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1 Study Plan Study plan - SAT Extension Info Go
 

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
 

Objective: To identify and use inductive and deductive reasoning

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3 Logic Disproof of Counter Example Info Go
 

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
 

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
 

Objective: To use proof by mathematical induction

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6 Logic Conditional statements (converse, inverse and contrapositive) (Stage 2) Info Go
 

Objective: On completion of the lesson the student will be able to form related conditional statements.

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7 Trigonometry part 1 Trigonometric Ratios Info Go
 

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle

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8 Trigonometry part 1 Using the Calculator Info Go
 

Objective: To determine trigonometric ratios using a calculator

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9 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 1 Sin] Info Go
 

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle

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10 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] Info Go
 

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle

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11 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] Info Go
 

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle

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12 Trigonometry part 1 Unknown in the Denominator [Case 4] Info Go
 

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator

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13 Trigonometry part 1 Bearings: The Compass Info Go
 

Objective: To change from true bearings to compass bearings and vice versa

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14 Trigonometry part 1 Angles of Elevation and Depression Info Go
 

Objective: To identify and distinguish between angles of depression and elevation

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15 Trigonometry part 1 Trigonometric Ratios in Practical Situations Info Go
 

Objective: To solve problems involving bearings and angles of elevation and depression

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16 Trigonometry part 1 Using the Calculator to Find an Angle Given a Trigonometric Ratio Info Go
 

Objective: To find angles in right-angled triangles given trigonometric ratios

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17 Trigonometry part 1 Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle Info Go
 

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems

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18 Trigonometry part 1 Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios Info Go
 

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees

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19 Trigonometry part 1 The Cosine Rule to find an unknown side [Case 1 SAS] Info Go
 

Objective: To complete the cosine rule to find a subject side for given triangles

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20 Trigonometry part 1 The Sine Rule to find an unknown side: Case 1 Info Go
 

Objective: To complete the cosine rule to find a subject angle for given triangles

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21 Trigonometry part 1 The Sine Rule: Finding a Side Info Go
 

Objective: To find an unknown side of a triangle using the sine rule

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22 Trigonometry part 1 The Sine Rule: Finding an Angle Info Go
 

Objective: To find an unknown angle of a triangle using the sine rule

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23 Trigonometry part 1 The Sine Area Formula for a Triangle Info Go
 

Objective: To use the sine formula for the area of a triangle to calculate area

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24 Co-ordinate geometry part 1 The Gradient Info Go
 

Objective: To find the gradient of a line given its angle of inclination or given rise and run

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25 Statistics part 1 Frequency distribution table Info Go
 

Objective: To construct a frequency distribution table for raw data and to interpret the table

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26 Statistics part 1 Frequency histograms and polygons Info Go
 

Objective: To construct and interpret frequency histograms and polygons

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27 Statistics part 1 Relative Frequency Info Go
 

Objective: To extend the frequency distribution table to include a relative frequency column

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28 Statistics part 1 The Range Info Go
 

Objective: To determine the range of data in either raw form or in a frequency distribution table

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29 Statistics part 1 The Mode Info Go
 

Objective: To find the mode from raw data and from a frequency distribution table

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30 Statistics part 1 The Mean Info Go
 

Objective: To calculate means from raw data and from a frequency table using an fx column

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31 Statistics part 1 The Median Info Go
 

Objective: To determine the median of a set of raw scores

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32 Statistics part 1 Cumulative Frequency Info Go
 

Objective: To construct cumulative frequency columns, histograms and polygons

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33 Statistics part 1 Calculating the Mean from a Frequency Distribution Info Go
 

Objective: To determine averages (mean, median and mode) from cumulative frequency polygons

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34 Probability The Binomial Theorem and Binomial Coefficients Info Go
 

Objective: To calculate binomial coefficients and expand binomial powers.

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35 Probability Simple events Info Go
 

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S)

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36 Probability Rolling a pair of dice Info Go
 

Objective: To find the probability of selected events when two dice are rolled

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37 Probability Experimental probability Info Go
 

Objective: To find the experimental probabilities of an experimental trial

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38 Probability Experimental probability Info Go
 

Objective: To use tree diagrams to determine sample spaces and compound probabilities

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39 Probability Tree diagrams: depending on previous outcomes Info Go
 

Objective: To use tree diagrams where the probability is dependent on previous outcomes

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40 Probability The Complementary Result Info Go
 

Objective: To calculate the probability of complementary events using P(E) = 1 - P(not E)

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41 Probability P[A or B] When A and B are NOT mutually exclusive Info Go
 

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B)

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42 Probability Binomial probabilities using the Binomial Theorem Info Go
 

Objective: To calculate the binomial probability of a given number of successful trials

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43 Probability Counting techniques and ordered selections Info Go
 

Objective: To use counting techniques in probability

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44 Probability Unordered selections - combinations Info Go
 

Objective: To use the nCr formula to solve problems where unordered selections occur

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45 Matrices Matrices: basic concepts Info Go
 

Objective: To write and state the order of a matrix and to identify square matrices

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46 Matrices Addition and Subtraction of Matrices Info Go
 

Objective: To add and subtract matrices

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47 Matrices Scalar matrix: multiplication Info Go
 

Objective: To multiply a matrix by a scalar

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48 Matrices Multiplication of one matrix by another matrix Info Go
 

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA

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49 Matrices Translation in the number plane Info Go
 

Objective: To use matrix addition to translate points

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50 Matrices Translation by matrix multiplication Info Go
 

Objective: To transform points and objects by matrix multiplication

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51 Matrices Special Transformations: Reflections, Rotations and Enlargements Info Go
 

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication

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52 Matrices Vectors Info Go
 

Objective: To use vectors to find resultant speeds and displacements

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53 Matrices - Linear systems Number of Solutions Info Go
 

Objective: To determine solutions to systems of equations

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54 Matrices - Linear systems Vector Addition in 2 and 3D Info Go
 

Objective: To represent, add, subtract and determine the direction of vectors

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55 Matrices - Linear systems Optimal Solutions Info Go
 

Objective: To use linear programming to maximise or minimise an objective function

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56 Matrices - Linear systems Linear Systems with Matrices Info Go
 

Objective: To identify and describe matrices and perform row operations in matrices

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57 Matrices - Linear systems Row Echelon Form Info Go
 

Objective: To identify and create matrices in row echelon form and to solve systems of equations

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58 Matrices - Linear systems Gauss Jordan Elimination Info Go
 

Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations

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59 Graphs part 2 Graphing complex polynomials: quadratics with no real roots Info Go
 

Objective: To graph quadratics that have no real roots, hence don't cut the x-axis

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60 Graphs part 2 General equation of a circle: determine and graph the equation Info Go
 

Objective: To determine and graph the equation of a circle with radius a and centre (h,k)

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61 Graphs part 2 Graphing cubic curves Info Go
 

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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62 Graphs part 2 Absolute Value Equations Info Go
 

Objective: To graph equations involving absolute values

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63 Graphs part 2 The Rectangular Hyperbola Info Go
 

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x

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64 Graphs part 2 The Exponential Function Info Go
 

Objective: To graph exponential curves whose exponents are either positive or negative

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65 Graphs part 2 Logarithmic Functions Info Go
 

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b)

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66 Conic sections Introduction to Conic Sections and Their General Equation Info Go
 

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2

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67 Conic sections The Parabola Info Go
 

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px

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68 Conic sections Circles Info Go
 

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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69 Conic sections The Ellipsis Info Go
 

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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70 Conic sections The Hyperbola Info Go
 

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation

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71 Function Functions and Relations: domain and range Info Go
 

Objective: To identify and represent functions and relations

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72 Function Function Notation Info Go
 

Objective: To write and evaluate functions using function notation

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73 Function Selecting Appropriate Domain and Range Info Go
 

Objective: To determine appropriate domains for functions

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74 Function Domain and Range from Graphical Representations Info Go
 

Objective: To determine the range of a function from its graphical representation

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75 Function Evaluating and Graphing Piecewise Functions Info Go
 

Objective: To evaluate and graph piecewise functions

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76 Function Combining Functions Info Go
 

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide

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77 Function Simplifying Composite Functions Info Go
 

Objective: To simplify, evaluate and determine the domain of composite functions

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78 Function Inverse Functions Info Go
 

Objective: To find the inverse of a function and determine whether this inverse is itself a function

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79 Function Graphing Rational Functions Part 1 Info Go
 

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes

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80 Function Graphing Rational Functions Part 2 Info Go
 

Objective: To determine asymptotes and graph rational functions

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81 Function Parametric Equations Info Go
 

Objective: To interchange parametric and Cartesian equations and to identify graphs

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82 Function Polynomial Addition: in Combining and Simplifying Functions Info Go
 

Objective: To evaluate, simplify and graph rational functions

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83 Function Parametric Functions Info Go
 

Objective: To change Cartesian and parametric equations and to graph parametric functions

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84 Statistics part 2 Calculating mean, mode and median from grouped data Info Go
 

Objective: To identify class centres, get frequency counts and determine mean, mode and median values

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85 Statistics part 2 Using the Calculator for Statistics Info Go
 

Objective: To find a mean, using a data set or a frequency distribution table and calculator.

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86 Statistics part 2 Measures of Spread Info Go
 

Objective: To determine a range and use it in decision making

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87 Statistics part 2 Standard deviation applications Info Go
 

Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator

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88 Statistics part 2 Applications of Standard Deviation Info Go
 

Objective: To use standard deviation as a measure of deviation from a mean

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89 Statistics part 2 The Normal Distribution Info Go
 

Objective: To use the standard deviation of a normal distribution to find a percentage of scores within ranges

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90 Statistics part 2 Measures of Spread: the interquartile range Info Go
 

Objective: To find the upper and lower quartiles and the interquartile range

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91 Statistics part 1 Stem and Leaf Plots along with Box and Whisker Plots Info Go
 

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots

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92 Statistics part 1 The Scatter plot Info Go
 

Objective: To make a valid interpretation of data presented as a scatter plot

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93 Trigonometry part 2 Reciprocal Ratios Info Go
 

Objective: To find the trigonometric ratios for a given right-angled triangle

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94 Trigonometry part 2 Complementary Angle Results Info Go
 

Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality

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95 Trigonometry part 2 Trigonometric Identities Info Go
 

Objective: To simplify expressions using trigonometric equalities

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96 Trigonometry part 2 Angles of Any Magnitude Info Go
 

Objective: To assign angles to quadrants and to find trigonometric values for angles

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97 Trigonometry part 2 Trigonometric ratios of 0°, 90°, 180°, 270° and 360° Info Go
 

Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees

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98 Trigonometry part 2 Graphing the Trigonometric Ratios I: Sine Curve Info Go
 

Objective: To recognise the sine curve and explore shifts of phase and amplitude

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99 Trigonometry part 2 Graphing the Trigonometric Ratios II: Cosine Curve Info Go
 

Objective: To recognise the cosine curve and explore shifts of phase and amplitude

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100 Trigonometry part 2 Graphing the Trigonometric Ratios III: Tangent Curve Info Go
 

Objective: To recognise the tangent curve and explore shifts of phase and amplitude

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101 Trigonometry part 2 Graphing the Trigonometric Ratios IV: Reciprocal Ratios Info Go
 

Objective: To graph the primary trigonometric functions and their inverses

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102 Trigonometry part 2 Using One Trig. Ratio to Find Another Info Go
 

Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier.

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103 Trigonometry part 2 Solving Trigonometric Equations - Type I Info Go
 

Objective: To Solve trigonometric equations for angles from 0 to 360 degrees.

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104 Trigonometry part 2 Solving Trigonometric Equations - Type II Info Go
 

Objective: To solve trigonometric equations for angles from 0 to 360 degrees.

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105 Trigonometry part 2 Solving Trigonometric Equations - Type III Info Go
 

Objective: To solve trigonometric equations using tan? = sin?/cos?.

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106 Polar coordinates Polar Coordinates - Plotting and Converting Info Go
 

Objective: To plot polar points and convert polar coordinates to rectangular coordinates

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107 Polar coordinates Converting Rectangular Coordinates to Polar Form Info Go
 

Objective: To convert rectangular to polar coordinates

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108 Polar coordinates Graphing Polar Functions Info Go
 

Objective: To write the polar coordinates of a point for selected argument ranges

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109 Trigonometry part 2 Trigonometric Sum and Difference Identities Info Go
 

Objective: To evaluate trig functions of angles using sum and difference identities

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110 Trigonometry part 2 Double Angle Identities Info Go
 

Objective: To use double angle identities to evaluate trig. functions and solve trig equations

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111 Trigonometry part 2 Half-angle Identities Info Go
 

Objective: To evaluate trig. functions of angles using half-angle identities

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112 Trigonometry part 2 t Formulas Info Go
 

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae

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113 Logarithms The Graph of the Logarithmic Curve Info Go
 

Objective: To solve problems involving logarithmic curves

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114 Complex numbers Complex Numbers: Adding and Subtracting Info Go
 

Objective: To recognise and manipulate simple complex numbers and expressions

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115 Complex numbers Complex Numbers: Multiplying and Dividing Info Go
 

Objective: To perform multiplication and division of complex numbers

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116 Complex numbers Adding and Subtracting Complex Numbers using Vectors Info Go
 

Objective: To perform complex number operations graphically using vectors

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117 Complex numbers The Absolute Value of a Complex Number Info Go
 

Objective: To find the absolute value of a complex number

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118 Complex numbers Trigonometric Form of a Complex Number Info Go
 

Objective: To find the trigonometric form of a complex number

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119 Complex numbers Multiplication and Division of Complex Numbers in Trigonometric Form Info Go
 

Objective: To multiply and divide complex numbers using DeMoivre's Theorem

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120 Complex numbers DeMoivre's theorem Info Go
 

Objective: To find powers of complex numbers using DeMoivre's theorem

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121 Complex numbers The nth Root of Real and Complex Numbers Info Go
 

Objective: To find the roots of a complex function using DeMoivre's theorem

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122 Complex numbers Fundamental Theorem of Algebra Info Go
 

Objective: To find the nth zeros of a polynomial function both real and complex

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123 Polynomials Introduction to polynomials Info Go
 

Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic

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124 Polynomials The Sum, Difference and Product of Two Polynomials Info Go
 

Objective: To add, subtract and multiply polynomials

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125 Polynomials Polynomials and Long Division Info Go
 

Objective: To perform long division of polynomials, finding quotient and remainder

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126 Polynomials The Remainder Theorem Info Go
 

Objective: To determine a remainder when a first polynomial is divided by a second

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127 Polynomials More on Remainder Theorem Info Go
 

Objective: To determine polynomial coefficients given a divisor and remainder

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128 Polynomials The factor theorem Info Go
 

Objective: To use the factor theorem to show that (x-a) is a factor of P(x)

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129 Polynomials More on the factor theorem Info Go
 

Objective: To use the factor theorem to find algebraic variables in polynomials

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130 Polynomials Complete factorisations using the factor theorem Info Go
 

Objective: To use the factor theorem to derive factors of a polynomial

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131 Polynomials Polynomial equations Info Go
 

Objective: To practise solving polynomial equations

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132 Polynomials Graphs of polynomials Info Go
 

Objective: To derive graphs of polynomials by factorising

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133 Polynomials The Sum and Product of the Roots of Quadratic Equations. Info Go
 

Objective: Sum and product of roots of quadratic equations.

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134 Polynomials The Sum and Product of the Roots of Cubic and Quartic Equations. Info Go
 

Objective: Sum and product of toots of cubic and quartic equations.

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135 Polynomials Methods of Approximating Roots. Info Go
 

Objective: Methods of approximating roots.

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136 Polynomials Newton's Method of Approximation. Info Go
 

Objective: Newton's method of approximation.

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137 Calculus part 1 Limits Info Go
 

Objective: To find the limit value of a function as x approaches n

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138 Calculus part 1 Differentiation from First Principles Info Go
 

Objective: To differentiate functions from first principles

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139 Calculus part 1 Differentiation of y = x to the power of n Info Go
 

Objective: To differentiate algebraic functions using the laws of differentiation

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140 Calculus part 1 Meaning of dy over dx - Equations of Tangents and Normals Info Go
 

Objective: To find and use the slope of tangents and normals

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141 Calculus part 1 Function of a Function Rule, Product Rule, Quotient Rule. Info Go
 

Objective: To differentiate functions using the product, quotient and chain rules.

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142 Calculus part 1 Increasing, Decreasing and Stationary Functions. Info Go
 

Objective: To determine values of x for which f(x) is increasing, decreasing or stationary.

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143 Calculus part 1 The Second Derivative - Concavity. Info Go
 

Objective: To determine concavity of a curve at a point using the second derivative.

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144 Calculus part 1 Classification of Stationary Points. Info Go
 

Objective: To Locate and describe stationary points and points of inflection using differention.

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145 Series and sequences part 2 Geometric Means Info Go
 

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints

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146 Series and sequences part 2 The sum to n terms of a G.P. Info Go
 

Objective: To find the sum of n terms of a sequence

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147 Series and sequences part 2 Sigma notation Info Go
 

Objective: To evaluate progressions using sigma notation

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148 Series and sequences part 2 Limiting Sum or Sum to Infinity Info Go
 

Objective: To find the limiting sum of a sequence

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149 Series and sequences part 2 Recurring Decimals and the Infinite G.P. Info Go
 

Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction

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150 Series and sequences part 2 Compound Interest Info Go
 

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n

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151 Series and sequences part 2 Superannuation Info Go
 

Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time

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152 Series and sequences part 2 Time Payments Info Go
 

Objective: To calculate the payments required to pay off a loan

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153 Calculus part 2 Curve Sketching. Info Go
 

Objective: To practice curve sketching of polynomials using calculus techniques.

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154 Calculus part 2 Practical Applications of Maxima and Minima. Info Go
 

Objective: To use maxima and minima to solve practical problems.

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155 Calculus part 2 Antidifferentiation - Primitive Function. Info Go
 

Objective: To find primitive functions using antidifferentiation.

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156 Calculus part 2 Computation of Areas. Info Go
 

Objective: To calculate areas under curves using integration.

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157 Calculus part 2 Computation of Volumes of Revolution. Info Go
 

Objective: To calculate the volume of a solid using integration.

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158 Calculus part 2 The Trapezoidal rule and Simpson's rule Info Go
 

Objective: To use Simpson's rule to determine area under a curve.

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159 Exam Exam - SAT Extension Info Go
 

Objective: Exam

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