| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Self Assessment | Self Assessment - Grades 11 - 12: Pre-Calculus | Info | Go |
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Objective: Assessment |
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| 2 | 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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| 3 | 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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| 4 | 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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| 5 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | Info | Go |
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Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees |
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| 6 | Graphs part 2 | Absolute Value Equations | Info | Go |
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Objective: To graph equations involving absolute values |
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| 7 | 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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| 8 | 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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| 9 | 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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| 10 | 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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| 11 | Function | Function Notation | Info | Go |
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Objective: To write and evaluate functions using function notation |
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| 12 | Function | Selecting Appropriate Domain and Range | Info | Go |
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Objective: To determine appropriate domains for functions |
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| 13 | 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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| 14 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
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Objective: To evaluate and graph piecewise functions |
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| 15 | 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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| 16 | 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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| 17 | 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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| 18 | 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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| 19 | Function | Graphing Rational Functions Part 2 | Info | Go |
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Objective: To determine asymptotes and graph rational functions |
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| 20 | Function | Parametric Equations | Info | Go |
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Objective: To interchange parametric and Cartesian equations and to identify graphs |
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| 21 | 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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| 22 | 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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| 23 | 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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| 24 | 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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| 25 | 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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| 26 | 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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| 27 | 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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| 28 | 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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| 29 | Polynomials | Polynomial equations | Info | Go |
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Objective: To practise solving polynomial equations |
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| 30 | Polynomials | Graphs of polynomials | Info | Go |
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Objective: To derive graphs of polynomials by factorising |
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| 31 | Logarithms | Powers of 2 | Info | Go |
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Objective: To convert between logarithm statements and indice statements |
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| 32 | 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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| 33 | 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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| 34 | Logarithms | Laws of Logarithms | Info | Go |
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Objective: To review the logarithm laws |
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| 35 | 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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| 36 | 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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| 37 | 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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| 38 | Logarithms | Equations Involving Logarithms | Info | Go |
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Objective: To solve equations involving logarithms using the logarithm laws |
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| 39 | Logarithms | Using Logarithms to Solve Equations | Info | Go |
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Objective: To use logarithms to solve exponential equations |
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| 40 | Logarithms | Change of Base Formula | Info | Go |
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Objective: To evaluate log expressions using logarithms |
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| 41 | 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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| 42 | Logarithms | The Graph of the Logarithmic Curve | Info | Go |
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Objective: To solve problems involving logarithmic curves |
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| 43 | 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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| 44 | 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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| 45 | 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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| 46 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | Info | Go |
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Objective: To complete the cosine rule to find a subject side for given triangles |
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| 47 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | Info | Go |
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Objective: To complete the cosine rule to find a subject angle for given triangles |
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| 48 | Trigonometry part 1 | The Sine Rule: Finding a Side | Info | Go |
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Objective: To find an unknown side of a triangle using the sine rule |
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| 49 | Trigonometry part 1 | The Sine Rule: Finding an Angle | Info | Go |
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Objective: To find an unknown angle of a triangle using the sine rule |
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| 50 | Trigonometry part 1 | The Sine Area Formula for a Triangle | Info | Go |
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Objective: To use the sine formula for the area of a triangle to calculate area |
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| 51 | Trigonometry part 2 | Reciprocal Ratios | Info | Go |
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Objective: To find the trigonometric ratios for a given right-angled triangle |
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| 52 | Trigonometry part 2 | Complementary Angle Results | Info | Go |
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Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality |
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| 53 | Trigonometry part 2 | Trigonometric Identities | Info | Go |
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Objective: To simplify expressions using trigonometric equalities |
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| 54 | Trigonometry part 2 | Angles of Any Magnitude | Info | Go |
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Objective: To assign angles to quadrants and to find trigonometric values for angles |
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| 55 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | Info | Go |
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Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees |
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| 56 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | Info | Go |
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Objective: To recognise the sine curve and explore shifts of phase and amplitude |
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| 57 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | Info | Go |
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Objective: To recognise the cosine curve and explore shifts of phase and amplitude |
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| 58 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | Info | Go |
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Objective: To recognise the tangent curve and explore shifts of phase and amplitude |
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| 59 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | Info | Go |
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Objective: To graph the primary trigonometric functions and their inverses |
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| 60 | 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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| 61 | 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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| 62 | 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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| 63 | 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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| 64 | 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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| 65 | 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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| 66 | 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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| 67 | 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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| 68 | 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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| 69 | 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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| 70 | 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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| 71 | Matrices | Addition and Subtraction of Matrices | Info | Go |
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Objective: To add and subtract matrices |
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| 72 | Matrices | Scalar matrix: multiplication | Info | Go |
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Objective: To multiply a matrix by a scalar |
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| 73 | 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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| 74 | Matrices | Translation in the number plane | Info | Go |
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Objective: To use matrix addition to translate points |
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| 75 | Matrices | Translation by matrix multiplication | Info | Go |
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Objective: To transform points and objects by matrix multiplication |
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| 76 | 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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| 77 | Matrices | Vectors | Info | Go |
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Objective: To use vectors to find resultant speeds and displacements |
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| 78 | Matrices - Linear systems | Number of Solutions | Info | Go |
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Objective: To determine solutions to systems of equations |
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| 79 | 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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| 80 | 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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| 81 | 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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| 82 | 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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| 83 | 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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| 84 | Co-ordinate geometry part 2 | Intercept form of a straight line: find the equation when given x and y | Info | Go |
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Objective: To find the equation of a line given the x-axis and y-axis intercepts |
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| 85 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | Info | Go |
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Objective: To change the standard form of a straight line equation to the y = mx + b form |
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| 86 | Co-ordinate geometry part 2 | Perpendicular Lines | Info | Go |
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Objective: To identify the equation of a line that is perpendicular to a given linear equation |
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| 87 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | Info | Go |
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Objective: To identify the graph which matches a given inequality |
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| 88 | Co-ordinate geometry part 2 | Perpendicular Distance | Info | Go |
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Objective: To calculate the perpendicular distance from a point to a line and between lines |
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| 89 | Co-ordinate geometry part 2 | Line through the intersection of two given lines | Info | Go |
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Objective: To determine the equation of a line passing through the intersection of two lines |
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| 90 | Co-ordinate geometry part 2 | Angles between two lines | Info | Go |
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Objective: To find the angle between two given straight lines |
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| 91 | Co-ordinate geometry part 2 | Internal and external division of an interval | Info | Go |
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Objective: To find the value of k given the interval AB is divided at point P in the ratio of k to some value |
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| 92 | 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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| 93 | Series and sequences part 1 | Finding Tn Given Sn | Info | Go |
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Objective: To find the value of the n'th term in a sequence given the sum of the first n terms |
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| 94 | 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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| 95 | Series and sequences part 1 | Finding the position of a term in an A.P. | Info | Go |
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Objective: To find the position of a term in a sequence, given an arithmetic progression and a value term |
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| 96 | 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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| 97 | 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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| 98 | 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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| 99 | 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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| 100 | 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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| 101 | 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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| 102 | Logic | Mathematical induction | Info | Go |
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Objective: To use proof by mathematical induction |
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| 103 | 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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| 104 | 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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| 105 | Series and sequences part 2 | Sigma notation | Info | Go |
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Objective: To evaluate progressions using sigma notation |
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| 106 | 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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| 107 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | Info | Go |
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Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction |
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| 108 | Series and sequences part 2 | Compound Interest | Info | Go |
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Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n |
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| 109 | Series and sequences part 2 | Superannuation | Info | Go |
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Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time |
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| 110 | Series and sequences part 2 | Time Payments | Info | Go |
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Objective: To calculate the payments required to pay off a loan |
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| 111 | Series and sequences part 2 | Applications of arithmetic sequences | Info | Go |
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Objective: To learn about practical situations with arithmetic series |
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| 112 | 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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| 113 | Probability | Counting techniques and ordered selections | Info | Go |
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Objective: To use counting techniques in probability |
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| 114 | Probability | Unordered selections - combinations | Info | Go |
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Objective: To use the nCr formula to solve problems where unordered selections occur |
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| 115 | 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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| 116 | 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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| 117 | 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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| 118 | 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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| 119 | 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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| 120 | 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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| 121 | 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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| 122 | 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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| 123 | Calculus part 1 | Differentiation from First Principles | Info | Go |
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Objective: To differentiate functions from first principles |
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| 124 | 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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| 125 | 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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| 126 | Exam | Exam - Grades 11 - 12: Pre-Calculus | Info | Go |
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Objective: Exam |
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