Page 1 · Introduction
What is algebra?
Algebra is just arithmetic with a letter standing in for a number we don’t know yet. If you can work with numbers, you can work with algebra — the letter simply holds a place until you find its value.
The big ideaA letter like x is a mystery number. Algebra gives us neat ways to write about it, tidy it up (simplify), and work out what it must be (solve).
💡This is one of the first topics in Year 7 maths. Getting comfortable now makes the start of high school much smoother.
On the real testWhere this appearsAlgebra is a foundation of high-school maths from Year 7 onwards. Every later topic — equations, graphs, formulas — builds on these first ideas.
Page 2 · Letters for numbers
Writing algebra
In algebra we write multiplication without the × sign: 3 × n is written 3n. And n + n + n is just 3n. A letter on its own, like x, means ‘one of that number’ (1x).
Write ‘5 times a number n’ in algebra.
5 × n = 5n.
5n
If a pencil costs p cents, what do 4 pencils cost?
4 lots of p = 4p cents.
4p
Page 3 · Simplifying
Collecting like terms
‘Like terms’ use the same letter, so they can be added or subtracted. 2a + 3a = 5a. But 2a + 3b can’t be combined — different letters.
Simplify: 4x + 5x
Same letter, so add: 4 + 5 = 9. Answer 9x.
9x
Simplify: 7y − 3y
Same letter, so subtract: 7 − 3 = 4. Answer 4y.
4y
Page 4 · Substituting
Putting a number in
To ‘substitute’ means replacing the letter with a number, then working it out.
If x = 3, what is 2x + 1?
2 × 3 + 1 = 6 + 1 = 7.
7
If n = 5, what is 3n − 4?
3 × 5 − 4 = 15 − 4 = 11.
11
Page 5 · Solving
Finding the mystery number
To ‘solve’ means finding the value of the letter. Do the opposite operation to get the letter on its own.
Solve: x + 4 = 10
Take 4 off both sides: x = 10 − 4 = 6.
x = 6
Solve: 3x = 12
Divide both sides by 3: x = 12 ÷ 3 = 4.
x = 4
Level 1 · Easy
Warm up
Writing and simplifying. Tap to check.
1. Write ‘3 times a number y’ in algebra.
3 × y is written 3y.
2. Simplify: 2a + 3a
Same letter, add: 2 + 3 = 5, so 5a.
3. Simplify: 8m − 3m
8 − 3 = 5, so 5m.
Level 2 · Medium
Building up
Substituting numbers in.
1. If x = 4, what is 2x?
2 × 4 = 8.
2. If n = 6, what is n + 5?
6 + 5 = 11.
3. If y = 2, what is 4y − 3?
4 × 2 − 3 = 8 − 3 = 5.
Level 3 · Hard
Getting tougher
Solving simple equations.
1. Solve: x + 7 = 12
x = 12 − 7 = 5.
2. Solve: 4x = 20
x = 20 ÷ 4 = 5.
3. Solve: x − 3 = 8
x = 8 + 3 = 11.
Level 4 · Challenge
Challenge
Two-step reasoning. Take your time.
1. Solve: 2x + 1 = 11
Take 1 off: 2x = 10. Divide by 2: x = 5.
2. If x = 3 and y = 4, what is 2x + 3y?
2×3 + 3×4 = 6 + 12 = 18.
3. Solve: 3x − 2 = 13
Add 2: 3x = 15. Divide by 3: x = 5.
Page 10 · Well done
You’ve finished Introduction to Algebra
You can now write algebra, collect like terms, substitute numbers, and solve simple equations. These four skills are the foundation of all the maths you’ll meet in high school.
RememberA letter is just a mystery number. Simplify by collecting like terms; solve by doing the opposite operation to both sides.
🎉Great work getting through all four tiers. Try another module next — every one builds a different skill.
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