| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grade 12 Calculus AB | Info | Go |
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Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
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| 2 | Polynomials | Introduction to polynomials | Info | Go |
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Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic |
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| 3 | Polynomials | The Sum, Difference and Product of Two Polynomials | Info | Go |
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Objective: To add, subtract and multiply polynomials |
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| 4 | Polynomials | Polynomials and Long Division | Info | Go |
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Objective: To perform long division of polynomials, finding quotient and remainder |
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| 5 | Polynomials | The Remainder Theorem | Info | Go |
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Objective: To determine a remainder when a first polynomial is divided by a second |
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| 6 | Polynomials | More on Remainder Theorem | Info | Go |
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Objective: To determine polynomial coefficients given a divisor and remainder |
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| 7 | Polynomials | The factor theorem | Info | Go |
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Objective: To use the factor theorem to show that (x-a) is a factor of P(x) |
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| 8 | Polynomials | More on the factor theorem | Info | Go |
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Objective: To use the factor theorem to find algebraic variables in polynomials |
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| 9 | Polynomials | Complete factorisations using the factor theorem | Info | Go |
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Objective: To use the factor theorem to derive factors of a polynomial |
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| 10 | Polynomials | Polynomial equations | Info | Go |
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Objective: To practise solving polynomial equations |
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| 11 | Polynomials | Graphs of polynomials | Info | Go |
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Objective: To derive graphs of polynomials by factorising |
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| 12 | Polynomials | The Sum and Product of the Roots of Quadratic Equations. | Info | Go |
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Objective: Sum and product of roots of quadratic equations. |
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| 13 | Polynomials | The Sum and Product of the Roots of Cubic and Quartic Equations. | Info | Go |
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Objective: Sum and product of toots of cubic and quartic equations. |
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| 14 | Polynomials | Methods of Approximating Roots. | Info | Go |
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Objective: Methods of approximating roots. |
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| 15 | Polynomials | Newton's Method of Approximation. | Info | Go |
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Objective: Newton's method of approximation. |
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| 16 | Calculus part 1 | Limits | Info | Go |
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Objective: To find the limit value of a function as x approaches n |
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| 17 | Calculus part 1 | Differentiation from First Principles | Info | Go |
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Objective: To differentiate functions from first principles |
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| 18 | Calculus part 1 | Differentiation of y = x to the power of n | Info | Go |
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Objective: To differentiate algebraic functions using the laws of differentiation |
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| 19 | Calculus part 1 | Meaning of dy over dx - Equations of Tangents and Normals | Info | Go |
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Objective: To find and use the slope of tangents and normals |
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| 20 | Calculus part 1 | Function of a Function Rule, Product Rule, Quotient Rule. | Info | Go |
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Objective: To differentiate functions using the product, quotient and chain rules. |
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| 21 | Calculus part 1 | Increasing, Decreasing and Stationary Functions. | Info | Go |
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Objective: To determine values of x for which f(x) is increasing, decreasing or stationary. |
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| 22 | Calculus part 1 | The Second Derivative - Concavity. | Info | Go |
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Objective: To determine concavity of a curve at a point using the second derivative. |
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| 23 | Calculus part 1 | Classification of Stationary Points. | Info | Go |
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Objective: To Locate and describe stationary points and points of inflection using differention. |
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| 24 | Calculus part 2 | Curve Sketching. | Info | Go |
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Objective: To practice curve sketching of polynomials using calculus techniques. |
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| 25 | Calculus part 2 | Practical Applications of Maxima and Minima. | Info | Go |
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Objective: To use maxima and minima to solve practical problems. |
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| 26 | Calculus part 2 | Antidifferentiation - Primitive Function. | Info | Go |
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Objective: To find primitive functions using antidifferentiation. |
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| 27 | Calculus part 2 | Computation of Areas. | Info | Go |
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Objective: To calculate areas under curves using integration. |
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| 28 | Calculus part 2 | Computation of Volumes of Revolution. | Info | Go |
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Objective: To calculate the volume of a solid using integration. |
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| 29 | Calculus part 2 | The Trapezoidal rule and Simpson's rule | Info | Go |
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Objective: To use Simpson's rule to determine area under a curve. |
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| 30 | Exam | Exam - Grade 12 Calculus AB | Info | Go |
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Objective: Exam |
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