### QLD Year 11 B 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.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
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.
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.
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
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 Uniform motion Average speed
Objective: On completion of the lesson the student will be able to convert units for speed, distance and time.
33 Uniform motion Using subscripted variables
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time.
34 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.
35 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.
36 Uniform motion Uniform Motion With Unequal Distances or Time
Objective: To solve motion problems where either distance or time are different
37 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.
38 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.
39 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.
40 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
41 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.
42 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.
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 Functions Rational functions Part 1
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.
53 Functions Rational functions Part 2
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.
54 Functions Parametric equations (Stage 2)
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.
55 Functions Polynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.
56 Functions Parametric functions (Stage 2)
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.
57 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.
58 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.
59 Algebra-polynomials Polynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.
60 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.
61 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.
62 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.
63 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.
64 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.
65 Polynomial equations Polynomial equations
Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.
66 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.
67 Calculus Limits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.
68 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.
69 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.
70 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.
71 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.
72 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.
73 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.
74 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.
75 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.
76 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.
77 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.
78 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.
79 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.
80 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.
81 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.
82 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.
83 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.
84 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.
85 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.
86 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.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 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.
95 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.
96 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.
97 Trig equations Solving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
98 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.
99 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.
100 Rules for indices/exponents Adding indices when multiplying terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.
101 Indices/Exponents Subtracting indices when dividing terms with the same base
Objective: To subtract indices when dividing powers of the same base
102 Rules for indices/exponents Multiplying indices when raising a power to a power
Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.
103 Rules for indices/exponents Multiplying indices when raising to more than one term
Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.
104 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.
105 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.
106 Indices/Exponents Fractional Indices
Objective: To evaluate or simplify expressions containing fractional indices
107 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.
108 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.
109 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.
110 Scientific notation Changing scientific notation to numerals
Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.
111 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.
112 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.
113 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.
114 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.
115 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.
116 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.
117 Logarithms-Log laws Laws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.
118 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.
119 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.
120 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.
121 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.
122 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.
123 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.
124 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.
125 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).
126 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.
127 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.
128 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.
129 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.
130 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.
131 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.
132 Statistics Frequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
133 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
134 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
135 Statistics The range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
136 Statistic-probability The mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
137 Statistic-probability The mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
138 Statistic-probability The median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
139 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
140 Statistic-probability Calculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.
141 Statistics – grouped data Calculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
142 Statistics using a calculator Statistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
143 Statistics – Range and dispersion Range as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.
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.
145 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.
146 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.
147 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
148 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.
149 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
150 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.
151 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
152 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.
153 Probability Unordered selections – combinations
Objective: To use the nCr formula to solve problems where unordered selections occur
154 Exam Exam – Year 11 – Maths B
Objective: Exam