Year 9 - Algebra - Free practice
Year 9 Algebra Worksheets & Practice Tests
Binomial expansion, monic quadratic factorising, simplifying.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Year 9 algebra is the year FOIL (binomial expansion) and factorising x^2 + bx + c become routine. These worksheets give your student the repetition they need - both directions, plus mixed-format problems that show up on practice tests.
What's covered
Sub-skills your student will practise
- ✓Expanding (x + a)(x + b) using FOIL / distributive law
- ✓Factorising monic quadratics into two binomial factors
- ✓Difference of two squares pattern
- ✓Simplifying multi-term algebraic expressions
- ✓Mixed expand-then-factorise problems
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Frequently asked
Questions parents ask about algebra
What is binomial expansion?
Multiplying out a product of two two-term expressions, like (x + 2)(x + 3). The result is x^2 + 5x + 6. The method (FOIL: First, Outer, Inner, Last) is one of the few maths acronyms genuinely worth remembering.
How do students factorise a monic quadratic?
Find two numbers that multiply to the constant term and add to the x coefficient. For x^2 + 5x + 6, those numbers are 2 and 3, so it factorises as (x + 2)(x + 3). This is the inverse of FOIL.
What's difference of two squares?
A specific factorising pattern: a^2 - b^2 = (a + b)(a - b). So x^2 - 9 factorises as (x + 3)(x - 3). Recognising this pattern saves a lot of time on quadratic factorising questions.
Why does Year 9 spend so much time on factorising?
Because every quadratic equation solved in Year 9 or Year 10 starts with factorising. Students who are slow at factorising hit a wall by mid-Year 10. The fluency built in Year 9 pays off for the next four years of maths.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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