Foundation and Higher · substitution

Substitution.
Swap the letter,
then BIDMAS.

negatives go
in brackets

it just means —

Substitute

put a number in place of a letter

then work it out in order

step 1 of 4

Swap the letters

1. 3a means 3 × a. Write the × back in.

2. Multiply first, then add.

✓ 3a + 2b = 22

3a + 2b a = 4, b = 5

= 3 × 4 + 2 × 5

= 12 + 10

= 22

step 2 of 4

Watch the powers

1. Only the x is squared, not the 2.

2. Indices come before multiplying.

✓ 2x² = 18

2x² x = 3

= 2 × 3²

= 2 × 9

= 18 not 6² = 36

step 3 of 4

Negative numbers

1. Put every negative in brackets.

2. (−2)² = 4 and 3 × (−2) = −6.

3. Subtracting −6 is adding 6.

✓ The answer is 10, not −10 or −2

x² − 3x x = −2

= (−2)² − 3 × (−2)

= 4 − (−6)

= 4 + 6 = 10

step 4 of 4

Into a formula

1. at means a × t.

2. Multiply before you add: not 7 × 6.

✓ v = 17

v = u + at u = 5, a = 2, t = 6

v = 5 + 2 × 6

v = 5 + 12

v = 17

substitution —

Swap

each letter for its number

Brackets

around every negative

BIDMAS

indices, then ×, then +

3a means 3 × a.
Write the × back in.

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