| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - SAT Analysis | 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 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 3 | Logic | Disproof of Counter Example | Info | Go |
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Objective: To identify a statement as a counter example to disprove a statement |
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| 4 | Logic | Proof by Disproof of a Contradictory Statement | Info | Go |
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Objective: To prove that a statement is true by proving that the contradictory statement is false |
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| 5 | Logic | Mathematical induction | Info | Go |
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Objective: To use proof by mathematical induction |
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| 6 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | Info | Go |
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Objective: To graph quadratics that have no real roots, hence don't cut the x-axis |
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| 7 | Graphs part 2 | General equation of a circle: determine and graph the equation | Info | Go |
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Objective: To determine and graph the equation of a circle with radius a and centre (h,k) |
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| 8 | Graphs part 2 | Graphing cubic curves | Info | Go |
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Objective: To graph cubic curves whose equation is of the form y = (x - a)^3 + b or y = (a - x)^3 + b |
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| 9 | Graphs part 2 | Absolute Value Equations | Info | Go |
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Objective: To graph equations involving absolute values |
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| 10 | Graphs part 2 | The Rectangular Hyperbola | Info | Go |
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Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x |
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| 11 | Graphs part 2 | The Exponential Function | Info | Go |
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Objective: To graph exponential curves whose exponents are either positive or negative |
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| 12 | Graphs part 2 | Logarithmic Functions | Info | Go |
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Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) |
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| 13 | Conic sections | Introduction to Conic Sections and Their General Equation | Info | Go |
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Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 |
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| 14 | Conic sections | The Parabola | Info | Go |
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Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px |
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| 15 | Conic sections | Circles | Info | Go |
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Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles |
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| 16 | Conic sections | The Ellipsis | Info | Go |
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Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses |
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| 17 | Conic sections | The Hyperbola | Info | Go |
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Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation |
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| 18 | 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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| 19 | Function | Function Notation | Info | Go |
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Objective: To write and evaluate functions using function notation |
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| 20 | Function | Selecting Appropriate Domain and Range | Info | Go |
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Objective: To determine appropriate domains for functions |
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| 21 | 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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| 22 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
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Objective: To evaluate and graph piecewise functions |
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| 23 | 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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| 24 | 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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| 25 | 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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| 26 | 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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| 27 | Function | Graphing Rational Functions Part 2 | Info | Go |
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Objective: To determine asymptotes and graph rational functions |
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| 28 | Function | Parametric Equations | Info | Go |
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Objective: To interchange parametric and Cartesian equations and to identify graphs |
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| 29 | 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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| 30 | 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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| 31 | Polar coordinates | Polar Coordinates - Plotting and Converting | Info | Go |
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Objective: To plot polar points and convert polar coordinates to rectangular coordinates |
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| 32 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | Info | Go |
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Objective: To convert rectangular to polar coordinates |
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| 33 | Polar coordinates | Graphing Polar Functions | Info | Go |
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Objective: To write the polar coordinates of a point for selected argument ranges |
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| 34 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | Info | Go |
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Objective: To evaluate trig functions of angles using sum and difference identities |
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| 35 | Trigonometry part 2 | Double Angle Identities | Info | Go |
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Objective: To use double angle identities to evaluate trig. functions and solve trig equations |
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| 36 | Trigonometry part 2 | Half-angle Identities | Info | Go |
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Objective: To evaluate trig. functions of angles using half-angle identities |
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| 37 | Trigonometry part 2 | t Formulas | Info | Go |
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Objective: To write t-formulae for trig. functions. To solve equations using t-formulae |
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| 38 | Complex numbers | Complex Numbers: Adding and Subtracting | Info | Go |
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Objective: To recognise and manipulate simple complex numbers and expressions |
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| 39 | Complex numbers | Complex Numbers: Multiplying and Dividing | Info | Go |
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Objective: To perform multiplication and division of complex numbers |
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| 40 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | Info | Go |
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Objective: To perform complex number operations graphically using vectors |
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| 41 | Complex numbers | The Absolute Value of a Complex Number | Info | Go |
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Objective: To find the absolute value of a complex number |
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| 42 | Complex numbers | Trigonometric Form of a Complex Number | Info | Go |
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Objective: To find the trigonometric form of a complex number |
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| 43 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | Info | Go |
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Objective: To multiply and divide complex numbers using DeMoivre's Theorem |
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| 44 | Complex numbers | DeMoivre's theorem | Info | Go |
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Objective: To find powers of complex numbers using DeMoivre's theorem |
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| 45 | Complex numbers | The nth Root of Real and Complex Numbers | Info | Go |
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Objective: To find the roots of a complex function using DeMoivre's theorem |
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| 46 | Complex numbers | Fundamental Theorem of Algebra | Info | Go |
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Objective: To find the nth zeros of a polynomial function both real and complex |
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| 47 | 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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| 48 | Calculus part 1 | Differentiation from First Principles | Info | Go |
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Objective: To differentiate functions from first principles |
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| 49 | 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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| 50 | 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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| 51 | Series and sequences part 2 | Geometric Means | Info | Go |
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Objective: To find geometric means of a and b and insert geometric means between 2 endpoints |
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| 52 | Series and sequences part 2 | The sum to n terms of a G.P. | Info | Go |
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Objective: To find the sum of n terms of a sequence |
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| 53 | Series and sequences part 2 | Sigma notation | Info | Go |
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Objective: To evaluate progressions using sigma notation |
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| 54 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | Info | Go |
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Objective: To find the limiting sum of a sequence |
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| 55 | Exam | Exam - SAT Analysis | Info | Go |
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Objective: Exam |
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