Substitution

Foundation and Higher

The idea

To substitute, replace each letter with its value and follow the order of operations. With $a = -3$ , $2a^2 = 2 \times (-3)^2 = 18$ .

Watch out $2a^2$ means $2 \times a^2$ , not $(2a)^2$ .

Worked exampleNon-calculator4 marks

$a = 4$ and $b = -3$ .

(a) Work out the value of $a + b$ .

(b) Work out the value of $3a - 2b$ .

(c) Work out the value of $b^2$ .

(a) $4 + (-3) = 1$ .
(b) Put the values in, keeping $-3$ in a bracket. $3 \times 4 - 2 \times (-3) = 12 - (-6) = 12 + 6 = 18$
(c) $b^2 = (-3)^2 = (-3) \times (-3) = 9$ .

Answer (a) $1$ ; (b) $18$ ; (c) $9$

Question 1Calculator allowed2 marks

Work out 3a $-$ 2b when a = $-4$ and b = 5.

Question 2Non-calculator5 marks

$a=-2$ and $b=5$ .

(a) Work out $a^2-2ab$ .

(b) Work out $(a+b)^2$ .

Question 3Non-calculator5 marks

$s = ut + \frac{1}{2}at^2$

(a) Work out the value of $s$ when $u = 5$ , $a = -4$ and $t = 3$ .

(b) When $t = 4$ and $a = 3$ , the value of $s$ is $40$ . Find the value of $u$ .

173 official questions in 136 papers since 2017. The latest:

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