WOODBROOK SECONDARY SCHOOL

MATHEMATICS

SUBSTITUTION

FORM 4

1 | P a g e

In a football game, when a player gets exhausted or has to be removed from the field, he is

substituted for a next player that is on the bench. In other words, another person takes his place

on the field when he is removed from play. This is called substitution.

In algebra, substitution is performed when a letter variable is replaced by a number. It is useful to

write the substituted number in brackets ( ), to make computation easy with directed numbers.

Ex. Find the value of 𝑥 + 2 when 𝑥 = 4

Since 𝑥 = 4, replace 𝑥 with 4 in the expression,

𝑥 + 2 = (4) + 2

= 6

Ex. Find the value of 𝑎 − 𝑏 when 𝑎 = −2 𝑎𝑛𝑑 𝑏 = 3

Replace 𝑎 𝑤𝑖𝑡ℎ − 2 𝑎𝑛𝑑 𝑏 𝑤𝑖𝑡ℎ 3 𝑖𝑛 𝑡𝑒ℎ 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛,

𝑎 − 𝑏 = (−2) − (3)

= −2 − 3

= −5

The sum of two negative

numbers is the sum of their

values and keep the sign

WOODBROOK SECONDARY SCHOOL

MATHEMATICS

SUBSTITUTION

FORM 4

2 | P a g e

Ex. Find the value of 2𝑥 + 3𝑦 when 𝑥 = −1 𝑎𝑛𝑑 𝑦 = 2

Replace 𝑥 𝑤𝑖𝑡ℎ − 1 𝑎𝑛𝑑 𝑦 𝑤𝑖𝑡ℎ 2 𝑖𝑛 𝑡ℎ𝑒 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛,

2𝑥 + 3𝑦 = 2(−1) + 3(2)

= −2 + 6

=

Ex. Find the value of 𝑥2 − 𝑦2 when 𝑥 = −1 𝑎𝑛𝑑 𝑦 = −2

Replace 𝑥 𝑤𝑖𝑡ℎ − 1 𝑎𝑛𝑑 𝑦 𝑤𝑖𝑡ℎ − 2 𝑖𝑛 𝑡ℎ𝑒 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛,

𝑥2 − 𝑦2 = (−1)2 − (−2)2

= 1 − 4

=

Remember:

RULE ADDING OR

SUBTRACTING

MULTIPLYING OR

DIVIDING

Two like signs become a positive sign 3+(+2) = 3 + 2 = 5 3 × 2 = 6

6−(−3) = 6 + 3 = 9 (−3) × (−2) = 6

Two unlike signs become a negative sign 7+(−2) = 7 − 2 = 5 3 × (−2) = −6

8−(+2) = 8 − 2 = 6 (−3) × 2 = −6

The sum of a positive and negative

number is the difference in their values

and keeps the sign on the larger number

The square of a negative number is

always positive since the product of two

negative numbers is positive

WOODBROOK SECONDARY SCHOOL

MATHEMATICS

SUBSTITUTION

FORM 4

3 | P a g e

May/June 2010

Given that 𝑎 = −1, 𝑏 = 2 𝑎𝑛𝑑 𝑐 = −3, find the value of:

1. 𝑎 + 𝑏 + 𝑐 [1 mark]

2. 𝑏2 − 𝑐2 [1 mark]

1. 𝑎 + 𝑏 + 𝑐 = (−1) + 2 + (−3)

=

=

=

2. 𝑏2 − 𝑐2 = (2)2 − (−3)2

=

=

=

January 2002

If 𝑎 = 4, 𝑏 = −2 𝑎𝑛𝑑 𝑐 = 3, calculate the value of : 𝑎(𝑎−𝑏)

𝑏𝑐 [2 marks]

𝑎(𝑎−𝑏)

𝑏𝑐 =

4[4−(−2)]

(−2)(3)

=

=

=

The sum of a positive and negative

number is the difference in their values

and keeps the sign on the larger number

WOODBROOK SECONDARY SCHOOL

MATHEMATICS

SUBSTITUTION

FORM 4

4 | P a g e

January 2004

If 𝑝 = 5, 𝑞 = 0 𝑎𝑛𝑑 𝑟 = −3, evaluate:

1. 4𝑝 − 𝑞𝑟

2. 2𝑟3

1. 4𝑝 − 𝑞𝑟 = 4(5) − (0)(−3)

=

=

2. 2𝑟3 = 2(−3)3

=

=

May/June 2005

Using the formula 𝑡 = √5𝑚

12𝑛, calculate the value of t when 𝑚 = 20 𝑎𝑛𝑑 𝑛 = 48.

𝑡 = √12𝑚

12𝑛

= √5(20)

12(48)

= √100

576

= √0.174

= 0.42

I. First work out the brackets.

II. The cube of a negative number is negative