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Transcript
```Algebra
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
f lex i p
= 50mph
ac k s
1
Algebra
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
z-d
the formula
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
f lex i p
Subtract
ac k s
2
Algebra
For example the formula:
2h + ab
means
2xh + axb
We know from the BODMAS rule that multiplying has to be done
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:
f lex i p
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.
ac k s
3
Algebra
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
f lex i p
A =
ac k s
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
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.
f lex i p
work on next.
ac k s
5
Algebra
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
f lex i p
B)
1)
a)
b)
c)
d)
e)
f)
g)
h)
2)
43
3)
42
4)
65
5)
70
6)
42
7)
40
ac k s
13
18
40
58
18
36
55
70
C)
6
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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