| 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 |
Coordinate Geometry-the plane |
Distance formula. |
| Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. |
| 3 |
Coordinate Geometry-midpoint, slope |
Mid-point formula |
| Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. |
| 4 |
Coordinate Geometry-gradient |
Gradient |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. |
| 5 |
Coordinate Geometry-gradient |
Gradient formula. |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. |
| 6 |
Coordinate Geometry-straight line |
The straight line. |
| Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. |
| 7 |
Coordinate Geometry-slope, etc. |
Lines through the origin. |
| Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. |
| 8 |
Coordinate Geometry-equation of line |
General form of a line and the x and y Intercepts. |
| Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. |
| 9 |
Coordinate Geometry-intercept |
Slope intercept form of a line. |
| Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. |
| 10 |
Coordinate Geometry-point slope |
Point slope form of a line |
| Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. |
| 11 |
Co-ordinate Geometry-Two point formula |
Two point formula: equation of a line which joins a pair of points. |
| Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line. |
| 12 |
Co-ordinate Geometry-Intercept form |
Intercept form of a straight line: find the equation when given x and y |
| Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. |
| 13 |
Co-ordinate Geometry-Parallel lines equations |
Parallel lines: identify equation of a line parallel to another |
| Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines. |
| 14 |
Co-ordinate Geometry-Perpendicular lines |
Perpendicular lines. |
| Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line. |
| 15 |
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. |
| 16 |
Functions |
Notation and evaluations |
| Objective: On completion of the lesson the student will be understand different notations for functions. |
| 17 |
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. |
| 18 |
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. |
| 19 |
Functions |
Evaluating and graphing piecewise functions |
| Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. |
| 20 |
Functions |
Functions combinations |
| Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. |
| 21 |
Functions |
Composition of functions |
| Objective: On completion of the lesson the student will understand composition of functions or a function of a function. |
| 22 |
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. |
| 23 |
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. |
| 24 |
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. |
| 25 |
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. |
| 26 |
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. |
| 27 |
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. |
| 28 |
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. |
| 29 |
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. |
| 30 |
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. |
| 31 |
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. |
| 32 |
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. |
| 33 |
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. |
| 34 |
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. |
| 35 |
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. |
| 36 |
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. |
| 37 |
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. |
| 38 |
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 |
| 39 |
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. |
| 40 |
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. |
| 41 |
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 |
| 42 |
Algebraic expressions |
Algebraic expressions. |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. |
| 43 |
Algebraic expressions |
Substitution into algebraic expressions. |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. |
| 44 |
Algebraic expressions |
Directed numbers: addition and subtraction. |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. |
| 45 |
Algebraic expressions |
Directed numbers: multiplication and division. |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. |
| 46 |
Algebraic expressions |
Simplifying algebraic expressions: adding like terms. |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. |
| 47 |
Algebraic expressions |
Simplifying algebraic Expressions: subtracting like terms. |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. |
| 48 |
Algebraic expressions |
Simplifying Algebraic expressions: combining addition and subtraction. |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. |
| 49 |
Algebraic expressions |
Simplifying algebraic expressions: multiplication |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. |
| 50 |
Algebraic expressions |
Simplifying algebraic expressions: division |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. |
| 51 |
Algebraic expressions |
Expanding algebraic expressions: multiplication |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. |
| 52 |
Algebraic expressions |
Expanding algebraic expressions: negative multiplier |
| Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. |
| 53 |
Algebraic expressions |
Expanding and simplifying algebraic expressions |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. |
| 54 |
Algebraic equations |
Solving equations containing addition and subtraction |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. |
| 55 |
Algebraic equations |
Solving equations containing multiplication and division |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. |
| 56 |
Algebraic equations |
Solving two step equations |
| Objective: On completion of the lesson the student will be able to solve two step equations. |
| 57 |
Algebraic equations |
Solving equations containing binomial expressions |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
| 58 |
Algebraic equations |
Equations involving grouping symbols. |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
| 59 |
Algebraic equations |
Equations involving fractions. |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. |
| 60 |
Algebra- formulae |
Equations resulting from substitution into formulae. |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. |
| 61 |
Algebra- formulae |
Changing the subject of the formula. |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. |
| 62 |
Algebra-inequalities |
Solving Inequalities. |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. |
| 63 |
Algebra-factorising |
Simplifying easy algebraic fractions. |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. |
| 64 |
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. |
| 65 |
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. |
| 66 |
Factorisation |
Factorisation of algebraic fractions including binomials. |
| Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods. |
| 67 |
Algebraic fractions-binomial |
Cancelling binomial factors in algebraic fractions. |
| Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. |
| 68 |
Absolute value or modulus |
Simplifying absolute values |
| Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers. |
| 69 |
Absolute value or modulus |
Solving for the variable |
| Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. |
| 70 |
Absolute value or modulus |
Solving and graphing inequalities |
| Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. |
| 71 |
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. |
| 72 |
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. |
| 73 |
Graphing binomials |
Binomial products [non-monic]. |
| Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. |
| 74 |
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. |
| 75 |
Squaring binomial |
Squaring a binomial [non-monic]. |
| Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. |
| 76 |
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. |
| 77 |
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. |
| 78 |
Algebraic expressions-larger expansions |
Algebraic Expressions – Larger expansions. |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. |
| 79 |
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. |
| 80 |
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. |
| 81 |
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. |
| 82 |
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. |
| 83 |
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. |
| 84 |
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. |
| 85 |
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. |
| 86 |
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. |
| 87 |
Factorising quads |
Factorisation of non-monic quadratic trinomials |
| Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. |
| 88 |
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. |
| 89 |
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. |
| 90 |
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. |
| 91 |
Quadratic equations |
Introduction to quadratic equations. |
| Objective: On completion of the lesson the student will understand simple quadratic equations. |
| 92 |
Quadratic equations |
Quadratic equations with factorisation. |
| Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. |
| 93 |
Quadratic equations |
Solving quadratic equations. |
| Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. |
| 94 |
Quadratic equations |
Completing the square |
| Objective: On completion of the lesson the student will understand the process of completing the square. |
| 95 |
Quadratic equations |
Solving quadratic equations by completing the square |
| Objective: On completion of the lesson the student will understand the reasoning behind completing the square. |
| 96 |
Quadratic equations |
The quadratic formula |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula. |
| 97 |
Quadratic equations |
Problem solving with quadratic equations |
| Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. |
| 98 |
Quadratic equations |
Solving simultaneous quadratic equations graphically |
| Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. |
| 99 |
Co-ordinate Geometry-Inequalities |
Inequalities on the number plane. |
| Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities. |
| 100 |
Co-ordinate Geometry-Theorems |
Perpendicular distance |
| Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines. |
| 101 |
Co-ordinate Geometry-Theorems |
Line through intersection of two given lines |
| Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition. |
| 102 |
Co-ordinate Geometry-Theorems |
Angles between two lines |
| Objective: On completion of the lesson the student will be able to calculate the angle between given lines and derive the equation of a line given its angle to another line. |
| 103 |
Co-ordinate Geometry-Theorems |
Internal and external division of an interval |
| Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions. |
| 104 |
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. |
| 105 |
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. |
| 106 |
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. |
| 107 |
Algebra-polynomials |
Polynomials and long division. |
| Objective: On completion of the lesson the student will understand the long division process with polynomials. |
| 108 |
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. |
| 109 |
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. |
| 110 |
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. |
| 111 |
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. |
| 112 |
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. |
| 113 |
Polynomial equations |
Polynomial equations |
| Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. |
| 114 |
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. |
| 115 |
Roots quad equations |
Sum and product of roots of quadratic equations |
| Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots. |
| 116 |
Roots quad equations |
Sum and product of roots of cubic and quartic equations |
| Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations. |
| 117 |
Approx roots |
Methods of approximating roots |
| Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question. |
| 118 |
Newton’s approx |
Newton’s method of approximation |
| Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method. |
| 119 |
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. |
| 120 |
Rules for indices/exponents |
Subtracting indices when dividing terms with the same base |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. |
| 121 |
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. |
| 122 |
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. |
| 123 |
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. |
| 124 |
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. |
| 125 |
Fractional indices/exponents |
Fractional indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. |
| 126 |
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. |
| 127 |
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. |
| 128 |
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. |
| 129 |
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. |
| 130 |
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. |
| 131 |
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. |
| 132 |
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. |
| 133 |
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. |
| 134 |
Logarithms-Log laws |
Laws of logarithms. |
| Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. |
| 135 |
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. |
| 136 |
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. |
| 137 |
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. |
| 138 |
Logarithms-Equations and logs |
Equations involving logarithms. |
| Objective: On completion of the lesson the student will be able to solve equations with log terms. |
| 139 |
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. |
| 140 |
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. |
| 141 |
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. |
| 142 |
Logarithms-Log curves |
Working with log curves. |
| Objective: On completion of the lesson the student will be able to solve problems with log curves |
| 143 |
Time, distance, speed |
Average speed |
| Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object. |
| 144 |
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. |
| 145 |
Geometric transformations |
Geometry transformations without matrices: translation (Stage 2) |
| Objective: On completion of this lesson the student will perform translations in a number plane. |
| 146 |
Geometric transformations |
Geometry transformations without matrices: rotation (Stage 2) |
| Objective: On completion of this lesson the student will perform and construct rotations. |
| 147 |
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. |
| 148 |
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. |
| 149 |
Calculus |
Limits |
| Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. |
| 150 |
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. |
| 151 |
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. |
| 152 |
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. |
| 153 |
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. |
| 154 |
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. |
| 155 |
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. |
| 156 |
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. |
| 157 |
Statistic-probability |
Probability of Simple Events |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. |
| 158 |
Statistic-probability |
Rolling a pair of dice |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. |
| 159 |
Statistic-probability |
Experimental probability |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. |
| 160 |
Statistic-probability |
Tree diagrams – not depending on previous outcomes |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. |
| 161 |
Statistic-probability |
Tree diagrams – depending on previous outcomes |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. |
| 162 |
Statistic-probability |
The complementary result .. |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved. |
| 163 |
Statistic-probability |
P[A or B] When A and B are both mutually and NOT mutually exclusive |
| Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both. |
| 164 |
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. |
| 165 |
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 |
| 166 |
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. |
| 167 |
Statistic-probability |
Unordered selections – combinations |
| Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen. |
| 168 |
Exam |
Exam – Year 11 – Mathematical Methods Units 1 |
| Objective: Exam |
