Rearranging formulae: powers and roots

The Maths Habit

  1. Make x the subject of y = 4x − 9

    x = y + 94

  2. Make x the subject of y = x5 + 2

    x = 5(y − 2)

  3. Make x the subject of p = q − 3x

    x = q − p3

x2 = 49. What could x be?

7

−7

What undoes this?

x2 ±√

What undoes this?

√x Squaring

What undoes this?

x3 ∛

Undo a square with ±√

Undo a square root by squaring

Undo a cube with ∛

Make x the subject of y = 3x2 − 4

y=3x2 − 4+ 4
y + 4=3x2÷ 3
y + 43=x2±√
±√y + 43=x
x=±√y + 43

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of p = x2 + 9

p=x2 + 9− 9
p − 9=x2±√
±√p − 9=x
x=±√p − 9

Make x the subject of y = 3x2 − 4

y=3x2 − 4+ 4
y + 4=3x2÷ 3
y + 43=x2±√
±√y + 43=x
x=±√y + 43

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of m = x3 − 6

m=x3 − 6+ 6
m + 6=x3∛
∛m + 6=x
x=∛m + 6

Make x the subject of y = √x − 4

y=√x − 4+ 4
y + 4=√xsquare
(y + 4)2=x
x=(y + 4)2

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of p = 3√x

p=3√x÷ 3
p3=√xsquare
p29=x
x=p29

Make x the subject of y = √x − 4

y=√x − 4+ 4
y + 4=√xsquare
(y + 4)2=x
x=(y + 4)2

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of k = √x + 2

k=√x + 2square
k2=x + 2− 2
k2 − 2=x
x=k2 − 2

Make x the subject of y = (x − 4)2

y=(x − 4)2±√
±√y=x − 4+ 4
4 ± √y=x
x=4 ± √y

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of p = 2(x + 3)2

p=2(x + 3)2÷ 2
p2=(x + 3)2±√
±√p2=x + 3− 3
−3 ± √p2=x
x=−3 ± √p2

Make x the subject of y = (x − 4)2

y=(x − 4)2±√
±√y=x − 4+ 4
4 ± √y=x
x=4 ± √y

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of t = (x + 1)2 − 6

t=(x + 1)2 − 6+ 6
t + 6=(x + 1)2±√
±√t + 6=x + 1− 1
−1 ± √t + 6=x
x=−1 ± √t + 6

Make x the subject of y = 6x2

y=6x2× x2
x2y=6÷ y
x2=6y±√
x=±√6y

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of k = 4√x

k=4√x× √x
k√x=4÷ k
√x=4ksquare
x=16k2

Make x the subject of y = 6x2

y=6x2× x2
x2y=6÷ y
x2=6y±√
x=±√6y

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of a = cx2 + 2

a=cx2 + 2− 2
a − 2=cx2× x2
x2(a − 2)=c÷ (a − 2)
x2=ca − 2±√
x=±√ca − 2

Make x the subject of y = 6x2

y=6x2× x2
x2y=6÷ y
x2=6y±√
x=±√6y

BIDMAS in reverse

Bbrackets
Ipowers
D M÷ ×
A S+ −

Undo from the bottom up

Make x the subject of y = x2 + ab

y=x2 + ab× b
by=x2 + a− a
by − a=x2±√
x=±√by − a

Make x the subject of y = √x + 4

Ax = (y − 4)2
Bx = y2 − 4
Cx = √y − 4
Dx = y2 − 16
A: rightB: squared first: undo + 4 firstC: square rooted: undo √ by squaringD: squared each term: square all of one side

Rearranging formulae worksheet, page 1

Answer sheet

  1. A = πr2 is the area of a circle. Make r the subject. Then find r when A = 50, to 1 decimal place.

    r = √Aπ, r = 4.0

  2. Ola makes x the subject of y = x2 − 9 and writes x = y + 3. What has Ola done wrong?

    Square rooted each term. x = ±√y + 9

  1. Make x the subject of y = x2 − 8

    x = ±√y + 8

  2. Make x the subject of p = √x + 6

    x = (p − 6)2

  3. Make x the subject of t = (x − 3)2

    x = 3 ± √t

  4. Make x the subject of k = 5x2

    x = ±√5k
Exit tickets to print