You have selected Grades 11 - 12: Pre-Calculus

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122 Calculus part 1 Limits Info Go

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

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

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

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

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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

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

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

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

Objective: To identify the graph which matches a given inequality

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88 Co-ordinate geometry part 2 Perpendicular Distance Info Go

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

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

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

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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43 Complex numbers Complex Numbers: Adding and Subtracting Info Go

Objective: To recognise and manipulate simple complex numbers and expressions

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44 Complex numbers Complex Numbers: Multiplying and Dividing Info Go

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

Objective: To perform complex number operations graphically using vectors

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64 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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65 Complex numbers Trigonometric Form of a Complex Number Info Go

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

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

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67 Complex numbers DeMoivre's theorem Info Go

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

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

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

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112 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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115 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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116 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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117 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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118 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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126 Exam Exam - Grades 11 - 12: Pre-Calculus Info Go

Objective: Exam

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10 Function Functions and Relations: domain and range Info Go

Objective: To identify and represent functions and relations

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11 Function Function Notation Info Go

Objective: To write and evaluate functions using function notation

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12 Function Selecting Appropriate Domain and Range Info Go

Objective: To determine appropriate domains for functions

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13 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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14 Function Evaluating and Graphing Piecewise Functions Info Go

Objective: To evaluate and graph piecewise functions

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15 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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16 Function Simplifying Composite Functions Info Go

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

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17 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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18 Function Graphing Rational Functions Part 1 Info Go

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

Objective: To determine asymptotes and graph rational functions

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20 Function Parametric Equations Info Go

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

Objective: To evaluate, simplify and graph rational functions

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22 Function Parametric Functions Info Go

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

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2 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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3 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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4 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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6 Graphs part 2 Absolute Value Equations Info Go

Objective: To graph equations involving absolute values

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7 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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8 Graphs part 2 The Exponential Function Info Go

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

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9 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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31 Logarithms Powers of 2 Info Go

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

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

Objective: To solve Logrithmic Equation where the variable is the base x = 5

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34 Logarithms Laws of Logarithms Info Go

Objective: To review the logarithm laws

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35 Logarithms Using the Log Laws to Expand Logarithmic Expressions Info Go

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

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

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

Objective: To solve equations involving logarithms using the logarithm laws

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39 Logarithms Using Logarithms to Solve Equations Info Go

Objective: To use logarithms to solve exponential equations

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40 Logarithms Change of Base Formula Info Go

Objective: To evaluate log expressions using logarithms

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41 Logarithms The Graph of the Logarithmic Curve Info Go

Objective: To learn the properties of the logarithmic curve

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42 Logarithms The Graph of the Logarithmic Curve Info Go

Objective: To solve problems involving logarithmic curves

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102 Logic Mathematical induction Info Go

Objective: To use proof by mathematical induction

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70 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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71 Matrices Addition and Subtraction of Matrices Info Go

Objective: To add and subtract matrices

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72 Matrices Scalar matrix: multiplication Info Go

Objective: To multiply a matrix by a scalar

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73 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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74 Matrices Translation in the number plane Info Go

Objective: To use matrix addition to translate points

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75 Matrices Translation by matrix multiplication Info Go

Objective: To transform points and objects by matrix multiplication

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

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

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77 Matrices Vectors Info Go

Objective: To use vectors to find resultant speeds and displacements

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78 Matrices - Linear systems Number of Solutions Info Go

Objective: To determine solutions to systems of equations

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79 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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80 Matrices - Linear systems Optimal Solutions Info Go

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

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

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

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

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119 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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120 Polar coordinates Converting Rectangular Coordinates to Polar Form Info Go

Objective: To convert rectangular to polar coordinates

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121 Polar coordinates Graphing Polar Functions Info Go

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

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23 Polynomials Polynomials and Long Division Info Go

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

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24 Polynomials The Remainder Theorem Info Go

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

Objective: To determine polynomial coefficients given a divisor and remainder

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26 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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27 Polynomials More on the factor theorem Info Go

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

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

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29 Polynomials Polynomial equations Info Go

Objective: To practise solving polynomial equations

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30 Polynomials Graphs of polynomials Info Go

Objective: To derive graphs of polynomials by factorising

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113 Probability Counting techniques and ordered selections Info Go

Objective: To use counting techniques in probability

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114 Probability Unordered selections - combinations Info Go

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

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1 Self Assessment Self Assessment - Grades 11 - 12: Pre-Calculus Info Go

Objective: Assessment

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92 Series and sequences part 1 General Sequences Info Go

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

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

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

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

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

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

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

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

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

Objective: To find the first term given two terms of a geometric progression

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103 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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104 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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105 Series and sequences part 2 Sigma notation Info Go

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

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

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

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

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

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

Objective: To learn about practical situations with arithmetic series

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5 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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46 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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47 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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48 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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49 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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50 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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51 Trigonometry part 2 Reciprocal Ratios Info Go

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

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

Objective: To simplify expressions using trigonometric equalities

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54 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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55 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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56 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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57 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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58 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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59 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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60 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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61 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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62 Trigonometry part 2 Half-angle Identities Info Go

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

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63 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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