Year 13 (NCEA) Mathematics – New Zealand
Year 13 (NCEA) Mathematics
| # | TOPIC | TITLE | |
|---|---|---|---|
| 1 | Study Plan | Study plan – Year 13 | |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||
| 2 | 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. | |||
| 3 | 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. | |||
| 4 | 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. | |||
| 5 | 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. | |||
| 6 | 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. | |||
| 7 | 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. | |||
| 8 | Fractional indices/exponents | Fractional indices | |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||
| 9 | 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. | |||
| 10 | Algebraic equations | Equations involving fractions. | |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||
| 11 | 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. | |||
| 12 | 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. | |||
| 13 | 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. | |||
| 14 | Algebra-factorising | Simplifying easy algebraic fractions. | |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||
| 15 | 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. | |||
| 16 | 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. | |||
| 17 | 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. | |||
| 18 | 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. | |||
| 19 | 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. | |||
| 20 | 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. | |||
| 21 | 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. | |||
| 22 | Simultaneous equns | Simultaneous equations | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||
| 23 | Simultaneous equns | Elimination method | |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||
| 24 | Simultaneous equns | Elimination method part 2 | |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||
| 25 | Simultaneous equns | Applications of simultaneous equations | |
| Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. | |||
| 26 | 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. | |||
| 27 | 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. | |||
| 28 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation |
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| 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. | |||
| 29 | 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. | |||
| 30 | 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. | |||
| 31 | 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. | |||
| 32 | 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. | |||
| 33 | 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. | |||
| 34 | 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. | |||
| 35 | 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. | |||
| 36 | 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 | |||
| 37 | 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. | |||
| 38 | 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. | |||
| 39 | 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 | |||
| 40 | Circle Geometry | Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs. | |
| Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro | |||
| 41 | Circle Geometry | Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’ | |||
| 42 | Circle Geometry | Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal. | |
| Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre. | |||
| 43 | Circle Geometry | Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |
| Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |||
| 44 | Circle Geometry | Theorem – Angles in the same segment of a circle are equal. | |
| Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal. | |||
| 45 | Circle Geometry | Theorem – The angle of a semi-circle is a right angle. | |
| Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’ | |||
| 46 | Circle Geometry | Theorem – The opposite angles of a cyclic quadrilateral are supplementary. | |
| Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary. | |||
| 47 | Circle Geometry | Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle. | |
| Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite. | |||
| 48 | Circle Geometry | Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. | |
| Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact. | |||
| 49 | Circle Geometry | Theorem – Tangents to a circle from an external point are equal. | |
| Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal. | |||
| 50 | Circle Geometry | Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |
| Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |||
| 51 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. |
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| 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. | |||
| 52 | 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. | |||
| 53 | 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. | |||
| 54 | 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. | |||
| 55 | 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. | |||
| 56 | 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. | |||
| 57 | 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. | |||
| 58 | 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. | |||
| 59 | 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. | |||
| 60 | 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. | |||
| 61 | 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. | |||
| 62 | 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 | |||
| 63 | 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. | |||
| 64 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 65 | 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. | |||
| 66 | 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. | |||
| 67 | 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. | |||
| 68 | 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. | |||
| 69 | 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. | |||
| 70 | 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. | |||
| 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 | Logic | Inductive and deductive reasoning | |
| Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||
| 92 | Logic | Definition and use of counter examples | |
| Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||
| 93 | 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. | |||
| 94 | Logic | Mathematical induction | |
| Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series. | |||
| 95 | Quadratic equations | Completing the square | |
| Objective: On completion of the lesson the student will understand the process of completing the square. | |||
| 96 | 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. | |||
| 97 | Quadratic equations | The quadratic formula | |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||
| 98 | 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. | |||
| 99 | 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.. | |||
| 100 | 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. | |||
| 101 | 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. | |||
| 102 | Coordinate Geometry-gradient | Gradient |
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| 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. | |||
| 103 | 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. | |||
| 104 | 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. | |||
| 105 | 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. | |||
| 106 | 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. | |||
| 107 | 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. | |||
| 108 | 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. | |||
| 109 | 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. | |||
| 110 | 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. | |||
| 111 | 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. | |||
| 112 | 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. | |||
| 113 | 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. | |||
| 114 | 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. | |||
| 115 | 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. | |||
| 116 | Functions | Notation and evaluations | |
| Objective: On completion of the lesson the student will be understand different notations for functions. | |||
| 117 | 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. | |||
| 118 | 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. | |||
| 119 | Functions | Evaluating and graphing piecewise functions | |
| Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||
| 120 | Functions | Functions combinations | |
| Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||
| 121 | Functions | Composition of functions | |
| Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||
| 122 | 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. | |||
| 123 | 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. | |||
| 124 | 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. | |||
| 125 | 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. | |||
| 126 | 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. | |||
| 127 | 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. | |||
| 128 | 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. | |||
| 129 | 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. | |||
| 130 | 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. | |||
| 131 | 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. | |||
| 132 | 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. | |||
| 133 | 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. | |||
| 134 | 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. | |||
| 135 | Trig equations | Solving trigonometric equations – Type I. | |
| Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||
| 136 | 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. | |||
| 137 | 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. | |||
| 138 | 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. | |||
| 139 | 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. | |||
| 140 | 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. | |||
| 141 | Logarithms-Log laws | Laws of logarithms. | |
| Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||
| 142 | 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. | |||
| 143 | 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. | |||
| 144 | 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. | |||
| 145 | Logarithms-Equations and logs | Equations involving logarithms. | |
| Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||
| 146 | 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. | |||
| 147 | 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. | |||
| 148 | 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. | |||
| 149 | 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. | |||
| 150 | 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. | |||
| 151 | 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 | |||
| 152 | 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. | |||
| 153 | 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. | |||
| 154 | 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. | |||
| 155 | 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. | |||
| 156 | 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. | |||
| 157 | Calculus | Limits | |
| Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||
| 158 | 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. | |||
| 159 | 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. | |||
| 160 | 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. | |||
| 161 | 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. | |||
| 162 | 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. | |||
| 163 | 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. | |||
| 164 | 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. | |||
| 165 | 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. | |||
| 166 | 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). | |||
| 167 | 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. | |||
| 168 | 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. | |||
| 169 | 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. | |||
| 170 | 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. | |||
| 171 | Sequences and Series-Superannuation | Superannuation. |
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| 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. | |||
| 172 | 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. | |||
| 173 | 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. | |||
| 174 | 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. | |||
| 175 | 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. | |||
| 176 | 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. | |||
| 177 | 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. | |||
| 178 | 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. | |||
| 179 | 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. | |||
| 180 | 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. | |||
| 181 | 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. | |||
| 182 | Conic sections | Circles |
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| Objective: On completion of the lesson the student will identify the radius of a circle given in standard form. | |||
| 183 | Conic sections | Ellipses |
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| Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse. | |||
| 184 | Conic sections | Hyperbola |
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| Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola. | |||
| 185 | 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. | |||
| 186 | 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. | |||
| 187 | 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. | |||
| 188 | 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. | |||
| 189 | 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. | |||
| 190 | Algebra-polynomials | Polynomials and long division. | |
| Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||
| 191 | 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. | |||
| 192 | 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. | |||
| 193 | 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. | |||
| 194 | 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. | |||
| 195 | 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. | |||
| 196 | Polynomial equations | Polynomial equations | |
| Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||
| 197 | 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. | |||
| 198 | 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. | |||
| 199 | 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. | |||
| 200 | 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. | |||
| 201 | 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. | |||
| 202 | 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. | |||
| 203 | 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 | |||
| 204 | 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. | |||
| 205 | 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. | |||
| 206 | Polar coordinates | Plotting polar coordinates and converting polar to rectangular | |
| Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system. | |||
| 207 | Polar coordinates | Converting rectangular coordinates to polar form | |
| Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates. | |||
| 208 | Polar coordinates | Write and graph points in polar form with negative vectors (Stage 2) | |
| Objective: On completion of the lesson the student will be using negative angles and negative vector lengths. | |||
| 209 | 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. | |||
| 210 | Trigonometry | Double angle formulas (Stage 2) | |
| Objective: On completion of the lesson the student will derive and use the double angle trig identities. | |||
| 211 | 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. | |||
| 212 | Trigonometry | t Formulas (Stage 2) | |
| Objective: On completion of the lesson the student will solve trig equations using the t substitution. | |||
| 213 | 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. | |||
| 214 | 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. | |||
| 215 | 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. | |||
| 216 | Logarithms-Complex numbers | Absolute value | |
| Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers | |||
| 217 | 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. | |||
| 218 | 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. | |||
| 219 | 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. | |||
| 220 | 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. | |||
| 221 | 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. | |||
| 222 | Exam | Exam – Year 13 | |
| Objective: Exam | |||
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