| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Self Assessment | Self Assessment - Grade 8-12 Algebra II | Info | Go |
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Objective: Assessment |
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| 2 | Absolute value | Evaluating Absolute Value Expressions | Info | Go |
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Objective: To evaluate numeric and algebraic expressions involving absolute value |
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| 3 | Absolute value | Solving Absolute Value Equations | Info | Go |
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Objective: To solve equations involving absolute values |
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| 4 | Absolute value | Solving and Graphing Inequalities | Info | Go |
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Objective: To graph the solution set of absolute value inequalities |
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| 5 | Simultaneous equations | Simultaneous Equations | Info | Go |
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Objective: To solve simultaneous equations by substitution |
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| 6 | Simultaneous equations | Elimination method | Info | Go |
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Objective: To solve simultaneous equations by elimination |
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| 7 | Simultaneous equations | Elimination method part 2 | Info | Go |
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Objective: To solve more difficult simultaneous equations by elimination |
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| 8 | Simultaneous equns | Applications of simultaneous equations | Info | Go |
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Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. |
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| 9 | Matrices - Linear systems | Number of Solutions | Info | Go |
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Objective: To determine solutions to systems of equations |
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| 10 | Matrices - Linear systems | Vector Addition in 2 and 3D | Info | Go |
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Objective: To represent, add, subtract and determine the direction of vectors |
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| 11 | Matrices - Linear systems | Optimal Solutions | Info | Go |
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Objective: To use linear programming to maximise or minimise an objective function |
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| 12 | Matrices - Linear systems | Linear Systems with Matrices | Info | Go |
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Objective: To identify and describe matrices and perform row operations in matrices |
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| 13 | Matrices - Linear systems | Row Echelon Form | Info | Go |
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Objective: To identify and create matrices in row echelon form and to solve systems of equations |
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| 14 | Linear systems | Gauss Jordan elimination method (Stage 2) | Info | Go |
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Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method. |
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| 15 | Algebra - Basic | Factorisation of algebraic fractions including binomials | Info | Go |
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Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions |
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| 16 | Algebra - Basic | Cancelling binomial factors in algebraic fractions | Info | Go |
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Objective: To simplify algebraic fractions with binomials in both the numerator and denominator |
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| 17 | 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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| 18 | Algebra - Products and factors | Binomial Products | Info | Go |
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Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) |
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| 19 | Algebra - Products and factors | Binomial products with negative multiplier | Info | Go |
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Objective: To expand and simplify monic binomial products of the form (x - a)(x +/- b) |
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| 20 | Algebra - Products and factors | Binomial Products (nonmonic) | Info | Go |
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Objective: To expand and simplify nonmonic binomial products |
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| 21 | Algebra - Products and factors | Squaring a Binomial (monic) | Info | Go |
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Objective: To expand the square of a binomial by multiplication and by inspection |
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| 22 | Squaring binomial | Squaring a binomial [non-monic]. | Info | Go |
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Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. |
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| 23 | Algebra - Products and factors | Expansions Leading to the Difference of Two Squares | Info | Go |
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Objective: To expand the product of conjugate binomials leading to differences of squares |
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| 24 | Algebra - Products and factors | Products in Simplification of Algebraic Expressions | Info | Go |
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Objective: To simplify algebraic expressions containing binomial products |
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| 25 | Algebra - Products and factors | Larger Expansions | Info | Go |
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Objective: To expand and simplify the product of a binomial and a trinomial |
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| 26 | Algebra - Products and factors | Highest Common Factor | Info | Go |
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Objective: To factorise an expression by identifying and extracting the highest common factor |
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| 27 | Algebra - Products and factors | Factors by Grouping | Info | Go |
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Objective: To factorise a four-term expression by grouping |
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| 28 | Algebra - Products and factors | Difference of Two Squares | Info | Go |
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Objective: To factorise differences of two squares |
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| 29 | Algebra - Products and factors | Common factor and the difference of two squares | Info | Go |
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Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. |
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| 30 | Algebra - Products and factors | Quadratic Trinomials (monic): Case 1 | Info | Go |
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Objective: On completion of the lesson the student will understand the factorization of quadratic trinomial equations with all terms positive. |
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| 31 | Algebra - Products and factors | Quadratic Trinomials (monic): Case 2 | Info | Go |
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Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. |
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| 32 | Algebra - Products and factors | Quadratic Trinomials (monic): Case 3 | Info | Go |
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Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. |
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| 33 | Factorising quads | Factorising quadratic trinomials [monic] - Case 4. | Info | Go |
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Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. |
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| 34 | Algebra - Products and factors | Factorisation of nonmonic quadratic trinomials | Info | Go |
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Objective: To factorise nonmonic quadratic trinomials using the 'X' method |
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| 35 | Algebra - Products and factors | Factorisation of nonmonic quadratic trinomials: Moon method | Info | Go |
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Objective: To factorise nonmonic quadratic trinomials using the 'Moon' method |
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| 36 | Algebra - Products and factors | Sum and Difference of Two Cubes | Info | Go |
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Objective: To factorise the sum and difference of two cubes |
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| 37 | Algebraic fractions | Simplifying algebraic fractions. | Info | Go |
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Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. |
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| 38 | Trigonometry part 2 | Solving Trigonometric Equations - Type III | Info | Go |
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Objective: To solve trigonometric equations using tan? = sin?/cos?. |
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| 39 | 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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| 40 | Algebra - Basic | Simplifying easy algebraic fractions | Info | Go |
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Objective: To simplify simple algebraic fractions using cancellation of common factors |
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| 41 | Algebra - Basic | Simplifying algebraic fractions using the Index Laws | Info | Go |
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Objective: To use the index laws for division to simplify algebraic fractions |
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| 42 | Algebra - Basic | Algebraic fractions resulting in negative Indices | Info | Go |
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Objective: To simplify algebraic fractions using negative indices (as required) in the answer |
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| 43 | 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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| 44 | Algebra - Quadratic equations | Introduction to Quadratic Equations | Info | Go |
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Objective: To find the solutions of quadratic equations presented as a product of factors |
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| 45 | Algebra - Quadratic equations | Solving Quadratic Equations with Factorisation | Info | Go |
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Objective: To solve quadratic equations requiring factorisation |
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| 46 | Algebra - Quadratic equations | Solving Quadratic Equations | Info | Go |
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Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 |
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| 47 | Algebra - Quadratic equations | Completing the square | Info | Go |
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Objective: To complete an incomplete square |
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| 48 | Algebra - Quadratic equations | Solving Quadratic Equations by Completing the Square | Info | Go |
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Objective: To solve quadratic equations by completing the square |
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| 49 | Algebra - Quadratic equations | The Quadratic Formula | Info | Go |
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Objective: To find the roots of a quadratic equation by using the quadratic formula |
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| 50 | Quadratic equations | Problem solving with quadratic equations | Info | Go |
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Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. |
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| 51 | Algebra - Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | Info | Go |
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Objective: To determine points of intersection of quadratic and linear equations |
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| 52 | 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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| 53 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | Info | Go |
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Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. |
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| 54 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | Info | Go |
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Objective: To describe and sketch parabolas of the form y = x^2 + bx + c |
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| 55 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | Info | Go |
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Objective: To describe and sketch parabolas of the form y = (x - a)^2 |
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| 56 | Graphs part 1 | Graphing irrational roots | Info | Go |
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Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola |
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| 57 | Logarithms-Power of 2 | Powers of 2. | Info | Go |
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Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2. |
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| 58 | Logarithms | Equations of type log x to the base 3 = 4 | Info | Go |
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Objective: To find the value of x in a statement of type log x to the base 3 = 4 |
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| 59 | Logarithms | Equations of type log 32 to the base x = 5 | Info | Go |
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Objective: To solve Logrithmic Equation where the variable is the base x = 5 |
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| 60 | Logarithms | Laws of Logarithms | Info | Go |
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Objective: To review the logarithm laws |
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| 61 | Logarithms | Using the Log Laws to Expand Logarithmic Expressions | Info | Go |
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Objective: To expand expressions using the logarithm laws |
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| 62 | Logarithms | Using the Log Laws to Simplify Expressions Involving Logarithms | Info | Go |
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Objective: To simplify expressions using the logarithm laws |
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| 63 | Logarithms | Using the Log Laws to Find the Logarithms of Numbers | Info | Go |
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Objective: To find the logarithm of a number, with an unknown base, using the logarithm laws |
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| 64 | Logarithms-Equations and logs | Equations involving logarithms. | Info | Go |
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Objective: On completion of the lesson the student will be able to solve equations with log terms. |
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| 65 | Logarithms | Using Logarithms to Solve Equations | Info | Go |
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Objective: To use logarithms to solve exponential equations |
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| 66 | Logarithms | Change of Base Formula | Info | Go |
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Objective: To evaluate log expressions using logarithms |
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| 67 | Fractional indices/exponents | Fractional indices | Info | Go |
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Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. |
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| 68 | Indices/Exponents | Complex fractions as indices | Info | Go |
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Objective: To evaluate or simplify expressions containing complex fractional indices and radicals |
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| 69 | 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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| 70 | 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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| 71 | Conic sections | Introduction to conic sections and their general equation | Info | Go |
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Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation. |
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| 72 | 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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| 73 | 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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| 74 | 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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| 75 | 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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| 76 | Probability | Counting techniques and ordered selections | Info | Go |
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Objective: To use counting techniques in probability |
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| 77 | Statistic-probability | Unordered selections - combinations | Info | Go |
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Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen. |
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| 78 | Probability | The Binomial Theorem and Binomial Coefficients | Info | Go |
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Objective: To calculate binomial coefficients and expand binomial powers. |
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| 79 | Probability | Binomial probabilities using the Binomial Theorem | Info | Go |
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Objective: To calculate the binomial probability of a given number of successful trials |
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| 80 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 81 | Series and sequences part 1 | General Sequences | Info | Go |
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Objective: To use the general form of the n'th term of a sequence to find the first 3 terms |
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| 82 | Sequences and Series | Finding Tn given Sn. | Info | Go |
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Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. |
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| 83 | Series and sequences part 1 | The Arithmetic Progression | Info | Go |
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Objective: To find the common difference of a given arithmetic progression |
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| 84 | Arithmetic Progression | Finding the position of a term in an A.P. | Info | Go |
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Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression. |
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| 85 | Series and sequences part 1 | Given two terms of A.P. find the sequence | Info | Go |
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Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms |
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| 86 | Series and sequences part 1 | Arithmetic Means | Info | Go |
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Objective: To find the arithmetic mean of two values |
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| 87 | Series and sequences part 1 | The sum to n terms of an A.P. | Info | Go |
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Objective: To find the sum of n terms of an arithmetic progression given the first three terms |
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| 88 | Series and sequences part 1 | The Geometric Progression | Info | Go |
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Objective: To find the common ratio of a given geometric progression |
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| 89 | Series and sequences part 1 | Finding the position of a term in a G.P. | Info | Go |
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Objective: To find the place of a term in a given geometric progression |
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| 90 | Series and sequences part 1 | Given two terms of G.P. find the sequence | Info | Go |
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Objective: To find the first term given two terms of a geometric progression |
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| 91 | 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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| 92 | 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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| 93 | Series and sequences part 2 | Sigma notation | Info | Go |
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Objective: To evaluate progressions using sigma notation |
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| 94 | 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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| 95 | 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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| 96 | 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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| 97 | 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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| 98 | 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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| 99 | Exam | Exam - Grade 8-12 Algebra II | Info | Go |
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Objective: Exam |
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