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Unit F1 Section 1
Using Formulae

In formulae, letters are used to represent numbers. For example, the formula

A = lw

can be used to find the area of a rectangle. Here A is the area, l the length and w the width. In this formula, lw means l × w. Formulae are usually written in this way, without multiplication signs.

The perimeter of the rectangle would be given by the formula

P = 2l + 2w

Here again there are no multiplication signs, and 2l means 2 × l and 2w means 2 × w.

Worked Examples

1

The perimeter of a rectangle can be found using the formula

P = 2l + 2w

Find the perimeter if l = 8 and w = 4.

This gives

P = 2 × 8 + 2 × 4
= 16 + 8
= 24
2

The final speed of a car is v and can be calculated using the formula

v = u + at

where u is the initial speed, a is the acceleration and t is the time taken.

Find v if the acceleration is 2 ms−2, the time taken is 10 seconds and the initial speed is 4 ms−1.

The acceleration is 2 ms−2 so a = 2. The initial speed is 4 ms−1 so u = 4.

The time taken is 10 s so t = 10 .

Using the formula

v = u + a t

gives

v = 4 + 2 × 10
= 4 + 20
= 24 ms−1

Exercises

The area of a rectangle is found using the formula A = l w and the perimeter using P = 2l + 2w. Find the area and perimeter if:

(a)

l = 4 and w = 2

A =

P =

(b)

l = 10 and w = 3

A =

P =

(c)

l = 11 and w = 2

A =

P =

(d)

l = 5 and w = 4

A =

P =

The formula v = u + at is used to find the final speed.

Find v if:

(a)

u = 6, a = 2 and t = 5

v =
(b)

u = 0, a = 4 and t = 3

v =
(c)

u = 3, a = 1 and t = 12

v =
(d)

u = 12, a = 2 and t = 4

v =

The volume of a box is given by the formula

V = a b c

Find V if:

(a)

a = 2, b = 3 and c = 10

V =
(b)

a = 7, b = 5 and c = 3

V =
(c)

a = 4, b = 4 and c = 9

V =

Find the value of Q for each formula using the values given.

(a)

Q = 3x + 7y x = 4 and y = 2

Q =
(b)

Q = x2 + y x = 3 and y = 5

Q =
(c)

Q = xy + 4 x = 3 and y = 5

Q =
(d)

Q = 5x − 2y x = 10 and y = 2

Q =
(e)

Q = xy − 2 x = 10 and y = 2

Q =
(f)

Q = xy x = 24 and y = 2

Q =
(g)

Q = x + 4y x = 8 and y = 3

Q =
(h)

Q = 4x + 2y x = 5 and y = 11

Q =
(i)

Q = 3x + 2y + z x = 4, y = 2 and z = 10

Q =
(j)

Q = xy + yz x = 2, y = 5 and z = 8

Q =
(k)

Q = xyz x = 2, y = 5 and z = 3

Q =
(l)

Q = xy + 4z x = 8, y = 3 and z = 4

Q =
(m)

Q = x + yz x = 8, y = 10 and z = 3

Q =
(n)

Q = xy + z x = 50, y = 2 and z = 3

Q =

A rectangle has a length of a cm and a width of b cm.

The perimeter of a rectangle is given by the formula p = 2(a + b).

Calculate the perimeter of a rectangle when a = 4.5 and b = 4.2.

Perimeter = cm