Foundation and Higher · rearranging formulae

Change the subject.
Undo each step,
on both sides.

last thing done
is the first undone

one word to know —

Subject

the letter on its own

A = lw · A is the subject

step 1 of 4

Make x the subject

1. What happened to x? × 3, then + 2.

2. Undo in reverse: − 2 first, then ÷ 3.

✓ The whole of y − 2 is divided by 3

y = 3x + 2

y − 2 = 3x − 2

y − 23 = x ÷ 3

x = y − 23

step 2 of 4

Clear a fraction

1. × 2 on both sides: the fraction has gone.

2. h is multiplied by b, so divide by b.

✓ h = 2A ÷ b

A = bh2 make h the subject

2A = bh × 2

2Ab = h ÷ b

h = 2Ab

step 3 of 4

Undo a square

1. r was squared, then × π. Undo × π first.

2. Square root to undo the square.

✓ Root the whole of the other side

A = πr² make r the subject

Aπ = r² ÷ π

√Aπ = r square root

r = √Aπ

step 4 of 4 · Higher

Subject appears twice

1. Get every x term on one side.

2. Factorise so x appears once.

✓ Then divide by the bracket

ax + 3 = bx + 7

ax − bx = 4 x terms together

x(a − b) = 4 factorise

x = 4a − b

changing the subject —

Same both sides

every single step

Reverse order

undo the last thing first

Twice?

collect, then factorise

+ undoes −, × undoes ÷,
√ undoes squaring.

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