- 1. What Is a Quadratic Equation?
Identify quadratic equations, rearrange them into standard form, and verify their roots.
- 2. Factorising Simple Quadratics: $x^2 + bx + c = 0$
Learn to factorise monic quadratic expressions using the two-number hunt and solve equations using the Zero Product Property.
- 3. Factorising Monic Quadratics: Mixed Signs
Determine the signs of factors in a quadratic expression, and factorise special cases like the Difference of Two Squares.
- 4. Factorising Non-Monic Quadratics: $ax^2 + bx + c$
Learn to factorise non-monic quadratics using the AC-Method by splitting the middle term and grouping.
- 5. Perfect Square Trinomials and Factorisation Edge Cases
Master factorisation edge cases: perfect square trinomials with repeated roots, the c=0 case, and rearranging equations before solving.
- 6. EXAM PRACTICE SESSION 1: Factorisation
Apply factorisation techniques under exam conditions, analyze common errors, and use verification strategies.
- 7. Completing the Square: Monic Quadratics
Learn how to solve any monic quadratic equation by completing the square to handle irrational roots.
- 8. Completing the Square: Non-Monic Quadratics
Learn how to solve non-monic quadratic equations by dividing by the leading coefficient and completing the square.
- 9. Deriving the Quadratic Formula
Derive the quadratic formula by completing the square on the general equation, and use the discriminant to determine the nature of roots.
- 10. Applying the Quadratic Formula: Rational Roots
Master the 4-step process for applying the quadratic formula to equations that yield whole number or fraction roots, including rearranging non-standard equations first.
- 11. Applying the Formula: Irrational Roots, Surd Form, and No Real Roots
Use the quadratic formula when the discriminant is not a perfect square, express answers in exact surd form or to decimal precision, and identify equations with no real roots.
- 12. Exam Practice Session 2: Algebraic Methods
Identify and correct the three most common exam errors in completing the square and the quadratic formula: the missing root, the negative-c collision, and the forgotten denominator.
- 13. Drawing the Parabola: Tables of Values
Construct accurate tables of values for quadratic functions, use symmetry as a self-check, and plot smooth parabolic curves on a Cartesian plane.
- 14. Minimum and Maximum Values from the Graph
Identify and calculate the minimum or maximum value of a quadratic function by reading the vertex from a drawn graph, from completed-square form, and by applying the formula x = −b/2a.
- 15. Line of Symmetry
Define the axis of symmetry of a parabola, write its equation correctly in the form x = k, calculate it using the formula x = −b/2a or by averaging the roots, and use symmetry to predict missing values in a table.
- 16. Forming a Quadratic Equation from a Graph
Reconstruct the equation of a parabola from its roots and one other point using the factored form template y = a(x − r₁)(x − r₂), solve for the scaling factor a, and expand into standard form.
- 17. EXAM PRACTICE SESSION 3: Graphical Methods + Full Unit Review
Construct tables, plot graphs, and extract critical features under exam conditions.
