A5: Rearranging Formulae

Rearrange v = u + at to make t the subject.

Solution:

Step 1: Subtract u from both sides: v - u = at

Step 2: Divide both sides by a: ^{v - u}⁄_a = t

Answer: t = ^{v - u}⁄_a

Rearrange A = πr² to make r the subject.

Solution:

Step 1: Divide both sides by π: ^A⁄_π = r²

Step 2: Take the square root: √(^A⁄_π) = r

Answer: r = √(^A⁄_π)

Rearrange A = lb to make b the subject.

Solution:

Divide both sides by l: ^A⁄_l = b

Answer: b = ^A⁄_l

Rearrange s = ^d⁄_t to make d the subject.

Solution:

Multiply both sides by t: st = d

Answer: d = st

Rearrange y = mx + c to make x the subject.

Solution:

Step 1: Subtract c from both sides: y - c = mx

Step 2: Divide both sides by m: ^{y - c}⁄_m = x

Answer: x = ^{y - c}⁄_m

Rearrange A = ½bh to make h the subject.

Solution:

Step 1: Multiply both sides by 2: 2A = bh

Step 2: Divide both sides by b: ^2A⁄_b = h

Answer: h = ^2A⁄_b

Rearrange E = ½mv² to make v the subject.

Solution:

Step 1: Multiply both sides by 2: 2E = mv²

Step 2: Divide both sides by m: ^2E⁄_m = v²

Step 3: Take square root: v = √(^2E⁄_m)

Rearrange ax + b = cx + d to make x the subject.

Solution:

Step 1: Subtract cx from both sides: ax - cx + b = d

Step 2: Subtract b from both sides: ax - cx = d - b

Step 3: Factorise left side: x(a - c) = d - b

Step 4: Divide by (a - c): x = ^{d - b}⁄_{a - c}

Rearrange T = 5c + 8 to make c the subject.

Subtract 8: T − 8 = 5c  →  Divide by 5: c = (T − 8)/5

M1 for subtracting 8 first, A1 for the division. Undo in reverse order: +8 was LAST, so it comes off FIRST.

Rearrange V = πr²h to make r the subject.

÷ πh: V/(πh) = r²  →  Square root: r = √(V/(πh))

M1 for dividing by πh, A1 for the root. The root undoes the SQUARE — last-in-first-out again.

The formula for converting Celsius to Fahrenheit is F = 1.8C + 32. Rearrange to make C the subject, then convert 95°F to Celsius.

Subtract 32: F − 32 = 1.8C  →  Divide by 1.8: C = (F − 32)/1.8

95°F: C = (95 − 32)/1.8 = 63/1.8 = 35°C

M1 for the rearrangement, A1 for C = (F − 32)/1.8, A1 for 35°C. Applied rearrangements (conversion, physics) are the standard exam context.

Q1. a − 2 = 3b → b = (a − 2)/3

Q2. Divide by m: a = F/m

Q3. Divide by 2π: r = C/(2π)

Q4. Subtract u², divide by 2a: s = (v² − u²)/(2a)

Q5. P/2 = l + w → w = P/2 − l

Q6. ax − bx = 8 → x(a − b) = 8 → x = 8/(a − b) — factorise when x appears twice

Q7. y/4 = x − 3 → x = y/4 + 3

Q8. A/(2l) − wh = lw → hmm, divide first: A/2 = lw + wh = w(l + h) → w = A/(2(l + h))