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AQA GCSE Maths

Solving equations, rearranging and sequences — AQA GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 5 minutes to read.

Equations

  • Do the same thing to both sides; work backwards through the operations.
  • Expand brackets first, collect like terms, then solve.
  • Simultaneous equations: make one variable's coefficients match, then add or subtract.

Sequences and rearranging

  • nth term of a linear sequence: (common difference)n + (first term − difference).
  • To rearrange, isolate the target letter using inverse operations.
  • Quadratic sequences have a constant second difference.

Key terms

Coefficient
The number in front of a variable.
nth term
A rule that gives any term in a sequence from its position.
Subject of a formula
The letter on its own on one side.
Quadratic formula
A formula used to solve any quadratic equation ax² + bx + c = 0.
Completing the square
Rewriting a quadratic as a squared bracket plus/minus a constant.
Simultaneous equations
Two or more equations solved together to find values that satisfy them both.

Common exam traps

  • Forgetting to multiply every term inside the bracket.
  • Sign errors when subtracting a negative.
  • Giving a term instead of an expression when asked for the nth term.

Practice questions with answers

  1. 1. Solve 3(x − 2) = 15.

    Answer: x = 7

    3x − 6 = 15 → 3x = 21 → x = 7.

  2. 2. Find the nth term of 5, 8, 11, 14...

    Answer: 3n + 2

    Difference is 3; 5 − 3 = 2.

  3. 3. Make x the subject: y = 4x + 3.

    • • x = (y − 3)/4
    • • x = y/4 − 3
    • • x = 4y − 3
    • • x = (y + 3)/4

    Answer: x = (y − 3)/4

    Subtract 3, then divide by 4.

  4. 4. Expand and simplify (x + 3)(x − 2).

    Answer: x² + x − 6

    x² − 2x + 3x − 6.

  5. 5. Solve 5x + 3 = 2x + 18.

    Answer: x = 5

    Subtract 2x: 3x + 3 = 18. Subtract 3: 3x = 15. Divide by 3: x = 5.

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