01Quadratics3 groups · 13 lessonsSolving Quadratics1.1Solving Quadratic Equations1.2Factorising Quadratics by Hand1.3Fractions and Valid Roots1.4Completing the Square1.5Using the Completed Square Form1.6The Quadratic Formula1.7Quadratics in Another FormThe Quadratic Graph1.8The Graph and the Vertex1.9Quadratic Range and Restricted Domains1.10Quadratic InequalitiesRoots and Intersections1.11The Discriminant1.12Where a Line Meets a Curve1.13Tangency and Parameter Conditions
02Functions3 groups · 9 lessonsFunction Language2.1Functions and Domains2.2One-One and Many-One Functions2.3The Range of a FunctionCombining and Reversing Functions2.4Composite Functions2.5Inverse Functions2.6The graph of a function and its inverseTransforming Graphs2.7The Four Function Transformations2.8Describing Function Transformations2.9Combined Function Transformations
03Coordinate Geometry3 groups · 10 lessonsCoordinates and Lines3.1Distance and Midpoint3.2Gradient and Line Relationships3.3Equations of Straight Lines3.4Perpendicular BisectorsCircle Equations and Geometry3.5The Equation of a Circle3.6Expanded Circle Equations3.7Circles Through Three Points3.8Circle Geometry and TangentsLine-Circle Problems3.9Line-Circle Intersections3.10Intersection and Tangency Conditions
04Circular Measure3 groups · 10 lessonsRadians and Sectors4.1Radians4.2Length of an Arc4.3Area of a SectorChords and Segments4.4Chords and Segment Perimeters4.5Area of a Circular SegmentCircular Geometry Problems4.6Exact Circular-Measure Problems4.7Shaded-Region Problems4.8Perimeters with Arcs and Straight Lines4.9Overlapping Circles4.10Fixed-Perimeter Sectors
05Trigonometry3 groups · 13 lessonsRatios and Angles5.1Trig Ratios and the Unit Circle5.2Exact Values and Reference Angles5.3Finding Related Trig RatiosGraphs and Inverses5.4Graphs of sin, cos and tan5.5Transforming Trigonometric Graphs5.6Reading Trigonometric Graphs5.7Inverse Trigonometric Functions5.8Inverses of Restricted Trig FunctionsEquations and Identities5.9Solving Trigonometric Equations5.10Trigonometric Identities5.11Quadratic Trig Equations5.12Multiple-Angle Trig Equations5.13Equations with Trigonometric Identities
06Series4 groups · 15 lessonsArithmetic Progressions6.1Arithmetic Progressions6.2Sums of Arithmetic Progressions6.3Finding Terms from Sums6.4Selecting and Counting AP TermsGeometric Progressions6.5Geometric Progressions6.6Finite Geometric Series6.7Infinite Geometric Series6.8Selected Geometric Series6.9Modelling Geometric SeriesLinked Progressions6.10Linked ProgressionsBinomial Expansion6.11The Binomial Expansion6.12Finding Binomial Terms6.13Products of Binomial Expansions6.14Unknown Binomial Coefficients6.15Using Binomial Expansions
07Differentiation3 groups · 12 lessonsDerivatives and Gradients7.1Derivatives and the Gradient Function7.2Calculating Chord GradientsDifferentiation Rules7.3The Power Rule7.4Differentiating Roots and Fractions7.5The Chain Rule7.6Second DerivativesApplying Derivatives7.7Finding Points with a Given Gradient7.8Tangents and Normals7.9Intersections of Tangents and Normals7.10Areas from Tangents and Normals7.11Unknown Coefficients from Gradients7.12Conditions on Derivatives
08Further Differentiation3 groups · 14 lessonsFunction Behaviour8.1Increasing and Decreasing Functions8.2Stationary Points8.3Sketching Curves Using Stationary Points8.4Conditions from Stationary Points8.5Counting Stationary Points8.6Finding the Minimum GradientOptimisation8.7Optimisation8.8Maximising the Volume of a Box8.9Minimising Surface Area8.10Optimisation with Geometric ConstraintsRates of Change8.11Rates of Change8.12Connected Rates on a Curve8.13Finding Unknown Rates8.14Filling and Emptying Containers
09Integration4 groups · 20 lessonsFinding Original Functions9.1Reversing Differentiation9.2Preparing Expressions for Integration9.3Finding the Constant of Integration9.4Finding a Curve from Conditions9.5Integrating Twice9.6Integrating Powers of a Linear Bracket9.7Recognising Reverse Chain RuleDefinite Integrals and Area9.8Definite Integrals9.9Area Under a Curve9.10Integrating with Respect to y9.11Area Between Curves9.12Areas with Changing Boundaries9.13Finding an Unknown Integration LimitImproper Integrals9.14Infinite Integration Limits9.15Integrals with Undefined EndpointsVolumes of Revolution9.16Volumes of Revolution9.17Rotation About the y-axis9.18Hollow Solids of Revolution9.19Finding Unknowns from a Volume9.20Water Volumes in a Curved Container
