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Algebra and sequences appear regularly on the SET 11+ maths papers. The SET is known for testing problem-solving and reasoning skills, and algebra questions are a key part of that. You may be asked to find unknown values, write expressions, and spot patterns in number sequences. On Stage 2, you will need to show your working when solving equations. This lesson covers all the algebra and sequence skills you need.
Algebra uses letters to stand for unknown numbers. Instead of writing "a number", we write a letter such as n, x, or a.
| Expression | Meaning |
|---|---|
| 3n | 3 × n (three times n) |
| n + 7 | n plus 7 |
| 2n - 4 | Two times n, minus 4 |
| n/5 | n divided by 5 |
| n² | n × n (n squared) |
Remember: In algebra, we do not usually write the multiplication sign. We write 3n instead of 3 × n.
To simplify, collect like terms — group the letters that are the same.
Example: Simplify 4a + 3b + 2a - b
Substitution means replacing a letter with a number.
Example: If x = 5 and y = 3, find the value of 4x - 2y + 7.
SET Tip: Always show each substitution step on Stage 2. You earn marks for working, not just the answer.
To solve an equation, you need to find the value of the unknown letter by using inverse (opposite) operations.
Solve: 3x + 5 = 26
I think of a number, double it, and subtract 4. The answer is 18. What is my number?
A function machine applies operations in order:
Input --> [× 4] --> [+ 3] --> Output
If the input is 6: 6 × 4 = 24, then 24 + 3 = 27.
To work backwards (find the input from the output), reverse the operations:
If the output is 35: 35 - 3 = 32, then 32 ÷ 4 = 8.
A sequence is a list of numbers that follow a rule.
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