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QLD Year 11 B and C Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Year 11
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Graphing binomials Binomial products.
Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression.
3 Graphing binomials Binomial products with negative multiplier
Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.
4 Graphing binomials Binomial products [non-monic].
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.
5 Squaring binomial Squaring a binomial. [monic]
Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial.
6 Algebra – Products and factors Squaring a Binomial (nonmonic)
Objective: To expand the square of a nonmonic binomial by inspection
7 Factorising Expansions leading to the difference of two squares
Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares.
8 Algebraic expressions-products Products in simplification of algebraic expressions
Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing.
9 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
10 Algebra-highest common factor Highest common factor.
Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.
11 Geometry-circles The equation of a circle: to find radii of circles
Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.
12 Geometry-circles The semicircle: to select the equation given the semi circle and vice versa
Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.
13 Geometry-parabola The parabola: to describe properties of a parabola from its equation
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.
14 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c.
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.
15 Functions and graphs Graphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
16 Graphing roots Graphing irrational roots
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.
17 Coordinate geometry Solve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
18 Factors by grouping Factors by grouping.
Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.
19 Difference of 2 squares Difference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
20 Common fact and diff Common factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
21 Quadratic trinomials Quadratic trinomials [monic] – Case 1.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
22 Factorising quads Factorising quadratic trinomials [monic] – Case 2.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
23 Factorising quads Factorising quadratic trinomials [monic] – Case 3.
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.
24 Factorising quads Factorising quadratic trinomials [monic] – Case 4.
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.
25 Factorising quads Factorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
26 Factorising quads Factorisation of non-monic quadratic trinomials – moon method
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
27 Sum/diff 2 cubes Sum and difference of two cubes.
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.
28 Algebraic fractions Simplifying algebraic fractions.
Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.
29 Graphing-polynomials Graphing complex polynomials: quadratics with no real roots
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.
30 Graphing-polynomials General equation of a circle: determine and graph the equation
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.
31 Graphing-cubic curves Graphing cubic curves
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.
32 Absolute value equations Absolute value equations
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
33 Rect.hyperbola The rectangular hyperbola.
Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.
34 Exponential function The exponential function.
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.
35 Uniform motion Average speed
Objective: On completion of the lesson the student will be able to convert units for speed, distance and time.
36 Uniform motion Using subscripted variables
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time.
37 Uniform motion Uniform motion with equal distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time.
38 Uniform motion Uniform motion adding the distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, adding distances for total distance and time.
39 Uniform motion Uniform Motion With Unequal Distances or Time
Objective: To solve motion problems where either distance or time are different
40 Uniform motion Uniform motion of all types
Objective: On completion of the lesson the student will use all types of subscripted variables for calculations to determine speed, distance and time.
41 Motion under acceleration Motion under gravity – objects in vertical motion
Objective: On completion of the lesson the student will convert rates and use equations of motion that include uniform acceleration.
42 Motion under acceleration Introducing initial velocity
Objective: On completion of the lesson the student will use equations of motion that include uniform acceleration and an initial velocity.
43 Log functions Logarithmic functions.
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
44 Functions Definition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
45 Functions Notation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
46 Functions More on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
47 Functions Domain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
48 Functions Evaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
49 Functions Functions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
50 Functions Composition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
51 Functions Inverse functions
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.
52 Algebra-polynomials Introduction to polynomials
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.
53 Algebra-polynomials The sum, difference and product of two polynomials.
Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.
54 Algebra-polynomials Polynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.
55 Remainder theorem The remainder theorem.
Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied.
56 Remainder theorem More on remainder theorem
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.
57 Factor theorem The factor theorem
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.
58 Factor theorem More on the factor theorem
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.
59 Factor theorem Complete factorisations using the factor theorem
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.
60 Polynomial equations Polynomial equations
Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.
61 Graphs, polynomials Graphs of polynomials
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.
62 Calculus Limits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.
63 Calculus=1st prin Differentiation from first principles.
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.
64 Calculus=1st prin Differentiation of y = x to the power of n.
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.
65 Calculus-differential, integ Meaning of dy over dx – equations of tangents and normals.
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.
66 Calculus-differential, integ Function of a function rule, product rule, quotient rule.
Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.
67 Calculus-differential, integ Increasing, decreasing and stationary functions.
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.
68 Calculus First Derivative – turning points and curve sketching
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.
69 Calculus-2nd derivative The second derivative – concavity.
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.
70 Calculus – Curve sketching Curve sketching
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.
71 Calculus – Maxima minima Practical applications of maxima and minima
Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.
72 Trigonometry-elevation Angles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.
73 Trigonometry-practical Trigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
74 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
75 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.
76 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
77 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
78 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
79 Trigonometry-sine rule The sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
80 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
81 Trigonometry-areas The area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
82 Trig-reciprocal ratios Reciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
83 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
84 Trig identities Trigonometric identities
Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.
85 Trig larger angles Angles of any magnitude
Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.
86 Trig larger angles Trigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.
87 Graph sine Graphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.
88 Graph cosine Graphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.
89 Graphs tan curve Graphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.
90 Graph reciprocals Graphing the trigonometric ratios – IV Reciprocal ratios.
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.
91 Trig larger angles Using one ratio to find another.
Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.
92 Trig equations Solving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
93 Trig equations Solving trigonometric equations – Type II.
Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains.
94 Trig equations Solving trigonometric equations – Type III.
Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains.
95 Rules for indices/exponents Terms raised to the power of zero
Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.
96 Rules for indices/exponents Negative Indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.
97 Fractional indices/exponents Fractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
98 Fractional indices/exponents Complex fractions as indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.
99 Scientific notation Scientific notation with larger numbers
Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation.
100 Scientific notation Scientific notation with small numbers
Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.
101 Standard/Scientific notation Changing scientific notation to numerals
Objective: To interpret scientific notation by writing in base 10 numerals
102 Significant figures Significant figures
Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.
103 Algebraic fractions Simplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
104 Algebra-negative indices Algebraic fractions resulting in negative indices.
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.
105 Logarithms-Power of 2 Powers of 2.
Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.
106 Logarithms-Equations and logs Equations of type log x to the base 3 = 4.
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.
107 Logarithms-Equations and logs Equations of type log 32 to the base x = 5.
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.
108 Logarithms-Log laws Laws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.
109 Logarithms-Log laws expansion Using the log laws to expand logarithmic expressions.
Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.
110 Logarithms-Log laws simplifying Using the log laws to simplify expressions involving logarithms.
Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.
111 Logarithms-Log laws numbers Using the log laws to find the logarithms of numbers.
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.
112 Logarithms-Equations and logs Equations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.
113 Logarithms-Logs to solve equations Using logarithms to solve equations.
Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.
114 Logarithms-Change base formula Change of base formula
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.
115 Logarithms-Graph-log curve The graph of the logarithmic curve
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.
116 Logarithms-Log curves Working with log curves.
Objective: On completion of the lesson the student will be able to solve problems with log curves
117 Sequences and Series General sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.
118 Sequences and Series Finding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.
119 Arithmetic Progression The arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
120 Arithmetic Progression Finding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.
121 Arithmetic Progression Given two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms
122 Arithmetic Progression Arithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
123 Arithmetic Progression The sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.
124 Geometric Progression The geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
125 Geometric Progression Finding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.
126 Geometric Progression Given two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
127 Sequences and Series-Geometric means Geometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.
128 Sequences and Series-Sum of gp The sum to n terms of a G.P.
Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).
129 Sequences and Series-Sigma notation Sigma notation
Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.
130 Sequences and Series-Sum-infinity Limiting sum or sum to infinity.
Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.
131 Sequences and Series-Recurring decimal infinity Recurring decimals and the infinite G.P.
Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.
132 Sequences and Series-Compound interest Compound interest
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.
133 Sequences and Series-Superannuation Superannuation.
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.
134 Sequences and Series-Time payments Time payments.
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.
135 Sequences and Series Applications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
136 Calculus – Integration Integration – anti-differentiation, primitive function
Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.
137 Calculus – Computation area Computation of an area
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.
138 Calculus – Computation volumes Computation of volumes of revolution
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.
139 Calculus – Trapezoidal and Simpson’s rules The Trapezium rule and Simpson’s rule
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.
140 Statistics – Spread Measures of spread
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.
141 Statistics – Standard deviation Standard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.
142 Statistics – Standard deviation Normal distribution
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.
143 Statistics – Interquartile range Measures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range
144 Statistics Stem and Leaf Plots along with Box and Whisker Plots
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.
145 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
146 Statistic-probability Binomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.
147 Statistic-probability Binomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem
148 Statistic-probability Counting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.
149 Probability Unordered selections – combinations
Objective: To use the nCr formula to solve problems where unordered selections occur
150 Number theory – sets Number sets and their members
Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.
151 Number theory – operations Properties of real numbers using addition and multiplication
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.
152 Number theory – equations Transformations that produce equivalent equations
Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.
153 Logic Inductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
154 Logic Definition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
155 Logic Indirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
156 Logic Mathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
157 Logic Conditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
158 Translations Transformations – reflections
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.
159 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
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.
160 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
161 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
162 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
163 Geometric transformations The definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.
164 Logarithms-Complex numbers Imaginary numbers and standard form
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.
165 Logarithms-Complex numbers Complex numbers – multiplication and division
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.
166 Logarithms-Complex numbers Plotting complex number and graphical representation
Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.
167 Logarithms-Complex numbers Absolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers
168 Logarithms-Complex numbers Trigonometric form of a complex number
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.
169 Logarithms-Complex numbers Multiplication and division of complex numbers in trig form (Stage 2)
Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.
170 Logarithms-Complex numbers DeMoivre’s theorem (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.
171 Logarithms-Complex numbers The nth root of real and complex numbers (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.
172 Logarithms-Complex numbers Fundamental theorem of algebra (Stage 2)
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.
173 Matrices Basic concepts – Matrices
Objective: On completion of the lesson the student will have had an introduction to matrices
174 Matrices Addition and subtraction of matrices
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.
175 Matrices Scalar matrix multiplication
Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.
176 Matrices Multiplication of one matrix by another matrix
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.
177 Matrices Translation in the number plane
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.
178 Matrices Translation by matrix multiplication
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.
179 Transformations Special transformations – reflections, rotations and enlargements.
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.
180 Vectors Vectors
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.
181 Simultaneous equations Number of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
182 Vectors 2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
183 Linear systems Optimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
184 Linear systems Linear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
185 Linear systems Row-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
186 Linear systems Gauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.
187 Conic sections Introduction to conic sections and their general equation
Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation.
188 Conic sections The parabola x. = 4ay
Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.
189 Conic sections Circles
Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.
190 Conic sections Ellipses
Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.
191 Conic sections Hyperbola
Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.
192 Trigonometry Sin(A+B) etc sum and difference identities (Stage 2)
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.
193 Trigonometry Double angle formulas (Stage 2)
Objective: On completion of the lesson the student will derive and use the double angle trig identities.
194 Trigonometry Half angle identities (Stage 2)
Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities.
195 Trigonometry t Formulas (Stage 2)
Objective: On completion of the lesson the student will solve trig equations using the t substitution.
196 Exam Exam – Year 11 – Maths B & C
Objective: Exam