Grade 11

Solve quadratic equations using factorisation, completing the square and the quadratic formula; solve quadratic and rational inequalities using sign analysis; and solve systems of one linear and one quadratic equation simultaneously.

Identify equations with no real solutions using the discriminant, apply rational exponents and surd operations, work with error margins, and find the nth term of quadratic number patterns using the second difference method.

Use distance, gradient and midpoint formulas, find equations of lines through two points, apply parallel and perpendicular gradient rules, determine inclinations using tan θ, and solve mixed problems involving triangles on the Cartesian plane.

Apply simple decay and compound decay formulas, compare growth and decay scenarios, solve problems involving depreciation of assets, and interpret the effects of different decay rates over time.

Derive exact values for special angles, prove trigonometric identities, apply reduction formulae, find general solutions of trig equations, and use the Sine, Cosine and Area Rules to solve 2D problems.

Extend your understanding of functions to include horizontal transformations using the parameters k and p, sketch and interpret graphs of quadratic, hyperbolic and exponential functions, and determine equations from graphs.

Prove and apply similarity conditions for triangles, use the Proportionality Theorem and Midpoint Theorem, prove the Theorem of Pythagoras using similar triangles, and solve riders using AA and SSS similarity.

Learn circle terminology, prove and apply the chord-perpendicularity theorem, the angle at the centre theorem, angles in the same segment, equal chords, and the angle in a semicircle theorem with its converse.

Apply the effect of a constant factor k on volume and surface area, solve problems involving complex combined solids with added or removed pieces, and tackle real-world capacity, painting and cost problems.

Distinguish between independent and dependent events, apply the product rule, analyse Venn diagrams, contingency tables and tree diagrams, and use the complementary and addition rules to solve multi-step probability problems.

Summarise data using the five number summary and box and whisker diagrams, draw and interpret ogives, calculate variance and standard deviation, identify skewness, and determine suitable regression models for bivariate data.