Year 6 Arithmetic (SATs) Algebra and formulae: check-up and practice test questions

Method. Cost is the number of notebooks times the price.

1. Use letters. C = 4 × n.
   C = 4n
2. Write the answer.
   C = 4n

Check. If n = 3, C = 12. ✓

Method. Replace a with 4, then multiply and add.

1. Substitute. 2 × 4 + 9.
   2 × 4 + 9
2. Multiply. 8 + 9.
   8 + 9
3. Add. 8 + 9 = 17.
   17
4. Write the answer.
   17

Check. 17 - 9 = 8 = 2 × 4. ✓

Method. Replace m and n, then multiply and subtract.

1. Substitute. 5 × 3 - 4.
   5 × 3 - 4
2. Multiply. 15 - 4.
   15 - 4
3. Subtract. 15 - 4 = 11.
   11
4. Write the answer.
   11

Check. 11 + 4 = 15 = 5 × 3. ✓

Method. Find the step, then add it.

1. Find the step. 13 - 9 = 4.
   4
2. Add the step. 21 + 4 = 25 and 25 + 4 = 29.
   25, 29
3. Write the answer.
   25 and 29

Check. The rule is add 4. ✓

Method. Find the difference between two terms.

1. Find the step. 25 - 30 = -5.
   -5
2. Write it in words. Each term is 5 less than the one before.
   subtract 5
3. Write the answer.
   subtract 5

Check. 15 - 20 = -5 as well. ✓

Method. Add the step of 5 nine times.

1. Find the step. 9 - 4 = 5.
   5
2. Add nine steps. 4 + 9 × 5 = 4 + 45.
   49
3. Write the answer.
   49

Check. 4 + 45 = 49. ✓

Method. Take 9 from 16.

1. Subtract. 16 - 9 = 7.
   7
2. Write the answer.
   7

Check. 7 + 9 = 16. ✓

Method. Add the two equations.

1. Add. 2x = 14.
   2x = 14
2. Divide. x = 7.
   7
3. Write the answer.
   7

Check. 7 + 4 = 11 and 7 - 4 = 3. ✓

Method. Go through the number of 5p coins, in order.

1. Try 0, 1 and 2 five-pence coins. Then 10p, 5p and 0p are made with 1p coins.
   (0, 10), (1, 5), (2, 0)
2. Count. There are 3 ways.
   3
3. Write the answer.
   3

Check. Each way makes 10p. ✓

Method. Go through x in order and find y.

1. x = 4. y = 0.
   (4, 0)
2. x = 3. y = 1.
   (3, 1)
3. x = 2. y = 2.
   (2, 2)
4. Write the answer.
   (4, 0), (3, 1), (2, 2).

Check. Each pair adds to 4. ✓

Method. Cost is the price per metre times the number of metres.

1. Use letters. C = 3 × m.
   C = 3m
2. Write the answer.
   C = 3m

Check. If m = 4, C = 12. ✓

Method. Replace p with 5, then multiply and subtract.

1. Substitute. 6 × 5 - 2.
   6 × 5 - 2
2. Multiply. 30 - 2.
   30 - 2
3. Subtract. 30 - 2 = 28.
   28
4. Write the answer.
   28

Check. 28 + 2 = 30 = 6 × 5. ✓

Method. Replace a and b, then work out each part.

1. Substitute. 3 × 6 + 2 × 5.
   3 × 6 + 2 × 5
2. Work out each part. 18 and 10.
   18 + 10
3. Add. 18 + 10 = 28.
   28
4. Write the answer.
   28

Check. 18 + 10 = 28. ✓

Method. Find the step, then subtract it.

1. Find the step. 37 - 40 = -3.
   -3
2. Subtract the step. 31 - 3 = 28.
   28
3. Write the answer.
   28

Check. 28 + 3 = 31. ✓

Method. Find the step between two terms.

1. Find the step. 7 - 2 = 5.
   5
2. Write it in words. Each term is 5 more than the one before.
   add 5
3. Write the answer.
   add 5

Check. 12 - 7 = 5. ✓

Method. Add the step of 4 nine times.

1. Find the step. 10 - 6 = 4.
   4
2. Add nine steps. 6 + 9 × 4 = 6 + 36.
   42
3. Write the answer.
   42

Check. 6 + 36 = 42. ✓

Method. Add the two equations.

1. Add. 2x = 18, so x = 9.
   x = 9
2. Find y. 9 + y = 15, so y = 6.
   y = 6
3. Write the answer.
   x = 9 and y = 6

Check. 9 - 6 = 3. ✓

Method. Go through the number of 3p coins in order: 0, 1, 2, 3 and 4.

1. Try 0 three-pence coins. 12 ÷ 2 = 6 two-pence coins.
   6 two-pence coins
2. Try 2 three-pence coins. 12 - 6 = 6p left, so 3 two-pence coins.
   3 two-pence coins
3. Try 4 three-pence coins. 12 - 12 = 0, so 0 two-pence coins.
   0 two-pence coins
4. Count the ways. Odd numbers of 3p coins leave an odd amount, so they do not work. There are 3 ways.
   3 ways
5. Write the answer.
   3 ways

Check. 6 × 2 = 12, 3 × 2 + 2 × 3 = 12 and 4 × 3 = 12. ✓

Method. Pupils in the classes plus the extra pupils.

1. Pupils in the classes. 30 × c.
   30c
2. Add the extra. P = 30c + 4.
   P = 30c + 4
3. Write the answer.
   P = 30c + 4

Check. If c = 2, P = 64. ✓

Method. Put both values into both equations.

1. Check the sum. 7 + 3 = 10.
   10
2. Check the difference. 7 - 3 = 4.
   4
3. Write the answer.
   Yes, because 7 + 3 = 10 and 7 - 3 = 4.

Check. Both equations are true. ✓

Method. Work out the first value, then undo the steps for the second.

1. Substitute x = 5. 4 × 5 - 3 = 20 - 3 = 17.
   17
2. Solve 4x - 3 = 25. Add 3 to get 28, then divide by 4.
   28 ÷ 4 = 7
3. Write the answer.
   17, then x = 7

Check. 4 × 7 - 3 = 25. ✓

Method. Go through a from 1 to 9, and find b each time.

1. List a and b. a = 1 gives b = 9; a = 9 gives b = 1; each a from 1 to 9 gives one b.
   9 pairs
2. Write the answer.
   9

Check. Each of the 9 values of a has one b from 1 to 9. ✓