Page 29 - Mathematics Coursebook

2.5 Deriving and using formulae

2.5 Deriving and using formulae

A formula is a mathematical rule that shows the relationship
between two quantities (variables).
You can write a formula using words: Area of rectangle = length × width
or using letters: A = l × w
You can substitute numbers into expressions and formulae.
When l = 5 cm and w = 4 cm A = 5 × 4 = 20 cm 2
You can write or derive your own formulae to help you solve problems.

Worked example 2.5

a Work out the value of the expression a + 3b when a = 2 and b = 4.
b Write a formula for the number of days in any number of weeks, in:
i words ii letters.
c Use the formula in part b to work out the number of days in 8 weeks.

a a + 3b = 2 + 3 × 4 Substitute 2 for a and 4 for b in the expression.
= 2 + 12 Remember that multiplication comes before Remember the order of
= 14 addition. operations: division and
multiplication must be
done before addition and
subtraction.
b i number of days
= 7 × number of weeks There are 7 days in a week, so multiply
the number of weeks by 7.
ii d = 7w Choose d for days and w for weeks and Always write the number
write 7 × w as 7w. before the letter, so write
c d = 7 × 8 Substitute w = 8 into the formula. 7w not w7.
= 56

) Exercise 2.5

1 Work out the value of each expression.
a a + 5 when a = 3 b x − 9 when x = 20 c f + g when f = 7 and g = 4

d m − n when m = 100 and n = 25 e 3k when k = 5 f p + 2q when p = 5 and q = 3
y
g 4 when y = 32 h c − 4d when c = 10 i 2h + 3t when h = 8
and d = 2 and t = 5

j w v when w = 16 and v = 9 k 30 – 2 when c = 6 l xy when x = 19 and y = 11
2 c 2
2 a Write a formula for the number of minutes in any number of hours, in:
i words ii letters.
b Use your formula in part a ii to work out the number of minutes in 5 hours.

3 Use the formula V = IR to work out V when:
a I = 3 and R = 7 b I = 4 and R = 9. IR means I × R

28 2 Sequences, expressions and formulae