Year 6 Maths reasoning (SATs) Practice paper: reasoning: check-up and practice test questions

Method. Find the column of the 8.

1. Find the column. The 8 is in the ten thousands column.
   ten thousands
2. Value. 8 x 10,000 = 80,000.
   80,000
3. Write the answer.
   80,000

Check. 80,000. ✓

Method. Brackets, then multiply, then subtract.

1. Brackets. 4 + 1 = 5.
   5
2. Multiply. 2 x 5 = 10.
   10
3. Subtract. 15 - 10 = 5.
   5
4. Write the answer.
   5

Check. 15 - 10 = 5. ✓

Method. Divide top and bottom by 6.

1. HCF. The highest common factor of 18 and 24 is 6.
   6
2. Divide. 18 / 6 = 3 and 24 / 6 = 4.
   3/4
3. Write the answer.
   3/4

Check. 3/4 is in simplest form. ✓

Method. Multiply the price by the number of tins.

1. Multiply. 12 x 7 = 84.
   84
2. Write the answer.
   84

Check. 84 / 7 = 12. ✓

Method. Length x width.

1. Multiply. 11 x 6 = 66.
   66 cm²
2. Write the answer.
   66

Check. 66 / 6 = 11. ✓

Method. Subtract 4 each time.

1. Difference. 26 - 30 = -4.
   -4
2. Next term. 22 - 4 = 18.
   18
3. Write the answer.
   18

Check. 18 + 4 = 22. ✓

Method. Look at the signs of x and y.

1. Signs. x is negative and y is negative.
   -, -
2. Quadrant. Both negative is the third quadrant.
   third
3. Write the answer.
   third

Check. Third quadrant: both negative. ✓

Method. The total is 5 x 6 = 30.

1. Total. 5 x 6 = 30.
   30
2. Fifth number. 30 - 22 = 8.
   8
3. Write the answer.
   8

Check. 22 + 8 = 30. ✓

Method. Add the two right angles.

1. Two right angles. 90 + 90 = 180.
   180
2. Third angle. 180 - 180 = 0, which is not possible.
   0
3. Write the answer.
   Because two right angles add up to 180 degrees, which leaves 0 degrees for the third angle.

Check. 90 + 90 = 180. ✓

Method. The difference is 3, and the formula starts with 3n.

1. Difference. 5 - 2 = 3.
   3n
2. Adjust. When n = 1, 3 - 1 = 2.
   3n - 1
3. Write the answer.
   3n - 1

Check. 3 x 2 - 1 = 5. ✓

Method. Read each part of the number.

1. Millions. 3,000,000 is three million.
   three million
2. Thousands. 4,000 is four thousand.
   four thousand
3. Units. 50 is fifty.
   fifty
4. Write the answer.
   three million, four thousand and fifty

Check. 3,000,000 + 4,000 + 50 = 3,004,050. ✓

Method. Use a common denominator of 6.

1. Write with 6. 1/2 = 3/6, 2/3 = 4/6 and 1/6 stays.
   3/6 + 4/6 + 1/6
2. Add. 3 + 4 + 1 = 8, so 8/6 = 4/3.
   4/3
3. Write the answer.
   4/3

Check. 8/6 = 4/3. ✓

Method. Divide the cost in pence by the number of apples.

1. Pence. 3.60 pounds = 360 pence.
   360
2. One apple. 360 / 12 = 30 pence.
   30
3. Write the answer.
   30

Check. 30 x 12 = 360. ✓

Method. Add the three angles, then take from 360.

1. Add. 90 + 90 + 70 = 250.
   250
2. Subtract. 360 - 250 = 110.
   110
3. Write the answer.
   110

Check. 250 + 110 = 360. ✓

Method. Multiply length, width and height.

1. Multiply. 4 x 3 = 12, then 12 x 5 = 60.
   60
2. Write the answer.
   60

Check. 60 / 5 = 12. ✓

Method. Use first term + (n - 1) x difference.

1. Steps. The 15th term is 14 steps after the first.
   14
2. Work out. 7 + 14 x 4 = 7 + 56 = 63.
   63
3. Write the answer.
   63

Check. 7 + 56 = 63. ✓

Method. Add 3 to both sides, then divide by 5.

1. Add 3. 5x = 25.
   25
2. Divide. x = 25 / 5 = 5.
   5
3. Write the answer.
   5

Check. 5 x 5 - 3 = 22. ✓

Method. Check the sign of x and y.

1. Sign of x. x = 4 is positive.
   +
2. Sign of y. y = -4 is negative, so the point is in the fourth quadrant.
   fourth
3. Write the answer.
   Because the x-coordinate is positive, and the second quadrant needs a negative x and a positive y.

Check. Positive x and negative y gives the fourth quadrant. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. With 360 pupils, a sector of 90 degrees is a quarter, so it shows 90 pupils, and the sectors always add to 360 degrees.
   A sector of 90 degrees shows 90 pupils, All the sectors add up to 360 degrees
3. Leave the others unticked. These do not match.
   A sector of 90 degrees shows 45 pupils, A sector of 180 degrees shows a quarter of the pupils are not ticked
4. Write the answer.
   A sector of 90 degrees shows 90 pupils, All the sectors add up to 360 degrees

Check. Each ticked option is true. ✓

Method. The total is 4 x 7 = 28.

1. Total. 4 x 7 = 28.
   28
2. Find x. 28 - (3 + 7 + 9) = 28 - 19 = 9.
   9
3. Write the answer.
   9

Check. 3 + 7 + 9 + 9 = 28. ✓