Download Working Out Formulae

Algebra
N1/L2.4
WORKING OUT FORMULAE
A formula is a quick way of writing down a general method for solving a problem,
which can be used whatever the numbers are.
For example, to find the area of any rectangle we multiply the length by the width.
The formula is
A = L x W
or just
A = LW
where A = Area L = Length W = Width
To find the speed a car drives at we take the distance travelled and divide it by
the time taken.
S = D
T
where S = Speed D = Distance and T = Time
We can then use the formula for a particular case.
For example: to find the area of a room which is 5m long and 3m wide, we
substitute the numbers for the letters in the formula.
A = L x W
L= 5
W= 3
Area = 5 x 3 m
= 15m²
To find the speed of a car which travels 200 miles in 4 hours, we replace the
letters in the formula by the numbers.
S = D
T
D = 200
T = 4
S = 200 mph
4
= 50mph
1
Algebra
N1/L2.4
A)
Try working out the solutions to these questions
1)
A = LW
Find A when L = 20 and W = 9
2)
V = lwh
Find V when l = 5 w = 3 and h = 4
3)
l=
Find l when z = 150 d = 25
4)
C= L+8
5)
Rob’s total wage is found with the formula t = w + 30. What is his total
wage (t) when w = 175?
6)
Jean’s take home pay is found with the formula w = g – d. Find w when g =
300 and d = 140
7)
The distance travelled by a bike can be found with the formula d = st.
Find d when s = 12 and t = 3
8)
A bakery makes bread using the formula: T = b + 50 to find the total
needed. How many loaves are baked when b = 95?
9)
The number of bricks in one course of a wall is found with the formula
z-d
Find C when L = 125
L
.
20
How many are used when L = 800?
10) The perimeter of a garden is P = 2L + 2W. What is P when L = 12 and W =
8
11)
PRT
Interest on money is found by the formula I = 100
How much interest is due when P = 500 R = 2 and T = 2?
When formulae are more complicated it helps to remember the order of
operations:
Brackets come first
Of
Divide
(BODMAS)
Multiply
Add
Subtract
2
Algebra
N1/L2.4
For example the formula:
2h + ab
means
2xh + axb
We know from the BODMAS rule that multiplying has to be done before adding.
So if h = 3, a = 4 and b = 10
2h + ab
=
2 x 3 + 4 x 10
=
6
+ 40
= 46
If a number is multiplying a bracket, the multiplication sign is usually left out.
eg.
c (3 + b)
Means c x (3 + b)
We know that the bracket has to be done first.
So if c = 6 and b = 5
c (3 + b)
= 6 x (3 + 5)
= 6 x 8
= 48
B)
Try solving these:
1)
a=2
b=4
c=5
y = 10
a) ab + c
c) bc + ay
e) 3( a + b)
g) 2ay + 3c
b) 2y – a
d) ab + cy
f) b(2a + c)
h) 3ac + 2bc
2)
A = lb + 3c
Find A when l = 4 b = 7 and c = 5
3)
The cost of hiring a motorbike is given in the formula C = 12 + 6d
where d is the number of days. Find C when d = 5.
3
Algebra
N1/L2.4
4)
The formula for the time it takes to cook a recipe is
T = 15w + 20
Find T when w = 3.
5)
V = lbh + 4lh
Find V when l = 5 b = 3 and h = 2.
6)
C = y (2 + b)
Find C if y = 3 b = 12.
7)
T = r (a + 2c)
Find T when r = 5 a = 2 and c = 3
When an expression has to be divided in a formula, any complex parts can be
worked out first.
For example:
R=
 + 2a  All of these have to be divided by 3, so
3
it’s simpler to work out  + 2a first.
So if  = 2 and a = 5
R=
2 + 10
3
R=
12
3
R= 4
C)
Try working out these formulae:
1)

2)
P =
y + z
y
3)
C =
t(2 + s)
when t = 3 s = 6  = 4

4)
Try finding the area of these trapezium shapes using the formula
= b + 2a
A =
when b = 2 and a = 7
when  = 3 y = 2 and z = 10
h x (a + b)
2
where h is the height and a and b
are the parallel sides.
a) h = 6
a = 7
b = 2
b) h = 10
a = 5
b = 3
c) h = 4
a = 6
b = 5
4
Algebra
N1/L2.4
5)
a) Try to work out a formula to find the area of this apartment
a
b
t
s
b) What is the actual area if a = 4 b = 3 s = 6 t = 2 ?
6)
a) You buy cinema tickets for yourself and 2 children. Your ticket will
cost twice as much as a child's ticket. You also pay 3 pounds in bus
fares.
If the child's ticket cost t pounds, what is the total cost of the
outing?
b) The child's ticket cost £1.50 at this cinema. Substitute this into
your formula and find the actual cost.
Check your answers then discuss with your tutor what you need to work on next.
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Algebra
N1/L2.4
Answers
Working Out Formulae
A)
1)
A = 180
2)
V = 60
3)
l=
4)
c = 133
5)
t = 205
6)
w = 160
7)
d = 36
8)
T = 145
9)
40 bricks
125
10) P = 40
11) I = 20
B)
1)
a)
b)
c)
d)
e)
f)
g)
h)
2)
43
3)
42
4)
65
5)
70
6)
42
7)
40
13
18
40
58
18
36
55
70
C)
1)
 = 16
2)
P = 8
3)
C = 6
4)
a) A = 27
b) A = 40
c) A = 22
5)
a) ab + st
b) 24
6)
a) 4t + 3
b) £9
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