| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grade 11-12 Algebra II | 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 | 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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| 3 | Function | Function Notation | Info | Go |
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Objective: To write and evaluate functions using function notation |
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| 4 | Function | Selecting Appropriate Domain and Range | Info | Go |
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Objective: To determine appropriate domains for functions |
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| 5 | 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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| 6 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
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Objective: To evaluate and graph piecewise functions |
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| 7 | Co-ordinate geometry part 1 | The Gradient | Info | Go |
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Objective: To find the gradient of a line given its angle of inclination or given rise and run |
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| 8 | Co-ordinate geometry part 1 | The Gradient Formula | Info | Go |
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Objective: To use the gradient formula to find the gradient of straight lines |
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| 9 | Co-ordinate geometry part 1 | The Straight Line | Info | Go |
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Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b |
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| 10 | Co-ordinate geometry part 1 | Lines Through the Origin | Info | Go |
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Objective: To state the equation of lines passing through the origin and to graph y = mx |
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| 11 | Co-ordinate geometry part 1 | General Form of a Line and the x and y Intercepts | Info | Go |
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Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area |
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| 12 | Co-ordinate geometry part 1 | Slope Intercept Form of a Line | Info | Go |
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Objective: To change equation to slope intercept form and graph it and to find equation given graph |
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| 13 | Co-ordinate geometry part 1 | Point Slope Form of a Line | Info | Go |
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Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1) |
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| 14 | Graphs part 1 | The Circle: to find radii of circles | Info | Go |
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Objective: To find radii of circles, centre (0, 0) using x^2 + y^2 = a^2 and write equations of circles |
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| 15 | Graphs part 1 | The semicircle: to select the equation given the semicircle and vice versa | Info | Go |
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Objective: To select the equation given a semicircle and vice versa |
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| 16 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | Info | Go |
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Objective: To describe properties of a parabola from its equation and sketch the parabola |
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| 17 | 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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| 18 | 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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| 19 | 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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| 20 | Graphs part 1 | Solving Simultaneous Equations graphically | Info | Go |
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Objective: To solve simultaneous equations graphically |
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| 21 | Matrices - Linear systems | Number of Solutions | Info | Go |
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Objective: To determine solutions to systems of equations |
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| 22 | 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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| 23 | 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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| 24 | Statistics part 1 | The Scatter plot | Info | Go |
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Objective: To make a valid interpretation of data presented as a scatter plot |
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| 25 | Algebra - Basic | Solving Two-Step Equations | Info | Go |
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Objective: To solve two-step equations without division in the initial problem |
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| 26 | Algebra - Basic | Solving Equations Containing Binomial Expressions | Info | Go |
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Objective: To solve equations with binomial expressions on each side |
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| 27 | Algebra - Basic | Equations involving Grouping Symbols | Info | Go |
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Objective: To solve equations containing grouping symbols on each side |
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| 28 | Algebra - Basic | Equations involving fractions | Info | Go |
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Objective: To solve fraction equations with the unknown in either the numerator or denominator |
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| 29 | Algebra - Basic | Equations Resulting from Substitution into Formulae | Info | Go |
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Objective: To solve equations created by substituting values into formulae |
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| 30 | Algebra - Basic | Changing the Subject of the Formula | Info | Go |
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Objective: To change the subject of algebraic formulae using equation-solving techniques |
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| 31 | Algebra - Basic | Inequalities | Info | Go |
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Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign |
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| 32 | 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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| 33 | 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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| 34 | 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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| 35 | 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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| 36 | 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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| 37 | 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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| 38 | Absolute value | Solving Absolute Value Equations | Info | Go |
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Objective: To solve equations involving absolute values |
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| 39 | 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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| 40 | Indices/Exponents | Adding indices when multiplying terms with the same base | Info | Go |
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Objective: To add indices when multiplying powers that have the same base |
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| 41 | Indices/Exponents | Subtracting indices when dividing terms with the same base | Info | Go |
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Objective: To subtract indices when dividing powers of the same base |
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| 42 | Indices/Exponents | Multiplying indices when raising a power to a power | Info | Go |
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Objective: To multiply indices when raising a power to a power |
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| 43 | Indices/Exponents | Multiplying indices when raising to more than one term | Info | Go |
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Objective: To raise power products to a power |
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| 44 | Indices/Exponents | Terms raised to the power of zero | Info | Go |
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Objective: To evaluate expressions where quantities are raised to the power 0 |
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| 45 | Indices/Exponents | Negative Indices | Info | Go |
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Objective: To evaluate or simplify expressions containing negative indices |
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| 46 | Indices/Exponents | Fractional Indices | Info | Go |
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Objective: To evaluate or simplify expressions containing fractional indices |
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| 47 | 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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| 48 | 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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| 49 | 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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| 50 | 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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| 51 | Algebra - Products and factors | Quadratic Trinomials (monic): Case 4 | Info | Go |
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Objective: On completion of the lesson the student will understand how to factorize all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. |
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| 52 | 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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| 53 | 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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| 54 | 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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| 55 | Algebra - Products and factors | Simplifying algebraic fractions | Info | Go |
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Objective: To simplify algebraic fractions by factorisation and cancellation |
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| 56 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 57 | 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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| 58 | 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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| 59 | 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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| 60 | 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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| 61 | Algebra - Quadratic equations | Completing the square | Info | Go |
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Objective: To complete an incomplete square |
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| 62 | 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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| 63 | 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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| 64 | Algebra - Quadratic equations | Problem solving with quadratic equations | Info | Go |
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Objective: To solve problems which require finding the roots of a quadratic equation |
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| 65 | 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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| 66 | 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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| 67 | 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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| 68 | 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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| 69 | 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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| 70 | 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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| 71 | Matrices | Matrices: basic concepts | Info | Go |
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Objective: To write and state the order of a matrix and to identify square matrices |
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| 72 | Matrices | Addition and Subtraction of Matrices | Info | Go |
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Objective: To add and subtract matrices |
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| 73 | Matrices | Scalar matrix: multiplication | Info | Go |
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Objective: To multiply a matrix by a scalar |
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| 74 | Matrices | Multiplication of one matrix by another matrix | Info | Go |
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Objective: To perform matrix multiplication and to recognise that AB is not equal to BA |
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| 75 | Matrices | Translation in the number plane | Info | Go |
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Objective: To use matrix addition to translate points |
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| 76 | Matrices | Translation by matrix multiplication | Info | Go |
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Objective: To transform points and objects by matrix multiplication |
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| 77 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | Info | Go |
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Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication |
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| 78 | Matrices | Vectors | Info | Go |
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Objective: To use vectors to find resultant speeds and displacements |
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| 79 | 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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| 80 | 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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| 81 | Matrices - Linear systems | Gauss Jordan Elimination | Info | Go |
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Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations |
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| 82 | 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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| 83 | 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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| 84 | Graphs part 2 | Absolute Value Equations | Info | Go |
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Objective: To graph equations involving absolute values |
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| 85 | 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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| 86 | 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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| 87 | 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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| 88 | 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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| 89 | 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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| 90 | 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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| 91 | 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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| 92 | 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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| 93 | 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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| 94 | 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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| 95 | 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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| 96 | Function | Graphing Rational Functions Part 2 | Info | Go |
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Objective: To determine asymptotes and graph rational functions |
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| 97 | Function | Parametric Equations | Info | Go |
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Objective: To interchange parametric and Cartesian equations and to identify graphs |
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| 98 | 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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| 99 | 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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| 100 | Logarithms | Powers of 2 | Info | Go |
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Objective: To convert between logarithm statements and indice statements |
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| 101 | 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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| 102 | 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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| 103 | Logarithms | Laws of Logarithms | Info | Go |
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Objective: To review the logarithm laws |
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| 104 | 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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| 105 | 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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| 106 | 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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| 107 | Logarithms | Equations Involving Logarithms | Info | Go |
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Objective: To solve equations involving logarithms using the logarithm laws |
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| 108 | Logarithms | Using Logarithms to Solve Equations | Info | Go |
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Objective: To use logarithms to solve exponential equations |
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| 109 | Logarithms | Change of Base Formula | Info | Go |
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Objective: To evaluate log expressions using logarithms |
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| 110 | Logarithms | The Graph of the Logarithmic Curve | Info | Go |
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Objective: To learn the properties of the logarithmic curve |
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| 111 | Logarithms | The Graph of the Logarithmic Curve | Info | Go |
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Objective: To solve problems involving logarithmic curves |
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| 112 | Exam | Exam - Grade 11-12 Algebra II | Info | Go |
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Objective: Exam |
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