| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Self Assessment | Self Assessment - Grade 8-12 Calculus | Info | Go |
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Objective: Assessment |
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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 | 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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| 6 | Polynomials | Graphs of polynomials | Info | Go |
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Objective: To derive graphs of polynomials by factorising |
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| 7 | Function | Functions and Relations: domain and range | Info | Go |
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Objective: To identify and represent functions and relations |
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| 8 | Function | Function Notation | Info | Go |
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Objective: To write and evaluate functions using function notation |
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| 9 | Functions | More on domain and range | Info | Go |
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Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation. |
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| 10 | Function | Domain and Range from Graphical Representations | Info | Go |
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Objective: To determine the range of a function from its graphical representation |
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| 11 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
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Objective: To evaluate and graph piecewise functions |
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| 12 | Function | Combining Functions | Info | Go |
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Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide |
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| 13 | Function | Simplifying Composite Functions | Info | Go |
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Objective: To simplify, evaluate and determine the domain of composite functions |
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| 14 | Function | Inverse Functions | Info | Go |
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Objective: To find the inverse of a function and determine whether this inverse is itself a function |
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| 15 | Function | Graphing Rational Functions Part 1 | Info | Go |
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Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes |
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| 16 | Functions | Rational functions Part 2 | Info | Go |
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Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes. |
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| 17 | Calculus=1st prin | Differentiation from first principles. | Info | Go |
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Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve. |
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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 | Turning points and the first derivative. | Info | Go |
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Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve. |
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| 23 | Function | Parametric Equations | Info | Go |
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Objective: To interchange parametric and Cartesian equations and to identify graphs |
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| 24 | Function | Polynomial Addition: in Combining and Simplifying Functions | Info | Go |
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Objective: To evaluate, simplify and graph rational functions |
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| 25 | Function | Parametric Functions | Info | Go |
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Objective: To change Cartesian and parametric equations and to graph parametric functions |
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| 26 | 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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| 27 | 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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| 28 | 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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| 29 | Polynomials | Methods of Approximating Roots. | Info | Go |
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Objective: Methods of approximating roots. |
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| 30 | Polynomials | Newton's Method of Approximation. | Info | Go |
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Objective: Newton's method of approximation. |
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| 31 | Calculus part 2 | Antidifferentiation - Primitive Function. | Info | Go |
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Objective: To find primitive functions using antidifferentiation. |
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| 32 | Calculus part 2 | Computation of Areas. | Info | Go |
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Objective: To calculate areas under curves using integration. |
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| 33 | 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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| 34 | 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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| 35 | Exam | Exam - Grade 8-12 Calculus | Info | Go |
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Objective: Exam |
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