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CHAPTER 9
FORMULAS
AIM: To find the value of a formula using substitution.
To change the subject of a formula, using the inverse operations.
To change the subject of a formula and calculate the value of the new subject.
9.1 SUBSTITUTION
One uses a recipe to bake a cake. A formula is like a recipe, guiding you to reach a certain result.
l
A b
The area of a rectangle is given by the formula A = l x b where
A = area
l = length of rectangle
b = width of rectangle.
A, l and b act like variables (unknowns). They can vary from situation to situation.
EXAMPLE 9.1
A person wants to paint his verandah. The length of the verandah is 7 metre and the width 3
metre. What is the total area he wants to paint?
We know the area of a rectangle is given by A = l x b.
So we substitute l = 7 and b = 3 in the formula:
A = 7x3
A = 21 m²
EXAMPLE 9.2
Suppose his verandah was 5 metre long and 2 metre in width, what would the area be?
We use A = l x b and substitute l = 5 and b = 2.
Area = 5 x 2
Area = 10 m²
, 56
EXAMPLE 9.3
The number of beats of a person's pulse is described by the formula n = 90t
where n = number of beats and
t = time in minutes.
Calculate the number of times his pulse beats in:
9.3.1 10 min
n = 90t
Substitute t = 10 minutes:
n = 90(10)
n = 900 beats
9.3.2 2 hours
n = 90t
Substitute t = 2 x 60 minutes:
n = 90(120)
n = 10800 beats
EXAMPLE 9.4
d = 110t expresses the distance a car travels at a speed of 110 km/h.
(Distance = speed x time). Calculate the distance travelled in:
9.4.1 2 hours
Distance travelled for t = 2 hours:
d = 110(2)
d = 220 km
9.4.2 5½ hours
Distance travelled for t = 5½ hours:
d = 110(5,5)
d = 605 km
EXAMPLE 9.5
Find the value of (a + b)(b + c) if a = 2, b = 3 and c = 4.
(a + b)(b + c) = (2 + 3)(3 + 4)
= 5 x 7
= 35
CHAPTER 9
FORMULAS
AIM: To find the value of a formula using substitution.
To change the subject of a formula, using the inverse operations.
To change the subject of a formula and calculate the value of the new subject.
9.1 SUBSTITUTION
One uses a recipe to bake a cake. A formula is like a recipe, guiding you to reach a certain result.
l
A b
The area of a rectangle is given by the formula A = l x b where
A = area
l = length of rectangle
b = width of rectangle.
A, l and b act like variables (unknowns). They can vary from situation to situation.
EXAMPLE 9.1
A person wants to paint his verandah. The length of the verandah is 7 metre and the width 3
metre. What is the total area he wants to paint?
We know the area of a rectangle is given by A = l x b.
So we substitute l = 7 and b = 3 in the formula:
A = 7x3
A = 21 m²
EXAMPLE 9.2
Suppose his verandah was 5 metre long and 2 metre in width, what would the area be?
We use A = l x b and substitute l = 5 and b = 2.
Area = 5 x 2
Area = 10 m²
, 56
EXAMPLE 9.3
The number of beats of a person's pulse is described by the formula n = 90t
where n = number of beats and
t = time in minutes.
Calculate the number of times his pulse beats in:
9.3.1 10 min
n = 90t
Substitute t = 10 minutes:
n = 90(10)
n = 900 beats
9.3.2 2 hours
n = 90t
Substitute t = 2 x 60 minutes:
n = 90(120)
n = 10800 beats
EXAMPLE 9.4
d = 110t expresses the distance a car travels at a speed of 110 km/h.
(Distance = speed x time). Calculate the distance travelled in:
9.4.1 2 hours
Distance travelled for t = 2 hours:
d = 110(2)
d = 220 km
9.4.2 5½ hours
Distance travelled for t = 5½ hours:
d = 110(5,5)
d = 605 km
EXAMPLE 9.5
Find the value of (a + b)(b + c) if a = 2, b = 3 and c = 4.
(a + b)(b + c) = (2 + 3)(3 + 4)
= 5 x 7
= 35
