Algebra
Term 1–2
Expanding · Factorising · Surds · Systems of equations
Objectifs d'apprentissage
ImprimerExpanding and Factorising
- 1. Expand single and double brackets, including $(a+b)(c+d)$ and special products $(a+b)^2$ and $(a-b)(a+b)$.
- 2. Factorise expressions by taking out the highest common factor.
- 3. Factorise quadratic expressions of the form $x^2 + bx + c$ (monic).
- 4. Factorise quadratic expressions of the form $ax^2 + bx + c$ with $a > 1$ (non-monic).
- 5. Factorise the difference of two squares, $a^2 - b^2$.
Solving Equations
- 6. Solve multi-step linear equations, including those with rational coefficients.
- 7. Solve linear equations with variables on both sides and with brackets.
- 8. Solve equations involving square and cube roots, recognising when both signs apply.
- 9. Solve linear equations with irrational coefficients (e.g. coefficients involving $\sqrt{2}$).
Algebraic Fractions and Systems
- 10. Simplify algebraic fractions where the numerator and denominator share a common factor.
- 11. Simplify algebraic fractions that require factorising a quadratic first.
- 12. Simplify algebraic fractions whose numerator or denominator contains surds.
- 13. Solve a system of two linear equations using substitution and elimination.
- 14. Model a real-world problem with a system of equations and interpret the solution in context.
- 15. Solve a system of three linear equations in three unknowns.
Évaluations
Algebraic manipulation end-of-unit test
Critère A
60 min
Test on expanding and factorising expressions (including quadratics), simplifying surds, and solving systems of linear equations.
Pack de révision
Ouvrir le hub de révision
Fluency Pack A — 40 questions
Fluency Pack B — 40 questions
Problem-solving — 12 unfamiliar tasks
Worked solutions (Pack A + B + problems)