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Day 1 6
Functions
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Harder graphs and transformationsLecture1.1
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Solve inequalities using both algebraic and graphical techniquesLecture1.2
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Inverse functions Parametric form of a functionLecture1.3
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Remainder and factor theoremsLecture1.4
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Sums and products of roots of polynomialsLecture1.5
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Exam-style practice problemsLecture1.6
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Day 2 5
Combinatorics
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Permutations and combinations with probabilitiesLecture2.1
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Proof involving perms and comsLecture2.2
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Pigeonhole principleLecture2.3
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Binomial expansion and Pascal’s triangleLecture2.4
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Exam-style practice problemsLecture2.5
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Day3 4
Trigonometric functions
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Inverse trig functions and propertiesLecture3.1
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Further trig identitiesLecture3.2
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Double angle formulaeLecture3.3
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T-formulae and R methodLecture3.4
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Day 4 5
Calculus
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Rates of change and related rates of changeLecture4.1
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Calculus with motionsLecture4.2
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Exponential growth and decay Integration by substitutionLecture4.3
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Find derivatives of inverse functionsLecture4.4
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Exam-style practice problemsLecture4.5
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Day 5 7
Further calculus/proof/statistical analysis
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Further integration techniquesLecture5.1
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Volumes of solids of revolutionLecture5.2
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Differential equationsLecture5.3
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Mathematical inductionLecture5.4
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Bernoulli and binomial distributionsLecture5.5
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Normal approximation for the sample proportionLecture5.6
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Exam-style practice problemsLecture5.7
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Day 6 6
Vectors/revision
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Vector representationLecture6.1
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Addition and subtraction of vectorsLecture6.2
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Modulus and unit vectorLecture6.3
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Dot product, parallel and perpendicular vectorsLecture6.4
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Vector with projectile motionLecture6.5
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Exam-style practice problemsLecture6.6
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