Topic 8 of 8 · Grade 7
Patterns and simple algebra
Find the rule and continue the pattern.
Notes for this topic 1 file, in order
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Number patterns
Find the rule and continue the pattern.
- 3, 7, 11, 15, … (add 4) → next is 19.
- 2, 4, 8, 16, … (multiply by 2) → next is 32.
- Square numbers: 1, 4, 9, 16, 25, …
Letters for numbers
In algebra, a letter stands for an unknown number. If x = 5, then 3x + 2 = 3 × 5 + 2 = 17.
Simplifying
Collect like terms: 2a + 3a = 5a; 4b + 2 − b = 3b + 2.
Solving simple equations
Do the same thing to both sides.
Worked example: Solve x + 9 = 20.
x = 20 − 9 = 11
Worked example: Solve 4y − 3 = 25.
4y = 28 → y = 7
Word problems
"A number multiplied by 3 and then increased by 5 gives 29." → 3n + 5 = 29 → 3n = 24 → n = 8.
Exam tip: Check your answer by putting it back into the equation.
Check yourself
- What is the next number: 5, 10, 20, 40, …?
- Simplify 6m − 2m + m.
- Solve 3k = 27.
Show answers
- 80
- 5m
- k = 9
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