EquateIt EquateIt
Book now
Year 9–10 · Year 9–10 Maths

Year 9–10 Maths — Number, Algebra and Equations

Year 9–10 algebra extends into quadratic equations, surds and more complex equation solving. These are the skills VCE Maths Methods assumes from day one — arriving in Year 11 with gaps here makes Unit 1 very difficult.

Key Concepts & Formulas

  • Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1; a⁻ⁿ = 1/aⁿ; a^(1/n) = ⁿ√a

  • Expanding: (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; (a + b)(a − b) = a² − b²

  • Factoring: look for common factors first; then difference of squares; then factoring quadratic ax² + bx + c

  • Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a — use when factoring is difficult

  • Completing the square: convert x² + bx + c to (x + b/2)² + (c − b²/4)

  • Surds: √a × √b = √(ab); √a / √b = √(a/b); rationalising the denominator: multiply by √a/√a

  • Like surds: 3√2 + 5√2 = 8√2; unlike surds (e.g. √2 and √3) cannot be combined

  • Simultaneous equations: substitution or elimination to find values satisfying both equations

  • Linear-quadratic simultaneous equations: substitute the linear into the quadratic → solve the resulting quadratic

Practice Questions

5 questions

Attempt each question before reading the hint. These are styled to match school assessment format.

Q1.Factorise fully: 2x² − 8x − 24.

2 marks
Show hint

Take out the common factor first.

Q2.Solve x² − 5x + 6 = 0 by factoring and verify using the quadratic formula.

3 marks

Q3.Simplify: √48 − 2√3.

2 marks

Q4.Solve simultaneously: y = 2x + 1 and y = x² − x + 3.

4 marks

Q5.Simplify (3 + √5)(3 − √5) and (1 + √2)².

3 marks

Common Mistakes to Avoid

These are the errors that students most frequently make in Number, Algebra and Equations — and that examiners are specifically watching for.

  • (a + b)² = a² + 2ab + b² — forgetting the middle term: (a + b)² ≠ a² + b²

  • Forgetting the ± in the quadratic formula — there are usually two solutions

  • Rationalising incorrectly — multiply numerator AND denominator by the surd

  • In linear-quadratic systems, stopping after finding x-values without substituting back to find y-values

Still finding Number, Algebra and Equations difficult?

One-to-one tutoring with a specialist Year 9–10 Maths tutor is the fastest way to close gaps and build exam confidence.

Find a Year 9–10 Maths tutor Book a free assessment

Book a free assessment

Tell us the student’s year level and subject. We’ll match a tutor and set up the free diagnostic — no obligation.

  • No lock-in contracts
  • In-person across Melbourne or online statewide
  • Qualified, WWCC-checked tutors

Five quick questions, one great match.

  1. 1 Who the tutoring is for
  2. 2 Year level
  3. 3 Subjects
  4. 4 The goal
  5. 5 In-person or online
Start — takes 60 seconds

Free first assessment · No obligation · We reply within 24 hours