Changing the Subject of a formula
Algebra
Changing the subject of a formula
Click on a set
Set 1
Set 3
Set 2
Set 4
Set 5
Set 6
Set 8
Set 7
Set 9
Set 10
Changing the subject of a formula:- set 1
1
If P=5L , change the subject of the formula to L. Hence find L when P=73.
2
If A = 3B+8 , change the subject of the formula to B. Hence find B when A=52.
3
If D=ST , change the subject of the formula to T. Hence find T when D=345 and
S=96.
4
If V=IR , change the subject of the formula to I. Hence find I when V=40 and
R=4.5.
5
If P=3(L+B) , change the subject of the formula to L. Hence find L when P=51
and B=6.
6
If A=L2 , change the subject of the formula to L. Hence find L when A=95.
7
If E=mgh , change the subject of the formula to h. Hence find h when E=2000 ,
g=9.8 and m=6.3.
8
If C=4.5n+20 , change the subject of the formula to n. Hence find n when C=120.
9
If A=7.5M - 4.5m , change the subject of the formula to M. Hence find M when
A=90 and m=8.2.
10
If A=3r2 , change the subject of the formula to r. Hence find r when A=80.
Changing the subject of a formula:- set 2
1
The perimeter of a hexagon is given by P=6L , where L is the length of a side of the
hexagon. Change the subject of the formula to L and hence find L when P=80
2
The volume of a cuboid is given by V=LBH. Change the subject of the formula to
H and hence find H when V=200 , L=8.6 and B=9.3
3
If C=d , change the subject of the formula to d. Hence find d when C=60.
4
The perimeter of a square is given by P=4L , where L is the length of a side of the
square. Change the subject of the formula to L and hence find L when P=62
5
The area of a circle is given by A=r2 , where r is the radius of the circle. Change
the subject of the formula to r and hence find r when A=150.
6
The formula v=u+gt is used in Physics. Change the subject to t. Find t when v=60,
u=24 and g=9.8
7
The perimeter of a rectangle is given by P=2(L+B). Change the subject of the
formula to L and hence find L when P=80 and B=14.
8
If E=mv2 , change the subject of the formula to v and hence find v when E=400
and m=25.
9
The volume of a cylinder is given by V=r2h. Change the subject of the formula to
r and hence find r when V=800 and h = 17.4
Changing the subject of a formula:- set 3
1
If P=5x , change the subject of the formula to x. Hence find x when P=78.
2
If T=8M+3 , change the subject of the formula to M. Hence find M when T=100.
3
If C=d , change the subject of the formula to d. Hence find d when C=40.
4
If y = x2 , change the subject of the formula to x. Hence find x when y=50.
5
If A=LB , change the subject of the formula to B. Hence find B when A=45 and
L=7.8.
6
If V=LBH , change the subject of the formula to B. Hence find B when V=125,
L=7.2 and H=6.1.
7
If E=mgh , change the subject of the formula to h. Hence find h when E=2000 ,
g=9.8 and m=6.3.
8
If P = 4L+3B , change the subject of the formula to L. Hence find L when P=63 and
B=8.6.
9
If y = mx+c , change the subject of the formula to m. Hence find m when y=8, x=5
and c=2.
10
The volume of a cylinder is given by V = r2h. Change the subject of the formula to
h and hence find h when V = 200 and r = 6.3
11
If A=2rh , change the subject of the formula to h. Hence find h when A=180 and
r = 6.3.
12
The area of a circle is given by A = r2 , where r is the radius of the circle. Change
the subject of the formula to r and hence find r when A=75.
Changing the subject of a formula:- set 4
1
If P=8.5L , change the subject of the formula to L. Hence find L when P=100.
2
If A = LB+5 , change the subject of the formula to B. Hence find B when A=80 and
L=10.
3
If V=AH , change the subject of the formula to H. Hence find H when V=700 and
A=120.
4
If T=3.5C , change the subject of the formula to C. Hence find C when T=240.
5
If P=4(L+B) , change the subject of the formula to L. Hence find L when P=81 and
B=4.5.
6
If P=4L+12 , change the subject of the formula to L. Hence find L when A=95.
7
If M=3N-80 , change the subject of the formula to N. Hence find N when M=66.
8
If C= 3D , change the subject of the formula to D. Hence find D when C=140.
9
If C=7.5(M – m) , change the subject of the formula to M. Hence find M when C=90
and m=5.
10
If y=mx+2 , change the subject of the formula to m. Hence find m when y=12 and
x=4.
Changing the subject of a formula:- set 5
1
If A=4LB , change the subject of the formula to B. Hence find
B when A=360 and L=7.8.
2
If V=L3 , change the subject of the formula to L. Hence find
L when V=600.
3
If P=6.5L , change the subject of the formula to L. Hence find
L when P=84.
4
If M=
3N
, change the subject of the formula to N. Hence
4
find N when M=96.
5
If E=mc2 , change the subject of the formula to c. Hence find
c when E=5000 and m=12.
6 If A= 1 bh , change the subject of the formula to b. Hence find
2
b when A=140 and h=6.5.
7
If V=LBH , change the subject of the formula to H. Hence
find H when V= 720, L=8.5 and B=2.6
8
If A=4L2 , change the subject of the formula to L. Hence find
L when A=90.
9
If P = mvg , change the subject of the formula to v. Hence
find v when P=67, g=9.8 and m=2.7.
10
If T=4L+3M , change the subject of the formula to M. Hence
find M when T=470 and L=17.5.
Changing the subject of a formula:- set 6
1
If P = 8L , change the subject of the formula to L. Hence find L when P=78.
2
If A = r2 , change the subject of the formula to r. Hence find r when A=140.
3
If V = r2h , change the subject of the formula to h. Hence find h when
V=1000 and r=10.
4
If A=
5
bh , change the subject of the formula to b. Hence find b when A=40
2
and h = 2.5.
5
If C = d , change the subject of the formula to d. Hence find d when C=67.
6
If P =5 (L+B) , change the subject of the formula to L. Hence find L when
P=48 and B=7.
7
D
If S= T
8
If A = rs , change the subject of the formula to s. Hence find s when A=120
and r=5
9
If V=
, change the subject of the formula to T. Hence find T when D=140
and S=60.
1
r2h, change the subject of the formula to r. Hence find r when V=90
3
and h=2.2
10
If S=
1 2
gt , change the subject of the formula to t. Hence find t when S=500
2 and g=9.8
Changing the subject of a formula:- set 7
1
If P=4x+3y , change the subject of the formula to x. Hence find x when P=80
and y=6
2
If V=LBH , change the subject of the formula to L. Hence find L when
V=1000, B=9 and H=14
3
If A=4LB , change the subject of the formula to L. Hence find L when A=90
and B=8.
4
If A=
1
bh, change the subject of the formula to h. Hence find h when A=93
2
and b =21.
5
If K=3T2 , change the subject of the formula to T. Hence find T when K=500 .
6
If y=mx+c, change the subject of the formula to x. Hence find x when y=14 ,
m=2 and c=4.
7
If C=8D+50 , change the subject of the formula to D. Hence find D when C=96
8
If P=
9
If R=
3 (A+100) , change the subject of the formula to A. Hence find A
4 when P=84.
1
(A+B) , change the subject of the formula to A. Hence find
2
A when R=40 and B=15.
10
If B=5.6x2+1 , change the subject of the formula to x. Hence find x when B=40
Changing the subject of a formula:- set 8
1
If v2 = u2+2gs , change the subject of the formula to s. Hence find s when v=78 , u=47
and g=9.8. ( This is a formula used a lot in Physics )
2
If C=
5
(F-32) , change the subject of the formula to F. Hence find F when
9 a) C=36 b) C=61 c) C=75 .
( You should recognize this formula )
3 If A = 3 L2 , change the subject of the formula to L. Hence find L when A = 208.
4
5
6
2
If A= 2rh + 2r2 is the
If V=
formula for the total surface area of the cylinder
shown, change the subject of the formula to h.
Hence find h when A=450 and r=6.4
4 r3 is the formula for the volume of a sphere , change the subject of the
3 formula to r. Hence find r when V=1400.
The total surface area of a cone is given by A = rs + r2. where s is the slant height
of the cone and r is the radius of the base. Change the subject of the formula to s and
hence find s when A = 650 and r = 5.2
Changing the subject of a formula:- set 9
1
If V = r2h , change the subject of the formula to r. Hence find r when
V=1400 and h=8.6.
2
If P=2L+2B , change the subject of the formula to L. Hence find L
when P=68 and B=9.2.
3
If e=mc2 , change the subject of the formula to c. Hence find c when
e= 1.8  106 and m=48.
4 r2 , change the subject of the formula to r. Hence find r
3 when A=200.
4
If A=
5
If A=2rh , change the subject of the formula to r. Hence find r when
A=450 and h=18.
6
If 1  1  1 , change the subject of the formula to f. Hence find f when
v u f
v=25 and u=40.
7
If T=
x 2  y 2 , change the subject of the formula to x. Hence find x
when T= 50 and y=4
8
If E=
1 mgh , change the subject of the formula to h. Hence find h
2 when E=285 , g=9.8 and m=17.8
9 If V= 14 r3 , change the subject of the formula to r. Hence find r when
3 V= 665
Changing the subject of a formula:- set 10
1
2
3
4
5
If P=
4
T  1 , change the subject of the formula to T. Hence find
7 T when P=5.4
a x , change the subject of the formula to x. Hence find x when

x b a=9 and b=7
PRT ,
change the subject of the formula to P. Hence find P when
If I 
100 I=8 , R=3 and T=5
If
If P=2(L+B), change the subject of the formula to B. Hence find B when
P=85 and L=7.9
, change the subject of the formula to r. Hence find r
If V= 3 r3
2 when V=600 .
6 If e= 1 mv2, change the subject of the formula to v. Hence find v when e=520
2 and m=19.5.
7 If F= 2 (D+50) , change the subject of the formula to D. Hence find D
3
when F=60
8 If C= 3 (F-45) , change the subject of the formula to F. Hence find F
8
when C=37.
Changing the subject of a formula
This unit contains 10 sets of questions on changing the
subject of a formula. The sets are graded getting more difficult
as you go. The last few sets reach the standard required in
examinations at Standard Grade Credit level.
This topic is covered in S3 so the sets
can be used for a third year
class or as revision work for an S4 class.