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SATs practice · Year 6Chapter 9 · Practice papers: arithmetic
Year 6 · Chapter 9

Practice papers: arithmetic

By the end of this chapter you will be able to

  • Work through a full practice paper without a calculator, and check the working
  • Use the feedback sheet to find which statements need more practice
  • Show a written check for a problem with more than one step
  • Manage time across a paper, using the practice guide

You should already know

  • Chapters 1 to 8 of this book

Where this leads

  • Year 6 maths for the full explanations of each topic

KS2 SATs practice for arithmetic (Year 6). Original questions in the style of the national tests. Content: Paper 1 (non-calculator): arithmetic and written methods drawn from chapters 1 to 5 and 7, in rising difficulty, Paper 2 (non-calculator): algebra, measures and conversions drawn from chapters 6 and 8, with two problems that need a written check, A feedback sheet names the statement each item tests, A timing guide: 30 minutes for Paper 1 and 40 minutes for Paper 2, as a practice guide only.

Exercise P  Do you remember?

Non-calculator
1
FWork out 4 × 9.
2
FWork out 1/2 of 18.
3
FWork out 2,500 + 1,750.
4
FWork out 3 + 4 × 2.
5
FRound 6,480 to the nearest 1,000.
9.1

Paper 1, part A (items 1 to 12)

Year 6
Paper 1: arithmetic and written methods drawn from chapters 1 to 5 and 7, in rising difficulty
Video lesson: Paper 1, part A (items 1 to 12)Coming soon
Practice material. Non-calculator practice. This book is practice in the style of the Year 6 arithmetic test. It is not the official test, and no official test item is used. Do every question without a calculator. Marks and timings are a practice guide only.
Story. This is practice Paper 1. It is a non-calculator paper, and it begins with questions that are quick to work out. Work through it steadily, and check each answer before you move on.

How to use this paper

Paper 1 has 24 items in two parts, and it draws on Chapters 1 to 5 and 7. Aim to finish in about 30 minutes. This is a practice guide, not the official timing.

Show your working on paper. Check each answer with an estimate or the opposite operation.

Key ideas

  • Work through the items in order, and check each one.
  • Use the working you learned in Chapters 1 to 5 and 7.
  • Every answer is written in the form the question asks for.
Worked example 9.1.1
Work out 3,056 × 24.

Method. Use partial products, one for each digit of 24.

  1. Multiply by the ones digit, 4 (4). Write the partial product.
    3,056 × 4 = 12,224
  2. Multiply by the tens digit, 2 (20). Write the partial product.
    3,056 × 20 = 61,120
  3. Add the partial products. Add them to get the answer.
    12,224 + 61,120 = 73,344
  4. Write the answer.
    73,344

Check. About 3,000 × 24 = 72,000, close to 73,344. ✓

Worked example 9.1.2
Work out 4,152 ÷ 8.

Method. Divide one digit at a time from the left.

  1. Bring down the next digit to make 4. 8 goes into 4 0 times.
    4 < 8, so 0, remainder 4
  2. Bring down the next digit to make 41. 8 goes into 41 5 times.
    41 - 40 = 1
  3. Bring down the next digit to make 15. 8 goes into 15 1 time.
    15 - 8 = 7
  4. Bring down the next digit to make 72. 8 goes into 72 9 times.
    72 - 72 = 0
  5. Write the answer.
    519

Check. 519 × 8 = 4,152. ✓

Worked example 9.1.3
Work out 3/5 of 45.

Method. Find one fifth, then multiply by 3.

  1. Find one fifth. 45 ÷ 5 = 9.
    9
  2. Multiply by 3. 9 × 3 = 27.
    27
  3. Write the answer.
    27

Check. 27 ÷ 3 = 9, and 9 × 5 = 45. ✓

Exercise 9A  Paper 1, part A

Non-calculator
1
FWork out 3,406 + 2,579.
2
FWork out 8,000 - 3,462.
3
FWork out 14 × 6.
4
FWork out 326 × 7.
5
FWork out 4,152 ÷ 8.
6
FWhat is the value of the 6 in 4,362,015?
7
FRound 45,678 to the nearest 1,000.
8
FWork out 3/4 + 1/8.
9
FWork out 0.6 × 5.
10
PSWork out 25% of 360.
11
PSA class of 40 pupils has boys : girls = 3 : 5. How many boys are there?
12
RWork out 7 + 3 × 4.
9.2

Paper 1, part B (items 13 to 24)

Year 6
Paper 1: arithmetic and written methods drawn from chapters 1 to 5 and 7, in rising difficulty
Video lesson: Paper 1, part B (items 13 to 24)Coming soon
Story. Part B of Paper 1 is harder. The numbers are bigger and some questions combine two steps.

Rule

For longer calculations, use a written method and check your answer with an estimate or the opposite operation. Decimals and fractions must be written in the form the question asks for.

Key ideas

  • Use the written method you practised in Chapters 1 to 5.
  • Check every answer with an estimate.
  • Decide whether a question wants a decimal, a fraction or a mixed number.
Worked example 9.2.1
Work out 2.46 × 36.

Method. Work out 246 × 36, then put the decimal point back.

  1. Multiply by the ones digit, 6 (6). Write the partial product.
    246 × 6 = 1,476
  2. Multiply by the tens digit, 3 (30). Write the partial product.
    246 × 30 = 7,380
  3. Add the partial products. Add them to get the answer.
    1,476 + 7,380 = 8,856
  4. Put the point back. The decimal has two places, so the answer has two places.
    88.56
  5. Write the answer.
    88.56

Check. About 2.5 × 36 = 90, close to 88.56. ✓

Worked example 9.2.2
Work out 1,000 ÷ 36. Give the remainder as a whole number.

Method. Divide one digit at a time, then write the remainder.

  1. Bring down the next digit to make 1. 36 goes into 1 0 times.
    1 < 36, so 0, remainder 1
  2. Bring down the next digit to make 10. 36 goes into 10 0 times.
    10 < 36, so 0, remainder 10
  3. Bring down the next digit to make 100. 36 goes into 100 2 times.
    100 - 72 = 28
  4. Bring down the next digit to make 280. 36 goes into 280 7 times.
    280 - 252 = 28
  5. Write the answer.
    27 remainder 28

Check. 36 × 27 + 28 = 1,000. ✓

Worked example 9.2.3
Work out 5,000,000 - 1,234,567.

Method. Take away 1,000,000 first, then take away the rest.

  1. Take away 1,000,000. 5,000,000 - 1,000,000 = 4,000,000.
    4,000,000
  2. Take away 234,567. 4,000,000 - 234,567 = 3,765,433.
    3,765,433
  3. Write the answer.
    3,765,433

Check. 3,765,433 + 1,234,567 = 5,000,000. ✓

Exercise 9B  Paper 1, part B

Non-calculator
1
FWork out 3,056 × 24.
2
FWork out 5,000,000 - 1,234,567.
3
FWork out 47.5 ÷ 5.
4
FWork out 2.46 × 36.
5
FWork out 1/2 ÷ 4.
6
PSShare 96 in the ratio 5 : 3. Write both shares, the bigger first.
7
FWork out 0.7 × 1000.
8
FRound 8.4653 to two decimal places.
9
PSWork out 6 2/5 + 1 3/4. Give the answer as a mixed number.
10
PSWork out 1,000 ÷ 36. Give the remainder as a whole number.
11
RWork out (18 - 6) × 4 ÷ 8 + 3.
12
PSA bag holds 24 cakes. One third of them are eaten. The rest are shared equally between 4 friends. How many cakes does each friend get?
9.3

Paper 2, part A (items 1 to 12)

Year 6
Paper 2 (non-calculator): algebra, formulae and sequences drawn from chapter 6, and measures from chapter 8
Video lesson: Paper 2, part A (items 1 to 12)Coming soon
Story. Paper 2 is also a non-calculator paper. Part A covers formulae, sequences, missing numbers and conversions.

How to use this paper

Paper 2 has 25 items in two parts, and it draws on Chapters 6 and 8. Aim to finish in about 40 minutes. This is a practice guide, not the official timing.

Two items in part B need a written check. Write the working for them.

Key ideas

  • Replace letters with numbers carefully when you substitute.
  • A sequence goes up or down by the same step each time.
  • Convert units first, then calculate.
Worked example 9.3.1
Use P = 3a + 2b to find P when a = 4 and b = 5.

Method. Replace the letters, then multiply and add.

  1. Substitute. 3 × 4 + 2 × 5.
    3 × 4 + 2 × 5
  2. Multiply. 12 + 10.
    12 + 10
  3. Add. 12 + 10 = 22.
    22
  4. Write the answer.
    22

Check. 22 - 10 = 12 = 3 × 4. ✓

Worked example 9.3.2
Find the next term of 7, 11, 15, 19, ...

Method. Find the step, then add it.

  1. Find the step. 11 - 7 = 4.
    4
  2. Add the step. 19 + 4 = 23.
    23
  3. Write the answer.
    23

Check. 23 - 19 = 4. ✓

Worked example 9.3.3
Convert 2.5 kg to grams.

Method. Multiply by 1000.

  1. Use the fact. 1 kg = 1000 g.
    1000 g
  2. Multiply. 2.5 × 1000 = 2,500.
    2,500 g
  3. Write the answer.
    2,500 g

Check. 2,500 ÷ 1000 = 2.5 kg. ✓

Exercise 9C  Paper 2, part A

Non-calculator
1
FUse P = 3a + 2b to find P when a = 4 and b = 5.
2
FA bus charges £4 per trip and a fixed fee of £3. Write a formula for the cost, C pounds, of n trips.
3
FFind the next term of 7, 11, 15, 19, ...
4
FWrite the term-to-term rule for 30, 26, 22, 18, ...
5
Fa + b = 13. If a = 5, what is b?
6
FAbout how many miles is 40 km? Use 8 km is about 5 miles.
7
FConvert 2.5 kg to grams.
8
PSAn L-shape is made from an 8 cm by 6 cm rectangle with a 4 cm by 2 cm corner removed. Find its perimeter.
9
PSFind the area of a rectangle 9 m long and 4 m wide.
10
PSHow many pairs of counting numbers a and b have a + b = 12 with a < b?
11
PSConvert 2.5 hours to minutes.
12
RFind all the pairs of whole numbers (x, y), with x and y at least 0, that satisfy x + 3y = 9. List them.
9.4

Paper 2, part B (items 13 to 25) and the feedback sheet

Year 6
Paper 2 (non-calculator): substitution, sequences, two unknowns, combinations and measures, with two items that need a written check
Video lesson: Paper 2, part B (items 13 to 25) and the feedback sheetComing soon
Story. This is the last part of the practice papers. Two of the questions need a written check, so write your working clearly.

Feedback sheet

ItemPaperStatement tested
1 to 12Paper 1Place value, the four operations, fractions, percentages, ratio and the order of operations (Chapters 1 to 5 and 7)
13 to 24Paper 1Long multiplication and division, decimals, rounding, sharing in a ratio, mixed numbers and the order of operations
1 to 12Paper 2Substitution, formulae in words and letters, linear sequences, missing numbers, combinations, conversions and perimeter
13 to 25Paper 2Two unknowns, sequences, combinations, metric conversions, time, perimeter and written checks

Use this sheet to choose which chapter to revisit. Any item you got wrong shows which statement needs more practice.

Key ideas

  • Show the working for multi-step problems.
  • Check each answer with the opposite operation.
  • Use the feedback sheet to find your next step.
Worked example 9.4.1
Use the formula T = 2c + 3a with c = 7 and a = 2 to find T.

Method. Replace the letters, then multiply and add.

  1. Substitute. 2 × 7 + 3 × 2.
    2 × 7 + 3 × 2
  2. Multiply. 14 + 6.
    14 + 6
  3. Add. 14 + 6 = 20.
    20
  4. Write the answer.
    20

Check. 20 - 6 = 14 = 2 × 7. ✓

Worked example 9.4.2
Solve x + y = 9 and 2x + y = 15 to find x and y.

Method. Subtract the first equation from the second.

  1. Subtract. (2x + y) - (x + y) = 15 - 9, so x = 6.
    x = 6
  2. Find y. 6 + y = 9, so y = 3.
    y = 3
  3. Write the answer.
    x = 6 and y = 3

Check. 2 × 6 + 3 = 15. ✓

Worked example 9.4.3
Find the 10th term of 12, 17, 22, ...

Method. Find the step, then add it nine times to the first term.

  1. Find the step. 17 - 12 = 5.
    5
  2. Add nine steps. 12 + 9 × 5 = 12 + 45.
    57
  3. Write the answer.
    57

Check. 12 + 45 = 57. ✓

Exercise 9D  Paper 2, part B

Non-calculator
1
FWork out 5x - 2y when x = 6 and y = 4.
2
FTickets cost C = 5a + 3c pounds. Find C when a = 2 adults and c = 7 children.
3
PSSolve 2x + y = 15 and x + y = 9. Find x.
4
PSFind the 10th term of 12, 17, 22, ...
5
FConvert 3.6 km to metres.
6
PSAbout how many kilometres is 15 miles? Use 5 miles is about 8 km.
7
RHow many pairs of counting numbers a and b, with a < b, have a × b = 36?
8
RHow many ways can 15p be made using 5p and 10p coins?
9
PSFind the area of a square with sides of 11 cm.
10
PSHow many 250 ml glasses can be filled from a jug holding 2.5 litres?
11
PSA train leaves at 10:35 and the journey takes 2 hours 50 minutes. What time does it arrive?
12
PSWRITTEN CHECK: An L-shaped garden is a 14 m by 9 m rectangle with a 6 m by 4 m corner removed. Find its perimeter. Write the working to check your answer.
13
PSWRITTEN CHECK: A school orders 36 boxes of 24 pencils. How many pencils are there? Write the working to check your answer.

Chapter summary

SkillMethod
Paper 1Non-calculator arithmetic from Chapters 1 to 5 and 7, in rising difficulty; about 30 minutes.
Paper 2Non-calculator algebra and measures from Chapters 6 and 8; about 40 minutes.
Written checkWrite the working for multi-step problems, and check with an estimate.
Feedback sheetEach item names the statement it tests, so you can revisit that chapter.
TimingThe times are a practice guide only, not the official test.

Can you…?

  • I can work through a full practice paper without a calculator
  • I can show a written check for a multi-step problem
  • I can use the feedback sheet to choose my next practice
  • I know which items test which statements

Key terms

practice guide
a guide to pace and timing, not a rule
written check
working that shows how an answer was checked
feedback sheet
a list of the statements each item tests

Exercise 9Z  Check-up

Non-calculator
1
Work out 4,000 + 3,600 + 500.
2
Work out 9 × 12.
3
Work out 3/4 of 60.
4
Write 0.45 as a percentage.
5
Share 45 in the ratio 4 : 5. Write the bigger share.
6
Use T = 6p - 2 to find T when p = 5.
7
Find the next term of 40, 37, 34, 31, ...
8
Convert 1.75 kg to grams.
9
Work out (25 - 9) ÷ 4 + 3.

Total 19 marks. Allow about 19 minutes.

Exercise 9X  Practice test questions

Non-calculator
1
FWork out 2,046 × 5.[1 mark]
2
FWork out 73 × 16.[2 marks]
3
FWork out 1,734 ÷ 18. Give the remainder.[2 marks]
4
FFind the value of 4x - 3 when x = 5.[1 mark]
5
FWrite the next term of 9, 6, 3, 0, ...[1 mark]
6
FConvert 4.2 km to metres.[1 mark]
7
FAbout how many miles is 56 km?[2 marks]
8
FA rectangle is 12 m long and 7 m wide. What is its area?[2 marks]
9
PSShare 120 in the ratio 1 : 3. Write the smaller share.[2 marks]
10
PSWork out 15 + 4 × 6 - 9.[2 marks]
11
RExplain why 2 : 5 and 4 : 10 are equivalent ratios.[3 marks]
← Chapter 8: Measures and conversions

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