Websink Prep UKKS2 Maths reasoning (SATs)Year 6 chaptersMaths reasoning (SATs) textbooksYear 6Browse allPast papersFind a tutorBecome a tutor
SATs practice · Year 6Chapter 9 · Practice paper: reasoning
Year 6 · Chapter 9

Practice paper: reasoning

By the end of this chapter you will be able to

  • Work through a practice paper without a calculator
  • Show working and give a reason for each explain item
  • Use the feedback sheet to find the statements to revise
  • Check each answer against the solution and mark your own paper

You should already know

  • Chapters 1 to 8 of this book

Where this leads

  • Revisit any chapter whose feedback items you missed

KS2 SATs practice for reasoning (Year 6). Original questions in the style of the national tests. Content: A full practice paper in the mixed style of the Year 6 reasoning test, drawn from chapters 1 to 8 (Year 5-6), Items rise in difficulty and use multi-part, show-your-working, explain, tick and complete answer types (Year 5-6), A feedback sheet names the statement each item tests (Year 5-6), A timing guide of 45 minutes, marked as a practice guide only (Year 5-6).

Exercise P  Do you remember?

Non-calculator
1
FWrite the value of the 5 in 2,345.
2
FWork out 3/4 of 20.
3
FWhat is the next term of the sequence 4, 7, 10, 13, __?
4
FWork out the area of a rectangle 6 cm long and 4 cm wide.
5
FWrite the angle that makes a straight line with 70 degrees.
9.1

Paper A

Year 6
A full practice paper in the mixed style of the Year 6 reasoning test, drawn from chapters 1 to 8 (Year 5-6)
Video lesson: Paper AComing soon
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. This is the first of two practice papers. Read each question carefully and show your working. The papers are in the style of the reasoning test: some items ask for a number, some ask you to explain, and some ask you to tick.

How to use this paper

Work without a calculator, and show your working in the space provided. Items get harder as you go. Write one reason for each explain item.

Timing guide (practice guide only, not the official test): 45 minutes for both papers together, about 22 minutes for each paper.

The feedback sheet in section 9.3 names the statement each item tests.

Key ideas

  • Show your working for every item with more than one step.
  • Explain items need a reason in words, not only a number.
  • If you are stuck, move on and come back to the item.
Worked example 9.1.1
Ava has 4 bags of 15 beads and 12 loose beads. She gives away 18 beads. How many does she have now?

Method. Work out the total first, then take away the beads given away.

  1. Total in bags. 4 x 15 = 60.
    60
  2. Add the loose beads. 60 + 12 = 72.
    72
  3. Take away. 72 - 18 = 54.
    54
  4. Write the answer.
    54

Check. 72 - 18 = 54. ✓

Worked example 9.1.2
Explain why 2/3 is greater than 1/2.

Method. Use a common denominator, then compare the tops.

  1. Common denominator. Use 6: 2/3 = 4/6 and 1/2 = 3/6.
    4/6 and 3/6
  2. Compare. With the same bottom number, 4 sixths is more than 3 sixths.
    4/6 > 3/6
  3. Write the answer.
    2/3 = 4/6 and 1/2 = 3/6, so 2/3 is greater.

Check. 4 > 3. ✓

Worked example 9.1.3
Tick the calculations that give 20: 4 x 5, 2 + 3 x 6, 5 x 2 + 2, 40 / 2.

Method. Work out each calculation, using the order of operations.

  1. Check each. 4 x 5 = 20; 2 + 3 x 6 = 2 + 18 = 20; 5 x 2 + 2 = 12; 40 / 2 = 20.
    20, 20, 12, 20
  2. Tick the ones that give 20. The first, second and fourth give 20.
    4 x 5, 2 + 3 x 6, 40 / 2
  3. Write the answer.
    4 x 5, 2 + 3 x 6, 40 / 2

Check. Three calculations give 20. ✓

Exercise 9A  Paper A: practice items, rising in difficulty

Non-calculator
1
FWrite the value of the 7 in 2,470,215.
2
FRound 384,976 to the nearest 1,000.
3
FPut these in order from smallest to largest: -4, 7, -10, 0.
4
FWork out 6 + 4 x 3 - 8 / 2.
5
FA shop has 3 packs of 24 pencils and 17 loose pencils. It sells 29 pencils. How many are left? Write the number.
6
FWhich is larger: 5/8 or 7/12? Write the fraction.
7
FWork out 2/3 + 1/4. Give your answer in its simplest form.
8
FWork out 3/4 of 36.
9
FSimplify the ratio 24:36.
10
FShare 60 pounds between Ann and Ben in the ratio 2:3. How much does Ann get, in pounds?
11
FFive pens cost 6.50 pounds. How much do 8 pens cost, in pounds?
12
PSWhich is better value: 3 for 2.10 pounds, or 5 for 3.25 pounds? Write the number of items in the better-value pack, 3 or 5.
13
FConvert 3.4 km into metres.
14
PSA train leaves at 09:35 and arrives at 11:20. How long is the journey? Write hours and minutes.
15
FFind the area of a triangle with base 12 cm and perpendicular height 9 cm.
16
FA rectangle is 15 cm long and 8 cm wide. What is its perimeter, in cm?
17
FThree angles meet at a point. Two of them are 130 degrees and 95 degrees. Find the third angle, in degrees.
18
FA triangle has angles of 48 degrees and 67 degrees. What is the third angle, in degrees?
19
RIs a rhombus always, sometimes or never a square? Write one word. Choose one: always, sometimes or never.
20
PSWhat is the interior angle of a regular hexagon, in degrees?
21
FThe point (-4, 3) is in which quadrant? Write first, second, third or fourth.
22
FTranslate the point (2, -1) by 3 right and 4 down. Write the new point.
23
FReflect the point (2, 3) in the y-axis. Write the new point.
24
FWhat is the next term of 3, 8, 13, __?
25
PSThe sequence is 5, 8, 11, 14, ... What is term number 12?
26
FSolve 4x + 3 = 27.
27
PSHow many pairs of whole numbers a and b, both at least 1, have a + b = 10 and a < b?
28
FThe mean of 4, 8, 6 and 10 is how much?
29
FFind the median of 9, 2, 7, 4 and 11.
30
PSA pie chart shows 120 pupils. One sector is 90 degrees. How many pupils does it show?
31
RExplain why the range of 3, 3, 3 and 3 is 0.
32
RThe sum of two odd numbers is always even. Write always, sometimes or never. Choose one: always, sometimes or never.
33
RTick the fractions that are equal to 0.75. Options: 3/4 | 6/8 | 7/10 | 0.75 | 3/5. Write the options you would tick, in the order given.
34
RIs 100 a term of the sequence 2, 5, 8, 11, ...? Write yes or no.
35
FIs an angle of 240 degrees acute, obtuse or reflex? Choose one: acute, obtuse or reflex.
36
PSA rectangle has area 36 cm2 and whole-number sides. Write the side lengths of the rectangle with the smallest perimeter.
37
FWhat is 35% of 60?
38
PSA rectangle has corners (1, 1), (7, 1), (7, 5) and (1, 5). What are the coordinates of its centre?
39
PSWrite the equation for: a number, multiplied by 3, then added to 5, gives 26. Solve it to find the number.
40
FFind the value of 4p + 6 when p = 9.
9.2

Paper B

Year 6
A full practice paper in the mixed style of the Year 6 reasoning test, drawn from chapters 1 to 8 (Year 5-6)
Video lesson: Paper BComing soon
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. This is the second practice paper. It is a little harder than Paper A, and several items ask for an explanation or a tick. Take your time, and check each answer before you move on.

How to use this paper

Work without a calculator. Show your working. Explain items need one clear reason in words.

Timing guide (practice guide only, not the official test): about 22 minutes for this paper, with Paper A.

Key ideas

  • Read the question twice, and check what it asks for.
  • Check the units in the answer, such as pounds, cm or degrees.
  • A tick question can have more than one correct option.
Worked example 9.2.1
Share 90 stickers between two people in the ratio 1:2. How many does the person with 2 parts get?

Method. Find the total parts, then one part, then the share.

  1. Total parts. 1 + 2 = 3.
    3
  2. One part. 90 / 3 = 30.
    30
  3. Share. 2 x 30 = 60.
    60
  4. Write the answer.
    60

Check. 30 + 60 = 90. ✓

Worked example 9.2.2
Ben says the mean of 3, 9 and 12 is 9, because 9 is in the middle. Explain whether he is right.

Method. Work out the mean by adding and dividing.

  1. Total. 3 + 9 + 12 = 24.
    24
  2. Mean. 24 / 3 = 8, not 9.
    8
  3. Write the answer.
    No, the mean is 8.

Check. 8 x 3 = 24. ✓

Worked example 9.2.3
Tick the options that are equal to 0.5: 1/2, 5/10, 0.05, 50%, 2/5.

Method. Check each option by changing it to the same form.

  1. Check each. 1/2 = 0.5; 5/10 = 0.5; 0.05 is not 0.5; 50% = 0.5; 2/5 = 0.4.
    0.5 for three options
  2. Tick the true ones. Tick 1/2, 5/10 and 50%.
    1/2, 5/10, 50%
  3. Write the answer.
    1/2, 5/10, 50%

Check. Three options equal a half. ✓

Exercise 9B  Paper B: practice items, rising in difficulty

Non-calculator
1
FWrite the number: eight million, sixty thousand, three hundred and four.
2
FRound 4,650 to the nearest 100.
3
FWork out (-12) + 20 - (-5).
4
FWork out (9 + 3) / 4 + 2 x 5.
5
PSFind two whole numbers whose product is 36 and whose sum is 13. Write the smaller number first.
6
FWrite 2.5 as a mixed number in its simplest form.
7
PSWork out 2 1/3 + 1 5/6. Give your answer as a mixed number in its simplest form.
8
FWork out 5 x 2/3. Give your answer as a mixed number.
9
RTick the options that are equal to 3/8. Options: 0.375 | 0.38 | 0.3750 | 3.8% | 37.5%. Write the options you would tick, in the order given.
10
FA ratio of apples to pears is 5:8. There are 40 pears. How many apples are there?
11
PSA photo 12 cm wide is enlarged to 30 cm wide. What is the scale factor?
12
RShare 280 sweets between three people in the ratio 3:4:7. How many sweets does the person with 7 parts get?
13
PSSix pens cost 8.40 pounds. How much do 4 pens cost, in pounds?
14
FHow many minutes are there in 2 hours 45 minutes?
15
PSRoughly how many kilometres is 25 miles? Use 5 miles = 8 km.
16
FA parallelogram has a base of 14 cm and a perpendicular height of 6 cm. What is its area, in cm2?
17
RTwo rectangles have an area of 24 square cm. One is 3 cm by 8 cm, and the other is 4 cm by 6 cm. Which has the smaller perimeter? Write the sides.
18
FA quadrilateral has angles of 110, 75 and 90 degrees. What is the fourth angle, in degrees?
19
PSThe angles of a triangle are in the ratio 1:2:3. What is the largest angle, in degrees?
20
RBen says a rectangle is always a square. Is he right? Write yes or no. Choose one: yes or no.
21
FWhat is the exterior angle of a regular decagon (10 sides), in degrees?
22
PSA rectangle has opposite corners at (-3, 1) and (5, -3). What are the coordinates of its centre?
23
PSReflect the triangle with corners (1, 2), (4, 2) and (4, 5) in the line x = 2. Write the new corners in the same order.
24
PSYou are facing South. You turn 3 quarter turns anticlockwise. Which direction are you facing now?
25
RThe nth term of a sequence is 5n + 2. Is 102 a term of this sequence? Write yes or no.
26
PSSolve 3(x + 4) = 27.
27
FThe formula is T = 5n - 3. Find T when n = 7.
28
RHow many pairs of whole numbers a and b, both at least 1, have a + b = 15 and a < b?
29
PSThe mean of five numbers is 9. Four of them are 7, 10, 12 and 8. What is the fifth number?
30
PSFind the median of 2, 9, 4, 12, 7 and 5.
31
PSA line graph shows 14 degrees at 10 am and 9 degrees at 2 pm. What is the change between these times? Write the change with its sign.
32
RA bar chart shows bike sales: January 12, February 18, March 15. Tick the statements that the chart supports. Options: Sales were higher in February than January | Sales were higher in March than February | Sales will rise next month | The most sales were in February. Write the options you would tick, in the order given.
33
PSAli has 30 pounds and buys 4 items that cost 4.75 pounds each. How much money is left, in pounds?
34
RWork out 3/5 of 2 hours. Write the answer in minutes.
35
RExplain why 3/4 of 20 pounds is more than 60% of 20 pounds.
36
FWhich of these shapes is a regular polygon? Choose one: a rectangle, a square or a rhombus.
37
PSAngle x is the base angle of an isosceles triangle. The apex angle is 40 degrees. What is angle x, in degrees?
38
RReflect the point (3, -2) in the x-axis, then translate it 1 right. Write the final point.
39
FConvert 2.25 m into centimetres.
40
FWrite 0.4 as a fraction in its simplest form.
9.3

Feedback sheet and timing guide

Year 6
A feedback sheet names the statement each item tests (Year 5-6), A timing guide of 45 minutes, marked as a practice guide only (Year 5-6)
Video lesson: Feedback sheet and timing guideComing soon
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. After you finish both papers, use the feedback sheet to find the items you got wrong. Each item names the statement it tests, so you know which chapter to revisit.

Timing guide

Practice guide only, not the official test. Allow about 45 minutes in total for both papers. Do not spend more than about 2 minutes on any single item; come back to it at the end.

Key ideas

  • Mark your own paper using the solutions after each item.
  • Note the statement for each item you got wrong, then revisit that chapter.
  • Count your correct items, and aim to improve on your last attempt.
Worked example 9.3.1
Item A1 is wrong. What should you revise?

Method. Use the feedback sheet, which names the statement tested.

  1. Find the item. Look up A1 in the feedback table.
    A1
  2. Read the statement. The statement is place value.
    Place value (chapter 1)
  3. Revise. Go back to chapter 1 and practise place value.
    Chapter 1
  4. Write the answer.
    Place value (chapter 1)

Check. The feedback table names the chapter. ✓

Worked example 9.3.2
You got 4 items wrong in Paper A, and all of them are fractions. Which chapter should you revise?

Method. Look for the statement that the wrong items share.

  1. Find the pattern. All four items test fractions.
    fractions
  2. Name the chapter. Fractions are in chapter 2.
    Chapter 2
  3. Write the answer.
    Chapter 2

Check. Fractions are chapter 2. ✓

Worked example 9.3.3
An explain item has the answer "the sum is even". Is a reason needed?

Method. Explain items need a reason in words, not only a number.

  1. Check the question. The question says to explain.
    explain
  2. Decide. A bare answer does not show the reason, so a reason is needed.
    Yes
  3. Write the answer.
    Yes

Check. A reason is needed for an explain item. ✓

ItemStatement it tests
A1Place value (chapter 1)
A2Rounding (chapter 1)
A3Negative numbers (chapter 1)
A4Order of operations (chapter 1)
A5Multi-step problems (chapter 1)
A6Comparing fractions (chapter 2)
A7Adding fractions (chapter 2)
A8Fractions of amounts (chapter 2)
A9Simplifying ratios (chapter 3)
A10Sharing in a ratio (chapter 3)
A11Unit method (chapter 3)
A12Best value (chapter 3)
A13Metric conversions (chapter 4)
A14Time and durations (chapter 4)
A15Area of a triangle (chapter 4)
A16Perimeter (chapter 4)
A17Angles at a point (chapter 5)
A18Angles in a triangle (chapter 5)
A19Classifying quadrilaterals (chapter 5)
A20Regular polygons (chapter 5)
A21Four quadrants (chapter 6)
A22Translation (chapter 6)
A23Reflection (chapter 6)
A24Linear sequences (chapter 7)
A25The nth term (chapter 7)
A26Solving equations (chapter 7)
A27Pairs with two unknowns (chapter 7)
A28Mean (chapter 8)
A29Median (chapter 8)
A30Pie charts (chapter 8)
A31Range (chapter 8)
A32Always, sometimes or never (chapter 1)
A33Equivalent fractions and decimals (chapter 2)
A34Is a term in a sequence? (chapter 7)
A35Angle types (chapter 5)
A36Same area, different perimeter (chapter 4)
A37Percentages (chapter 2)
A38Missing coordinates and centres (chapter 6)
A39Equations (chapter 7)
A40Substitution (chapter 7)
B1Place value (chapter 1)
B2Rounding (chapter 1)
B3Negative numbers (chapter 1)
B4Order of operations (chapter 1)
B5Factors and multi-step reasoning (chapter 1)
B6Fractions and decimals (chapter 2)
B7Adding mixed numbers (chapter 2)
B8Multiplying fractions (chapter 2)
B9Equivalent decimals and percentages (chapter 2)
B10Ratio (chapter 3)
B11Scale factor (chapter 3)
B12Sharing in a ratio (chapter 3)
B13Unit method (chapter 3)
B14Time (chapter 4)
B15Miles and kilometres (chapter 4)
B16Area of a parallelogram (chapter 4)
B17Same area, different perimeter (chapter 4)
B18Angles in a quadrilateral (chapter 5)
B19Angles in a triangle (chapter 5)
B20Classifying quadrilaterals (chapter 5)
B21Exterior angles (chapter 5)
B22Centre of a rectangle (chapter 6)
B23Reflection in x = k (chapter 6)
B24Compass turns (chapter 6)
B25Is a term in a sequence? (chapter 7)
B26Solving equations (chapter 7)
B27Substitution (chapter 7)
B28Pairs with two unknowns (chapter 7)
B29Missing value from a mean (chapter 8)
B30Median (chapter 8)
B31Line graphs (chapter 8)
B32Valid conclusions from graphs (chapter 8)
B33Multi-step money problems (chapter 1)
B34Fractions of measures (chapter 4)
B35Comparing fractions and percentages (chapter 2)
B36Regular polygons (chapter 5)
B37Isosceles triangles (chapter 5)
B38Reflection then translation (chapter 6)
B39Metric conversions (chapter 4)
B40Equivalent fractions and decimals (chapter 2)

Chapter summary

SkillMethod
Practice paperWork the items without a calculator, show your working, and give a reason for explain items.
Use the feedback sheetFind the statement for each wrong item, and revisit that chapter.
TimingAbout 45 minutes for both papers together, as a practice guide only.

Can you…?

  • I have worked through Paper A and Paper B without a calculator
  • I have shown my working and given a reason for each explain item
  • I have used the feedback sheet to find the statements to revisit
  • I have checked my answers against the solutions

Key terms

practice paper
a set of questions in the style of the test, for practice only
feedback sheet
a table that names the statement each item tests
statement
a learning objective from the programme of study that an item tests

Exercise 9Z  Check-up

Non-calculator
1
Write the value of the 8 in 5,082,140.
2
Work out 15 - 2 x (4 + 1).
3
Simplify the fraction 18/24.
4
A tin of paint costs 12 pounds. How much do 7 tins cost, in pounds?
5
A rectangle is 11 cm by 6 cm. Find its area, in cm2.
6
What is the next term of the sequence 30, 26, 22, __?
7
The point (-2, -5) is in which quadrant? Write first, second, third or fourth.
8
The mean of five numbers is 6. Four of them add up to 22. What is the fifth number?
9
Explain why a triangle cannot have two right angles.
10
Write the formula for the nth term of 2, 5, 8, 11.

Total 19 marks. Allow about 19 minutes.

Exercise 9X  Practice test questions

Non-calculator
1
FWrite the number 3,004,050 in words, using "million", "thousand" and "hundred".[1 mark]
2
PSWork out 1/2 + 2/3 + 1/6. Give your answer in its simplest form.[2 marks]
3
PSA bag of 12 apples costs 3.60 pounds. What is the cost of one apple, in pence?[2 marks]
4
PSThe angles of a quadrilateral are 90, 90 and 70 degrees. Find the fourth angle, in degrees.[2 marks]
5
FA cuboid is 4 cm by 3 cm by 5 cm. What is its volume, in cm3?[1 mark]
6
PSA sequence has the first term 7 and the difference 4. What is the 15th term?[2 marks]
7
PSSolve 5x - 3 = 22.[2 marks]
8
RExplain why the point (4, -4) is not in the second quadrant.[3 marks]
9
RTick the statements that are true about a pie chart of 360 pupils. Options: A sector of 90 degrees shows 90 pupils | A sector of 90 degrees shows 45 pupils | A sector of 180 degrees shows a quarter of the pupils | All the sectors add up to 360 degrees. Write the options you would tick, in the order given.[2 marks]
10
PSThe mean of 3, 7, 9 and x is 7. Find x.[2 marks]
← Chapter 8: Statistics and data

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings