# Queensland Curriculum

## Maths Year 12 B and C

Is your child struggling to finish their Year 12 B and C Maths homework?
Are they completely confident with Maths and keeping up in class?

Don’t worry – at some point almost every parent has been in the same position.

The Future School program is here to help you. Based on the Australian education curriculum, you can be reassured that you are providing the most relevant of assistance to your child, ensuring there will be no confusion.

Future School can remove much of the frustration a child feels when dealing with their Maths homework.

The services we offer range from personalised study plans, video tutorials supported by extensive worksheets and access to a tutor when required.

Benefits of the Future School program:

• Access to over 2000 lessons, catering for students at all levels
• Dynamic diagnostic tool that determines and targets weakness
• Detailed student monitoring and reporting
• Assessment exams at the end of the course
• Flexibility to work online at any time that’s convenient for you

#### Example of Study Topics:

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# TOPIC TITLE +/-
1 Study Plan Study plan - Year 12 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 Geometry-parabola The parabola: to describe properties of a parabola from its equation Info Go

Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.

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3 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c. Info Go

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.

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4 Functions and graphs Graphing perfect squares: y=(a-x) squared Info Go

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.

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5 Graphing roots Graphing irrational roots Info Go

Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.

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6 Factors by grouping Factors by grouping. Info Go

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.

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7 Difference of 2 squares Difference of two squares Info Go

Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.

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8 Common fact and diff Common factor and the difference of two squares Info Go

Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.

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Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.

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10 Factorising quads Factorising quadratic trinomials [monic] - Case 2. Info Go

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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11 Factorising quads Factorising quadratic trinomials [monic] - Case 3. Info Go

Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.

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12 Factorising quads Factorising quadratic trinomials [monic] - Case 4. Info Go

Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.

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Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.

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14 Factorising quads Factorisation of non-monic quadratic trinomials - moon method Info Go

Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.

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15 Sum/diff 2 cubes Sum and difference of two cubes. Info Go

Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.

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16 Algebraic fractions Simplifying algebraic fractions. Info Go

Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.

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17 Graphing-polynomials Graphing complex polynomials: quadratics with no real roots Info Go

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.

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18 Graphing-polynomials General equation of a circle: determine and graph the equation Info Go

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student's skills in logic and reasoning.

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19 Graphing-cubic curves Graphing cubic curves Info Go

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.

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20 Absolute value equations Absolute value equations Info Go

Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio

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21 Rect.hyperbola The rectangular hyperbola. Info Go

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.

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22 Exponential function The exponential function. Info Go

Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.

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23 Log functions Logarithmic functions. Info Go

Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit

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24 Functions Definition, domain and range Info Go

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.

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25 Functions Notation and evaluations Info Go

Objective: On completion of the lesson the student will be understand different notations for functions.

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26 Functions More on domain and range Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.

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27 Functions Domain and range from graphical representations Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.

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28 Functions Evaluating and graphing piecewise functions Info Go

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.

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29 Functions Functions combinations Info Go

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.

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30 Functions Composition of functions Info Go

Objective: On completion of the lesson the student will understand composition of functions or a function of a function.

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31 Functions Inverse functions Info Go

Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.

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32 Functions Rational functions Part 1 Info Go

Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.

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33 Functions Rational functions Part 2 Info Go

Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.

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34 Functions Parametric equations (Stage 2) Info Go

Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range.

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35 Functions Polynomial addition etc in combining and simplifying functions (Stage 2) Info Go

Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.

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36 Functions Parametric functions (Stage 2) Info Go

Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.

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37 Algebra-polynomials Introduction to polynomials Info Go

Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.

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38 Algebra-polynomials The sum, difference and product of two polynomials. Info Go

Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.

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39 Algebra-polynomials Polynomials and long division. Info Go

Objective: On completion of the lesson the student will understand the long division process with polynomials.

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40 Remainder theorem The remainder theorem. Info Go

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied.

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41 Remainder theorem More on remainder theorem Info Go

Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials.

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42 Factor theorem The factor theorem Info Go

Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial.

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43 Factor theorem More on the factor theorem Info Go

Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials.

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44 Factor theorem Complete factorisations using the factor theorem Info Go

Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros.

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45 Polynomial equations Polynomial equations Info Go

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.

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46 Graphs, polynomials Graphs of polynomials Info Go

Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.

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47 Calculus Limits Info Go

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.

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48 Calculus=1st prin Differentiation from first principles. Info Go

Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve.

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49 Calculus=1st prin Differentiation of y = x to the power of n. Info Go

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.

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50 Calculus-differential, integ Meaning of dy over dx - equations of tangents and normals. Info Go

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.

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51 Calculus-differential, integ Function of a function rule, product rule, quotient rule. Info Go

Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.

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52 Calculus-differential, integ Increasing, decreasing and stationary functions. Info Go

Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.

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53 Calculus First Derivative - turning points and curve sketching Info Go

Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.

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54 Calculus-2nd derivative The second derivative - concavity. Info Go

Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.

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55 Calculus - Curve sketching Curve sketching Info Go

Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.

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56 Calculus - Maxima minima Practical applications of maxima and minima Info Go

Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.

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57 Logarithms-Power of 2 Powers of 2. Info Go

Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.

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58 Logarithms-Equations and logs Equations of type log x to the base 3 = 4. Info Go

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.

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59 Logarithms-Equations and logs Equations of type log 32 to the base x = 5. Info Go

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.

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60 Logarithms-Log laws Laws of logarithms. Info Go

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.

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61 Logarithms-Log laws expansion Using the log laws to expand logarithmic expressions. Info Go

Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.

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62 Logarithms-Log laws simplifying Using the log laws to simplify expressions involving logarithms. Info Go

Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.

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63 Logarithms-Log laws numbers Using the log laws to find the logarithms of numbers. Info Go

Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.

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64 Logarithms-Equations and logs Equations involving logarithms. Info Go

Objective: On completion of the lesson the student will be able to solve equations with log terms.

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65 Logarithms-Logs to solve equations Using logarithms to solve equations. Info Go

Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.

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66 Logarithms-Change base formula Change of base formula Info Go

Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.

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67 Logarithms-Graph-log curve The graph of the logarithmic curve Info Go

Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves.

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68 Logarithms-Log curves Working with log curves. Info Go

Objective: On completion of the lesson the student will be able to solve problems with log curves

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69 Sequences and Series-Recurring decimal infinity Recurring decimals and the infinite G.P. Info Go

Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.

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70 Sequences and Series-Compound interest Compound interest Info Go

Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.

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71 Sequences and Series-Superannuation Superannuation. Info Go

Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.

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72 Sequences and Series-Time payments Time payments. Info Go

Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.

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73 Sequences and Series Applications of arithmetic sequences Info Go

Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.

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74 Calculus - Integration Integration - anti-differentiation, primitive function Info Go

Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.

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75 Calculus - Computation area Computation of an area Info Go

Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.

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76 Calculus - Computation volumes Computation of volumes of revolution Info Go

Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.

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77 Calculus - Trapezoidal and Simpson's rules The Trapezium rule and Simpson's rule Info Go

Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson's Rule to approximate an area beneath a curve.

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Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.

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79 Statistics - Standard deviation Standard deviation applications Info Go

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.

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80 Statistics - Standard deviation Normal distribution Info Go

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.

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81 Statistics - Interquartile range Measures of spread: the interquartile range Info Go

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range

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82 Statistics Stem and Leaf Plots along with Box and Whisker Plots Info Go

Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.

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83 Statistics Scatter Diagrams Info Go

Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.

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84 Number theory - sets Number sets and their members Info Go

Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.

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85 Number theory - operations Properties of real numbers using addition and multiplication Info Go

Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication.

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86 Number theory - equations Transformations that produce equivalent equations Info Go

Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.

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87 Logic Inductive and deductive reasoning Info Go

Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.

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88 Logic Definition and use of counter examples Info Go

Objective: On completion of this lesson the student will be able to create counter examples to statements.

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89 Logic Indirect proofs Info Go

Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.

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90 Logic Mathematical induction Info Go

Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.

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91 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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92 Translations Transformations - reflections Info Go

Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.

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93 Geometric transformations Geometry transformations without matrices: reflection (Stage 2) Info Go

Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.

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94 Geometric transformations Geometry transformations without matrices: translation (Stage 2) Info Go

Objective: On completion of this lesson the student will perform translations in a number plane.

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95 Geometric transformations Geometry transformations without matrices: rotation (Stage 2) Info Go

Objective: On completion of this lesson the student will perform and construct rotations.

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96 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2) Info Go

Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.

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97 Geometric transformations The definition and concept of combined transformations resulting in an equivalent single transformation. Info Go

Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.

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98 Logarithms-Complex numbers Imaginary numbers and standard form Info Go

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.

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99 Logarithms-Complex numbers Complex numbers - multiplication and division Info Go

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.

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100 Logarithms-Complex numbers Plotting complex number and graphical representation Info Go

Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.

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101 Logarithms-Complex numbers Absolute value Info Go

Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers

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102 Logarithms-Complex numbers Trigonometric form of a complex number Info Go

Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.

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103 Logarithms-Complex numbers Multiplication and division of complex numbers in trig form (Stage 2) Info Go

Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.

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104 Logarithms-Complex numbers DeMoivre's theorem (Stage 2) Info Go

Objective: On completion of the lesson the student will use DeMoivre's theorem to find powers of complex numbers in trig form.

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105 Logarithms-Complex numbers The nth root of real and complex numbers (Stage 2) Info Go

Objective: On completion of the lesson the student will use DeMoivre's theorem to find roots of complex numbers in trig form.

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106 Logarithms-Complex numbers Fundamental theorem of algebra (Stage 2) Info Go

Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.

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107 Matrices Basic concepts - Matrices Info Go

Objective: On completion of the lesson the student will have had an introduction to matrices

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108 Matrices Addition and subtraction of matrices Info Go

Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations.

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109 Matrices Scalar matrix multiplication Info Go

Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.

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110 Matrices Multiplication of one matrix by another matrix Info Go

Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.

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111 Matrices Translation in the number plane Info Go

Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.

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112 Matrices Translation by matrix multiplication Info Go

Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.

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113 Transformations Special transformations - reflections, rotations and enlargements. Info Go

Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.

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114 Vectors Vectors Info Go

Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.

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115 Simultaneous equations Number of solutions (Stage 2) Info Go

Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.

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116 Vectors 2 vector addition in 2 and 3D (stage 2) Info Go

Objective: On completion of the lesson the student will understand and use component forms for vector resolution.

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117 Linear systems Optimal solutions (Stage 2) - Vectors Info Go

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.

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118 Linear systems Linear systems with matrices (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.

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119 Linear systems Row-echelon form (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.

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120 Linear systems Gauss Jordan elimination method (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.

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121 Conic sections Introduction to conic sections and their general equation Info Go

Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation.

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122 Conic sections The parabola x. = 4ay Info Go

Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.

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123 Conic sections Circles Info Go

Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.

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124 Conic sections Ellipses Info Go

Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.

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125 Conic sections Hyperbola Info Go

Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.

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126 Trigonometry Sin(A+B) etc sum and difference identities (Stage 2) Info Go

Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios.

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127 Trigonometry Double angle formulas (Stage 2) Info Go

Objective: On completion of the lesson the student will derive and use the double angle trig identities.

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128 Trigonometry Half angle identities (Stage 2) Info Go

Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities.

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129 Trigonometry t Formulas (Stage 2) Info Go

Objective: On completion of the lesson the student will solve trig equations using the t substitution.

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130 Exam Exam - Year 12 - Maths B & C Info Go

Objective: Exam

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