Substituting into expressions/formulas | Year 7

01 / LEARN

The idea, step by step

Replace every matching letter

Evaluating an expression means replacing each letter by its given number. For $3 x + 2$ when $x = 4$ , first write $3 \times 4 + 2$ . This shows the intended multiplication instead of accidentally adding 3 and 4.

If the letter appears twice, use the same value twice. For $x^{2} + x$ at $x = 3$ , write $3^{2} + 3 = 12$ . Keep brackets where they appear and calculate powers before multiplication.

Follow the formula and its meaning

A formula may require several values. For $P = 2 (l + w)$ , find both length and width before starting. Substitute them in the right positions, add inside the brackets, then multiply. Do not change the rule to fit a convenient calculation.

The unit follows the quantity being found: a perimeter is a length, an area is in square units and a price is in dollars. Estimate the expected size or use another method to check whether the final value makes sense.

A common trap

Calculating $3 x^{2}$ as ${(3 x)}^{2}$ .

Instead: For $x = 4$ , calculate $3 \times 4^{2} = 3 \times 16$ , not $12^{2}$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

A repeated variable

Evaluate $2 a^{2} + a$ when $a = 3$ .

Substitute both copies: $2 \times 3^{2} + 3$ .
Calculate $3^{2} = 9$ .
Then $2 \times 9 + 3 = 21$ .

21.

Example 2

A perimeter formula

Use $P = 2 (l + w)$ for length 8 cm and width 5 cm.

$P = 2 (8 + 5)$ .
$P = 2 \times 13 = 26$ .
The perimeter unit is centimetres.

26 cm.

Check your understanding

Evaluate $5 n + 6$ when $n = 4$ .

Show answer

$5 \times 4 + 6 = 20 + 6 = 26$ .

03 / WORKSHEET

Your turn

6 questions · 11 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Evaluate $4 x + 3$ for $x = 5$ .
1 mark
Evaluate $7 a - 2$ for $a = 4$ .
1 mark
Evaluate $b^{2} + 2 b$ for $b = 6$ .
2 marks
Evaluate $3 (p + 4)$ for $p = 7$ .
2 marks
A museum charges $C = 4 n + 6$ dollars for $n$ children. Find the cost for 7 children.
2 marks
A rectangle is 9 cm long and 4 cm wide. Use $A = l w$ and $P = 2 (l + w)$ to find its area and perimeter.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Evaluate $4 x + 3$ for $x = 5$ .
1 mark
$4 \times 5 + 3 = 23$ .
23
Evaluate $7 a - 2$ for $a = 4$ .
1 mark
$7 \times 4 - 2 = 26$ .
26
Evaluate $b^{2} + 2 b$ for $b = 6$ .
2 marks
$6^{2} + 2 \times 6 = 36 + 12 = 48$ .
48
Evaluate $3 (p + 4)$ for $p = 7$ .
2 marks
$3 (7 + 4) = 3 \times 11 = 33$ .
33
A museum charges $C = 4 n + 6$ dollars for $n$ children. Find the cost for 7 children.
2 marks
$C = 4 \times 7 + 6 = 34$ .
The result is a cost in dollars.
34 dollars
A rectangle is 9 cm long and 4 cm wide. Use $A = l w$ and $P = 2 (l + w)$ to find its area and perimeter.
3 marks
$A = 9 \times 4 = 36$ cm².
$P = 2 (9 + 4) = 26$ cm.
Area 36 cm²; perimeter 26 cm.

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Curriculum reference & lesson scope

Australian Curriculum v9.0 / SA Curriculum Mathematics

Year 7 variables, expression notation, substitution, simple equivalence and formula tables. Digital methods are explained with supplied data; the topic test works by hand.

Official curriculum source ↗

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