Year 6 Maths reasoning (SATs): Paper A
Part of the Year 6 Maths reasoning (SATs) practice paper: reasoning chapter. Chapter overview · whole chapter on one page
Paper A
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.
Method. Work out the total first, then take away the beads given away.
- Total in bags. 4 x 15 = 60.60
- Add the loose beads. 60 + 12 = 72.72
- Take away. 72 - 18 = 54.54
- Write the answer. 54
Check. 72 - 18 = 54. ✓
Method. Use a common denominator, then compare the tops.
- Common denominator. Use 6: 2/3 = 4/6 and 1/2 = 3/6.4/6 and 3/6
- Compare. With the same bottom number, 4 sixths is more than 3 sixths.4/6 > 3/6
- Write the answer. 2/3 = 4/6 and 1/2 = 3/6, so 2/3 is greater.
Check. 4 > 3. ✓
Method. Work out each calculation, using the order of operations.
- 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
- Tick the ones that give 20. The first, second and fourth give 20.4 x 5, 2 + 3 x 6, 40 / 2
- 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-calculatorMethod. Find the column of the 7.
- Find the column. The 7 is in the ten thousands column.ten thousands
- Work out the value. 7 x 10,000 = 70,000.70,000
- Write the answer. 70,000
Check. 70,000 = 7 x 10,000. ✓
Method. Look at the hundreds digit.
- Look at the hundreds digit. The hundreds digit is 9, so round up.9
- Round. 384,000 + 1,000 = 385,000.385,000
- Write the answer. 385,000
Check. 385,000 is the nearest thousand. ✓
Method. Negative numbers are less than zero.
- Smallest. -10 is furthest left.-10
- Order. Then -4, 0, 7.-10, -4, 0, 7
- Write the answer. -10, -4, 0, 7
Check. -10 < -4 < 0 < 7. ✓
Method. Multiply and divide first, then add and subtract.
- Multiply and divide. 4 x 3 = 12 and 8 / 2 = 4.12 and 4
- Add and subtract. 6 + 12 - 4 = 14.14
- Write the answer. 14
Check. 6 + 12 - 4 = 14. ✓
Method. Find the total, then subtract.
- Total. 3 x 24 + 17 = 89.89
- Left. 89 - 29 = 60.60
- Write the answer. 60
Check. 60 + 29 = 89. ✓
Method. Use a common denominator of 24.
- Write with 24. 5/8 = 15/24 and 7/12 = 14/24.15/24 and 14/24
- Compare. 15 is more than 14, so 5/8 is larger.5/8
- Write the answer. 5/8
Check. 15/24 > 14/24. ✓
Method. Use a common denominator.
- Common denominator. 2/3 = 8/12 and 1/4 = 3/12.8/12 + 3/12
- Add. 8 + 3 = 11, so 11/12.11/12
- Write the answer. 11/12
Check. 11/12 is in simplest form. ✓
Method. Divide by 4, then multiply by 3.
- Divide by 4. 36 / 4 = 9.9
- Multiply by 3. 9 x 3 = 27.27
- Write the answer. 27
Check. 27 / 3 = 9. ✓
Method. Divide both parts by the highest common factor, 12.
- HCF. The highest common factor of 24 and 36 is 12.12
- Divide. 24 / 12 = 2 and 36 / 12 = 3.2:3
- Write the answer. 2:3
Check. 2 x 12 = 24 and 3 x 12 = 36. ✓
Method. Find the total parts, then one part.
- Total parts. 2 + 3 = 5 parts.5 parts
- Ann. One part is 60 / 5 = 12, so Ann gets 2 x 12 = 24 pounds.24
- Write the answer. 24
Check. 24 + 36 = 60. ✓
Method. Find the price of one pen, then multiply by 8.
- One pen. 6.50 / 5 = 1.30 pounds.1.30
- Eight pens. 1.30 x 8 = 10.40 pounds.10.40
- Write the answer. 10.40
Check. 10.40 / 8 = 1.30. ✓
Method. Find the price of one item for each pack.
- Pack of 3. 2.10 / 3 = 0.70 pounds each.70p
- Pack of 5. 3.25 / 5 = 0.65 pounds each, which is cheaper.65p
- Compare. The pack of 5 is better value.5
- Write the answer. 5
Check. 65p is less than 70p. ✓
Method. One kilometre is 1000 metres.
- Multiply. 3.4 x 1000 = 3400.3400 m
- Write the answer. 3400 m
Check. 3400 / 1000 = 3.4. ✓
Method. Count the minutes from 09:35 to 11:20.
- To 11:00. 09:35 to 11:00 is 1 hour 25 minutes.1 h 25 min
- To 11:20. 25 + 20 = 45, so 1 h 45 min.1 h 45 min
- Write the answer. 1 h 45 min
Check. 09:35 + 1 h 45 min = 11:20. ✓
Method. Multiply the base and the height, then halve.
- Multiply. 12 x 9 = 108.108
- Halve. 108 / 2 = 54.54 cm²
- Write the answer. 54 cm2
Check. 54 x 2 = 108. ✓
Method. Add all four sides.
- Add. 15 + 8 + 15 + 8 = 46.46
- Write the answer. 46
Check. 2 x (15 + 8) = 46. ✓
Method. Angles at a point add up to 360 degrees.
- Add the known angles. 130 + 95 = 225.225
- Subtract from 360. 360 - 225 = 135.135
- Write the answer. 135
Check. 225 + 135 = 360. ✓
Method. Angles in a triangle add up to 180 degrees.
- Add. 48 + 67 = 115.115
- Subtract from 180. 180 - 115 = 65.65
- Write the answer. 65
Check. 48 + 67 + 65 = 180. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. Some rhombuses have right angles, and those are squares.sometimes fits
- Reject the other choices. A rhombus is a square only when its angles are all right angles, so "always" and "never" are wrong.always and never do not fit
- Write the answer. sometimes
Check. sometimes is the one that fits. ✓
Method. Total of interior angles: (6 - 2) x 180 = 720. Share equally between 6.
- Total. (6 - 2) x 180 = 720.720
- Each angle. 720 / 6 = 120.120
- Write the answer. 120
Check. 120 x 6 = 720. ✓
Method. Look at the signs.
- x. x = -4 is negative.-
- y. y = 3 is positive, so it is the second quadrant.second
- Write the answer. second
Check. Second quadrant: x negative, y positive. ✓
Method. Add 3 to x and subtract 4 from y.
- x. 2 + 3 = 5.5
- y. -1 - 4 = -5.-5
- Write the answer. (5, -5)
Check. (5 - 3, -5 + 4) = (2, -1). ✓
Method. In the y-axis, the sign of x changes.
- Change x. x = 2 becomes -2.-2
- Keep y. y = 3 stays the same.(-2, 3)
- Write the answer. (-2, 3)
Check. (-2, 3) is the same distance from the y-axis. ✓
Method. Add the difference, which is 5.
- Difference. 8 - 3 = 5.5
- Next term. 13 + 5 = 18.18
- Write the answer. 18
Check. 18 - 13 = 5. ✓
Method. Use first term + (n - 1) x difference.
- Steps. Term 12 is 11 steps after term 1.11 steps
- Work out. 5 + 11 x 3 = 5 + 33 = 38.38
- Write the answer. 38
Check. 5 + 33 = 38. ✓
Method. Undo the addition, then the multiplication.
- Subtract 3. 4x = 27 - 3 = 24.24
- Divide by 4. x = 24 / 4 = 6.6
- Write the answer. 6
Check. 4 x 6 + 3 = 27. ✓
Method. List the pairs in order.
- List. 1 + 9, 2 + 8, 3 + 7, 4 + 6.4 pairs
- Count. There are 4 pairs.4
- Write the answer. 4
Check. Each pair adds to 10. ✓
Method. Add the values, then divide by 4.
- Total. 4 + 8 + 6 + 10 = 28.28
- Mean. 28 / 4 = 7.7
- Write the answer. 7
Check. 7 x 4 = 28. ✓
Method. Put the values in order first.
- Order. 2, 4, 7, 9, 11.2, 4, 7, 9, 11
- Middle. The middle value is 7.7
- Write the answer. 7
Check. Two values on each side of 7. ✓
Method. Find the fraction of the whole pie.
- Fraction. 90 / 360 = 1/4.1/4
- Pupils. 1/4 of 120 = 30.30
- Write the answer. 30
Check. 30 x 4 = 120. ✓
Method. Find the largest and smallest values.
- Largest and smallest. Both are 3.3 and 3
- Range. 3 - 3 = 0.0
- Write the answer. Because the largest and smallest values are both 3, so 3 - 3 = 0.
Check. 3 - 3 = 0. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. An odd number plus an odd number gives an even number: for example 3 + 5 = 8.always fits
- Reject the other choices. Odd plus odd is never odd, and it is not only sometimes even.sometimes and never do not fit
- Write the answer. always
Check. always is the one that fits. ✓
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. 3/4, 6/8 and 0.75 are all equal to three quarters.3/4, 6/8, 0.75
- Leave the others unticked. These do not match.7/10, 3/5 are not ticked
- Write the answer. 3/4, 6/8, 0.75
Check. Each ticked option is true. ✓
Watch out. 7/10 is 0.7, and 3/5 is 0.6.
Method. Check whether 98 is a multiple of 3.
- Difference. 100 - 2 = 98.98
- Divide. 98 / 3 is not a whole number, so 100 is not a term.no
- Write the answer. no
Check. 98 / 3 = 32 remainder 2. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. 240 degrees is more than 180 degrees and less than 360 degrees.reflex fits
- Reject the other choices. Acute is under 90 and obtuse is between 90 and 180, so both are wrong.acute and obtuse do not fit
- Write the answer. reflex
Check. reflex is the one that fits. ✓
Method. Find the pairs that multiply to 36.
- Pairs. 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6.1 x 36
- Smallest perimeter. The pair closest together is 6 and 6, with perimeter 24.6 cm by 6 cm
- Write the answer. 6 cm by 6 cm
Check. 6 x 6 = 36. ✓
Method. Find 1% first.
- 1%. 60 / 100 = 0.6.0.6
- 35%. 0.6 x 35 = 21.21
- Write the answer. 21
Check. 21 / 60 = 35%. ✓
Method. Halve the sum of opposite corners.
- x. (1 + 7) / 2 = 4.4
- y. (1 + 5) / 2 = 3.3
- Write the answer. (4, 3)
Check. (4, 3) is halfway. ✓
Method. Write the equation, then undo the operations.
- Equation. 3n + 5 = 26.3n + 5 = 26
- Solve. 3n = 21, so n = 7.7
- Write the answer. 7
Check. 3 x 7 + 5 = 26. ✓
Method. Replace p with 9, then multiply before you add.
- Substitute. 4 x 9 + 6.36 + 6
- Work out. 36 + 6 = 42.42
- Write the answer. 42
Check. 42 - 6 = 36. ✓