01Algebra4 groups · 17 lessonsModulus1.1Modulus as Distance and Equations1.2Modulus Equations with Restrictions1.3Equations with Two Moduli1.4Graphs and Modulus Intersections1.5Transforming Modulus Graphs and RangesModulus Inequalities1.6Modulus Inequalities1.7Modulus Inequalities with a Variable Side1.8Comparing Two Moduli1.9Sums of ModuliPolynomial Division1.10Polynomial Division1.11Division by Non-monic Linear Polynomials1.12Division by Quadratic PolynomialsFactors and Remainders1.13Factor and Remainder Theorems1.14Finding Unknown Polynomial Coefficients1.15Solving Polynomial Equations1.16Quadratic Factors and Unknown Roots1.17Polynomial Equations with Changed Inputs
02Logarithmic and exponential functions4 groups · 19 lessonsMeaning and Graphs2.1What a Logarithm Means2.2Natural Logarithms and Calculator Keys2.3Exponential and Logarithmic Graphs2.4Shifted Functions and Their InversesLogarithm Laws and Equations2.5The Logarithm Laws2.6Combining and Expanding Logarithms2.7Solving Logarithmic Equations2.8Quadratic Logarithmic Equations2.9Unknown Bases and Nested Logarithms2.10Simultaneous Logarithmic EquationsExponential Equations and Inequalities2.11Solving Exponential Equations2.12Equations with Repeated Powers2.13Exponential Inequalities2.14Exponential Models and Thresholds2.15Exponential Graph IntersectionsLinearising Relationships2.16Linearising Power Models2.17Linearising Exponential Models2.18Choosing Transformed Axes2.19Fitting Models to Logarithmic Data
03Trigonometry4 groups · 20 lessonsReciprocal Functions3.1Reciprocal Trig Ratios3.2Reciprocal Trig Graphs3.3Transforming Reciprocal Trig Graphs3.4Solving Reciprocal Trig Equations3.5Pythagorean Trig EquationsCompound and Double Angles3.6Compound-angle Formulae3.7Exact Values with Compound Angles3.8Equations with Compound Angles3.9Double-angle Formulae3.10Half-angle Values3.11Equations with Double AnglesIdentities and Equations3.12Further Trig Identities3.13Multiple-angle Identities3.14Using Identities in EquationsR-form3.15R-form3.16Choosing Sine or Cosine R-form3.17Solving R-form Equations3.18Ranges and Extrema of R-form3.19Squared and Reciprocal R-form3.20Hidden R-form
04Differentiation4 groups · 14 lessonsChoosing and Combining Rules4.1Choosing a Differentiation Rule4.2Using the Product Rule4.3Using the Quotient RuleExponential, Logarithmic and Trigonometric Derivatives4.4First Derivatives of eˣ and ln x4.5Composite Exponential Functions4.6Composite Logarithmic Functions4.7Trigonometric Derivatives4.8Inverse-tangent Derivative4.9Mixed Rules and Stationary PointsImplicit Curves4.10What Implicit Differentiation Means4.11Implicit Curve GradientsParametric Curves4.12What Parametric Differentiation Means4.13Parametric Tangents and Normals4.14Parametric Special Tangents and Direction
05Integration6 groups · 11 lessonsDirect Antiderivatives5.1Integration as reverse differentiation5.2Integrating a reciprocal linear function5.3Integrating sin, cos and sec²Trigonometric Rewriting5.4Integrating sin² and cos²Definite Integrals and Area5.5Definite Integrals and AreaRecognising Advanced Forms5.6Inverse-tangent integrals and mixed numerators5.7Recognising derivative over functionTransforming Integrals5.8Integration using a given substitution5.9Integrating after partial fractions5.10Integration by partsChoosing and Applying Methods5.11Choosing an Integration Method
06Numerical Solution of Equations3 groups · 4 lessonsLocating Roots6.1Locating a rootFixed-Point Iteration6.2From an equation to an iteration6.3Running and confirming an iterationApplying Numerical Methods6.4Using iteration in a longer problem
07Vectors3 groups · 9 lessonsVector Foundations7.1Vector language and operations7.2Displacement vectors from points7.3Position vectors and constructing points7.4Magnitude and unit vectorsScalar Product and Geometry7.5Scalar product and vector anglesVector Lines7.6Vector equation of a line7.7Angle between two lines7.8Parallel, intersecting and skew lines7.9Foot of a perpendicular from a point
08Further Algebra2 groups · 5 lessonsPartial Fractions8.1Equal-degree fractions before partial fractions8.2Choosing and solving partial fractionsBinomial Series8.3Binomial series for rational powers8.4Adapting a binomial series and its validity8.5Partial fractions with binomial series
09Differential equations3 groups · 7 lessonsMeaning and Solving9.1What a differential equation means9.2Solving a separable differential equation9.3Complete solutions and integration choicesForming Models9.4Forming an equation from a rate statement9.5Linked rates and net-rate modelsGrowth and Interpretation9.6Growth, decay and limiting values9.7Interpreting a differential-equation model
10Complex numbers3 groups · 7 lessonsComplex Foundations10.1Imaginary numbers and Cartesian form10.2Complex arithmetic and the conjugateArgand Geometry and Form10.3Argand diagrams, modulus and argument10.4Polar form, multiplication and divisionEquations and Loci10.5Complex roots and equations10.6Standard loci in the complex plane10.7Locus intersections and extreme values
