Title
Description
Calculating Tangents & Normals Using calculus, we can now find the equation of a tangent or normal to any differentiable function at any point within its domain.
Chain Rule
For differentiating functions within functions. Includes instances of how the chain rule plays out for exponentiated functions, exponentials, logarithms and trigonometric functions.
Deriving Powers of x
Derivation of the result for dy/dx when y = x^n, where n is a constant.
Differentiating 'Unnatural' Exponentials
Derivation of the result for dy/dx when y = a^x, where a is an arbitrary constant.
Linear Trigonometric Equations Illustrated worked solutions for finding angles that satisfy particular trigonometric equations.
Locus of a Parabola Finding the focus and directrix of a parabola, given its equation.
Primitives Introduction to the techniques required to find a function given its derivative.
Trigonometric Expansions Geometric deductive proofs of the sin(a+b) and tan(a+b) expansions. NB: this is 3-Unit content.

2-Unit Program Summary
Preliminary 2U JRAHS program

3-Unit Program Summary
Preliminary Extension 1 JRAHS program


Marking Schemes
Each of the files below includes (where appropriate) fully worked solutions for the relevant question, as well as a detailed marking scheme that describes where marks were allocated for each part.
Cambridge Ex 10E, Q20 A prickly calculus question involving first principles.
2008 2-Unit Prelim Final Selected questions only.
2009 2-Unit Half-Yearly Paper also available.
2009 2-Unit Prelim Final Paper also available.


Scans
Handwritten solutions to exercises or tests set in class.
Trigonometry Review Worksheet
Covers trigonometric equations, trigonometric identities, right-angle triangle trigonometry and use of the sine/cosine rule in problem solving.
2010 2-Unit Half-Yearly Retest
Includes paper and fully annotated marking scheme.
Quadratic Theory Review Test
Includes questions and fully worked solutions.
Radian Measure Review Test
Includes questions and fully worked solutions.


Videos
Recorded from actual lessons delivered in my classroom, sometimes divided up into sections for convenience. These can also be browsed through on the Maths playlist at WooTube.

Find a tangent's equation Once the basic rules of differentiation have been introduced, we can calculate the equation of a tangent to a curve at any point.

Introduction to Series and Sequences Defining terms, explaining the basic concepts with a few common examples.

Introduction to Arithmetic Progressions: 1, 2, 3 Covering the basic ideas and formulas related to progressions with a common difference.

Sigma Notation Introducing a shorthand method forĀ 

Introduction to Geometric Progressions: 1, 2 Covering the basic ideas and formulas related to progressions with a common ratio.

Limiting Sum of a Geometric Progression Investigating the curious case of an infinite series with a finite sum.

Superannuation: 1, 2, 3 Applying the theory of GPs to an common investment scenario.

APs and GPs: Tricky Question Worked example of a question with an interesting twist.

Time Payments: 1, 2, 3, 4, 5 Investigating what happens when we attempt to pay off a debt that keeps growing due to the duration of the loan.