Calculate:

\[ 167 \times 4 = \]

Worked Solution

Step 1: Short Multiplication

Multiply 167 by 4 using the column method.

✏ Working:

    167
 ×    4
 ──────
    668
    22

1. \(7 \times 4 = 28\) (write 8, carry 2)
2. \(6 \times 4 = 24\). Add carry: \(24 + 2 = 26\) (write 6, carry 2)
3. \(1 \times 4 = 4\). Add carry: \(4 + 2 = 6\).

Final Answer:

668

✓ (1m)

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Question 11 (1 mark)

Calculate:

\[ 4,912 – 824 = \]

Worked Solution

Step 1: Column Subtraction

Align digits carefully. Borrowing is required.

✏ Working:

        8910012
   4912
 -  824
 ──────
   4088

Breakdown:
Units: \(2 – 4\) (Can’t do). Borrow from 1 (tens). 1 becomes 0, 2 becomes 12. \(12 – 4 = 8\).
Tens: \(0 – 2\) (Can’t do). Borrow from 9 (hundreds). 9 becomes 8, 0 becomes 10. \(10 – 2 = 8\).
Hundreds: \(8 – 8 = 0\).
Thousands: \(4 – 0 = 4\).

Final Answer:

4,088

✓ (1m)

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Question 12 (1 mark)

Calculate:

\[ \frac{62}{100} – \frac{38}{100} = \]

Worked Solution

Step 1: Subtract Numerators

The denominators are both 100, so we just subtract the top numbers.

\(62 – 38 = 24\).

✏ Working:

\[ \frac{62 – 38}{100} = \frac{24}{100} \]

Step 2: Simplify (Optional but good practice)

Both numbers are divisible by 4.

\(24 \div 4 = 6\)
\(100 \div 4 = 25\)

\[ \frac{6}{25} \]

Final Answer:

\(\frac{24}{100}\) (or \(\frac{6}{25}\) or \(0.24\))

✓ (1m)

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Question 13 (1 mark)

Fill in the missing number:

\[ \Box – 100 = 1,059 \]

Worked Solution

Step 1: Inverse Operation

To find the missing number, we do the opposite of “subtracting 100”. We add 100 to the answer.

✏ Working:

\[ 1,059 + 100 = 1,159 \]

Final Answer:

1,159

✓ (1m)

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Question 14 (1 mark)

Calculate:

\[ 50 + (36 \div 6) = \]

Worked Solution

Step 1: Order of Operations (BODMAS)

We must do the brackets first.

\(36 \div 6 = 6\).

Step 2: Addition

Now add the result to 50.

\[ 50 + 6 = 56 \]

Final Answer:

56

✓ (1m)

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Question 15 (1 mark)

Calculate:

\[ \frac{4}{6} \times \frac{3}{5} = \]

Worked Solution

Step 1: Multiply Numerators and Denominators

Multiply top by top, and bottom by bottom.

✏ Working:

\[ \text{Top: } 4 \times 3 = 12 \]

\[ \text{Bottom: } 6 \times 5 = 30 \]

\[ \frac{12}{30} \]

Step 2: Simplify

Divide both by their greatest common divisor (6).

\[ \frac{12 \div 6}{30 \div 6} = \frac{2}{5} \]

Final Answer:

\(\frac{12}{30}\) or \(\frac{2}{5}\)

✓ (1m)

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Question 16 (1 mark)

Calculate:

\[ 30 \times 40 = \]

Worked Solution

Step 1: Use Related Facts

Ignore the zeros first: \(3 \times 4 = 12\).

There are two zeros in the question (one in 30, one in 40), so we multiply by 100.

\[ 3 \times 4 = 12 \]

\[ 12 \times 10 \times 10 = 1,200 \]

Final Answer:

1,200

✓ (1m)

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Question 17 (1 mark)

Calculate:

\[ 581 \div 7 = \]

Worked Solution

Step 1: Short Division (Bus Stop Method)

We divide 581 by 7.

✏ Working:

    083
   ┌───
 7 │581

1. 7 into 5 doesn’t go. Carry the 5 to make 58.
2. 7 into 58 goes 8 times (\(7 \times 8 = 56\)) with remainder 2. Carry the 2 to make 21.
3. 7 into 21 goes 3 times (\(7 \times 3 = 21\)).

Final Answer:

83

✓ (1m)

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Question 18 (1 mark)

Calculate:

\[ 0.04 \div 10 = \]

Worked Solution

Step 1: Place Value Movement

Dividing by 10 moves the digits one place to the right (or the decimal point one place to the left).

0.04 becomes 0.004.

Final Answer:

0.004

✓ (1m)

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Question 19 (1 mark)

Calculate:

\[ 2,345 \times 1,000 = \]

Worked Solution

Step 1: Place Value

Multiplying by 1,000 moves all digits 3 places to the left. We add three zeros.

\[ 2,345 \rightarrow 2,345,000 \]

Final Answer:

2,345,000

✓ (1m)

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Question 20 (2 marks)

Calculate:

\[ 714 \div 17 = \]

Show your method.

Worked Solution

Step 1: List Multiples of 17

It helps to write down the first few multiples of 17.

17, 34, 51, 68, 85…

Step 2: Long Division

How many 17s in 71? We can see 68 is close (\(4 \times 17\)).
Remainder is \(71 – 68 = 3\).
Bring down the 4 to make 34.
How many 17s in 34? Exactly 2.

✏ Working:

    042
   ┌───
 17│714
   -680 (40 x 17)
   ────
     34
    -34 (2 x 17)
    ───
      0

Final Answer:

42

✓ (2m)

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Question 21 (1 mark)

Calculate:

\[ 9 – 3.45 = \]

Worked Solution

Step 1: Column Subtraction with Decimals

Write 9 as 9.00 to align with 3.45. Borrowing is required.

✏ Working:

    89.9010
 -  3. 4 5
 ──────────
    5. 5 5

Final Answer:

5.55

✓ (1m)

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Question 22 (2 marks)

Calculate:

\[ 4,781 \times 23 = \]

Show your method.

Worked Solution

Step 1: Long Multiplication

First multiply by 3 (units). Then multiply by 20 (tens), remembering the placeholder zero.

✏ Working:

      4781
    ×   23
    ──────
     14343  (4781 × 3)
     22 
   + 95620  (4781 × 20)
     11
    ──────
    109963
     1

Row 1 (\(4781 \times 3\)):
\(1 \times 3 = 3\)
\(8 \times 3 = 24\) (4, carry 2)
\(7 \times 3 = 21 + 2 = 23\) (3, carry 2)
\(4 \times 3 = 12 + 2 = 14\) -> 14343.

Row 2 (\(4781 \times 20\)):
Place zero.
\(1 \times 2 = 2\)
\(8 \times 2 = 16\) (6, carry 1)
\(7 \times 2 = 14 + 1 = 15\) (5, carry 1)
\(4 \times 2 = 8 + 1 = 9\) -> 95620.

Final Answer:

109,963

✓ (2m)

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Question 23 (1 mark)

Calculate:

\[ \frac{3}{4} – \frac{3}{8} = \]

Worked Solution

Step 1: Find Common Denominator

We cannot subtract with different denominators. The common denominator for 4 and 8 is 8.

Multiply \(\frac{3}{4}\) by \(\frac{2}{2}\) to get eighths.

\[ \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \]

Step 2: Subtract

Now subtract \(\frac{3}{8}\) from \(\frac{6}{8}\).

\[ \frac{6}{8} – \frac{3}{8} = \frac{3}{8} \]

Final Answer:

\(\frac{3}{8}\)

✓ (1m)

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Question 24 (2 marks)

Calculate:

\[ 418 \times 46 = \]

Show your method.

Worked Solution

Step 1: Long Multiplication

Multiply 418 by 6, then 418 by 40.

✏ Working:

      418
    ×  46
    ─────
     2508  (418 × 6)
     14
   +16720  (418 × 40)
      3
    ─────
    19228
     1

Final Answer:

19,228

✓ (2m)

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Question 25 (1 mark)

Calculate:

\[ 37.8 – 14.671 = \]

Worked Solution

Step 1: Column Subtraction with Placeholders

Add zeros to 37.8 to match the decimal places of 14.671.

37.8 becomes 37.800.

✏ Working:

        789010
   37.800
 - 14.671
 ────────
   23.129

Final Answer:

23.129

✓ (1m)

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Question 26 (1 mark)

Calculate:

\[ \frac{1}{4} + \frac{1}{5} + \frac{1}{10} = \]

Worked Solution

Step 1: Find Common Denominator

We need a multiple of 4, 5, and 10. The lowest common multiple is 20.

Step 2: Convert Fractions

\[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \]

\[ \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20} \]

\[ \frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20} \]

Step 3: Add

\[ \frac{5}{20} + \frac{4}{20} + \frac{2}{20} = \frac{11}{20} \]

Final Answer:

\(\frac{11}{20}\)

✓ (1m)

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Question 27 (1 mark)

Calculate:

\[ \frac{4}{5} \div 4 = \]

Worked Solution

Step 1: Understanding Fraction Division

Dividing by 4 is the same as multiplying by \(\frac{1}{4}\).

\[ \frac{4}{5} \times \frac{1}{4} = \frac{4}{20} \]

Alternatively, if the numerator (4) is divisible by the divisor (4), you can just divide the top number:

\[ \frac{4 \div 4}{5} = \frac{1}{5} \]

Final Answer:

\(\frac{1}{5}\) (or \(\frac{4}{20}\))

✓ (1m)

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Question 28 (1 mark)

Calculate:

\[ \frac{5}{8} \div 2 = \]

Worked Solution

Step 1: Multiply Denominator by the Integer

Dividing a fraction by an integer is the same as multiplying the denominator.

\[ \frac{5}{8 \times 2} = \frac{5}{16} \]

Final Answer:

\(\frac{5}{16}\)

✓ (1m)

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Question 29 (1 mark)

Calculate:

\[ 45\% \text{ of } 460 = \]

Worked Solution

Step 1: Break Down Percentage

We can find 10%, 5%, etc.

100% = 460

10% = 46

5% = 23 (half of 10%)

Step 2: Construct 45%

45% = 40% + 5% OR 50% – 5%.

Method A (10% \(\times\) 4 + 5%):

40% = \(46 \times 4 = 184\)

45% = \(184 + 23 = 207\)

Method B (50% – 5%):

50% = 230 (half of 460)

5% = 23

45% = \(230 – 23 = 207\)

\[ 230 – 23 = 207 \]

Final Answer:

207

✓ (1m)

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Question 30 (1 mark)

Calculate:

\[ 2\frac{1}{3} + \frac{5}{6} = \]

Worked Solution

Step 1: Common Denominator

Convert \(2\frac{1}{3}\) to sixths or convert to improper fraction first.

\(2\frac{1}{3} = 2\frac{2}{6}\).

\[ 2\frac{2}{6} + \frac{5}{6} = 2\frac{7}{6} \]

Step 2: Simplify

\(\frac{7}{6}\) is \(1\frac{1}{6}\).

So, \(2 + 1\frac{1}{6} = 3\frac{1}{6}\).

Final Answer:

\(3\frac{1}{6}\) (or \(\frac{19}{6}\))

✓ (1m)

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Question 31 (1 mark)

Calculate:

\[ 7\% \text{ of } 500 = \]

Worked Solution

Step 1: Calculate 1%

1% of 500 is \(500 \div 100 = 5\).

Step 2: Calculate 7%

Multiply 1% by 7.

\[ 5 \times 7 = 35 \]

Final Answer:

35

✓ (1m)

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Question 32 (1 mark)

Calculate:

\[ \frac{2}{6} – \frac{1}{8} = \]

Worked Solution

Step 1: Find Common Denominator

Multiples of 6: 6, 12, 18, 24…

Multiples of 8: 8, 16, 24…

Lowest common multiple is 24.

\[ \frac{2}{6} = \frac{2 \times 4}{6 \times 4} = \frac{8}{24} \]

\[ \frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24} \]

Step 2: Subtract

\[ \frac{8}{24} – \frac{3}{24} = \frac{5}{24} \]

Final Answer:

\(\frac{5}{24}\)

✓ (1m)

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Question 33 (1 mark)

Calculate:

\[ 0.9 \times 200 = \]

Worked Solution

Step 1: Related Facts

We know \(9 \times 2 = 18\).

Here we have \(0.9 \times 200\).

We can do \(9 \times 200 = 1800\), then divide by 10 (because of 0.9). Result 180.

OR: \(0.9 \times 100 = 90\). Then \(90 \times 2 = 180\).

\[ 0.9 \times 200 = 180 \]

Final Answer:

180

✓ (1m)

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Question 34 (1 mark)

Calculate:

\[ 15\% \times 1,000 = \]

Worked Solution

Step 1: Calculate 10% and 5%

10% of 1,000 = 100.

5% is half of 10%, so 50.

Step 2: Add

\[ 100 + 50 = 150 \]

Final Answer:

150

✓ (1m)

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Question 35 (1 mark)

Calculate:

\[ 1\frac{1}{2} \times 57 = \]

Worked Solution

Step 1: Partitioning Method

\(1\frac{1}{2} \times 57\) means \((1 \times 57) + (\frac{1}{2} \times 57)\).

\(1 \times 57 = 57\).

\(\frac{1}{2}\) of 57 is \(57 \div 2 = 28.5\).

Step 2: Add results

\[ 57 + 28.5 = 85.5 \]

Final Answer:

85.5 (or \(85\frac{1}{2}\))

✓ (1m)

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Question 36 (2 marks)

Calculate:

\[ 2,242 \div 59 = \]

Show your method.

Worked Solution

Step 1: Estimate

59 is close to 60. \(2242 \approx 2400\). \(2400 \div 60 = 40\). So the answer should be close to 40 (likely slightly less).

Step 2: Long Division

1. 59 into 224: Try 3. \(3 \times 60 = 180\), so \(3 \times 59\) is \(180 – 3 = 177\).
\(224 – 177 = 47\).
2. Bring down 2. Number is 472.
3. 59 into 472: Try 8 (since \(8 \times 9\) ends in 2).
\(8 \times 50 = 400\). \(8 \times 9 = 72\). \(400 + 72 = 472\). Exactly.

✏ Working:

    0038
    ┌────
 59 │2242
    -177  (3 x 59)
    ────
      472
     -472 (8 x 59)
     ────
        0

Final Answer:

38

✓ (2m)

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