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Year 7 Maths · KS3 notes

Algebra basics

Clear notes with worked examples, then 4 practice questions with answers. Written by Beyond Tutors tutors for the KS3 National Curriculum.

Words to know

Term: $3a$ , $5$ , $-2b$
Expression: terms added or subtracted, e.g. $3a + 5b - 2$ (no equals sign)
Equation: has an equals sign and can be solved, e.g. $2x + 5 = 17$

SIMPLIFYING (collect like terms)

Only combine terms with the same letter.

$3a + 5b - a + 2b = 2a + 7b$

Substitution

Swap the letter for the number, then follow BIDMAS.

If $x = 4$ : $3x^2 = 3 \times 16 = 48$ (square first, then multiply)

Solving one- and two-step equations

Do the same thing to both sides, undoing in reverse order.

$2x + 5 = 17$

subtract 5: $2x = 12$

divide by 2: $x = 6$

Check: $2 \times 6 + 5 = 17$ ✓

Sequences

3, 7, 11, 15, … goes up by 4 each time.

$n$ th term: $4n - 1$ (the times-table of the difference, then adjust)

Practice questions

Try each one, then tap to see the answer and why.

Question 1 · Order of operations
Work out $5 + 3 \times (6 - 2)^2$ .
- A145
- B128
- C53
- D61
Show the answer
C: 53
Brackets: $6 - 2 = 4$ . Index: $4^2 = 16$ . Multiply: $3 \times 16 = 48$ . Add: $5 + 48 = 53$ .
Question 2 · Notation
Which expression means 'multiply n by 4, then subtract 3'?
- A $4(n - 3)$
- B $n - 12$
- C $4n - 3$
- D $3 - 4n$
Show the answer
C: $4n - 3$
Multiplying n by 4 gives $4n$ ; then subtract 3: $4n - 3$ .
Question 3 · Simplifying
Simplify $3a \times 4b$ .
- A $7ab$
- B $34ab$
- C $12a + b$
- D $12ab$
Show the answer
D: $12ab$
Multiply the numbers ( $3 \times 4 = 12$ ) and write the letters together: $12ab$ .
Question 4 · Forming equations
I think of a number, double it and add 7. The answer is 31. What was my number?
- A19
- B12
- C24
- D38
Show the answer
B: 12
$2n + 7 = 31$ , so $2n = 24$ and $n = 12$ .

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