| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grade 11 - Mathematics Applied 3/4 | Info | Go |
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Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
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| 2 | Number theory - sets | Number sets and their members | Info | Go |
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Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system. |
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| 3 | Number theory - operations | Properties of real numbers using addition and multiplication | Info | Go |
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Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication. |
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| 4 | Number theory - equations | Transformations that produce equivalent equations | Info | Go |
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Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations. |
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| 5 | Algebraic expressions | Algebraic expressions. | Info | Go |
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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. |
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| 6 | Algebraic expressions | Substitution into algebraic expressions. | Info | Go |
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Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. |
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| 7 | Algebraic expressions | Directed numbers: addition and subtraction. | Info | Go |
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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. |
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| 8 | Algebraic expressions | Directed numbers: multiplication and division. | Info | Go |
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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. |
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| 9 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | Info | Go |
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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. |
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| 10 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | Info | Go |
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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. |
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| 11 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | Info | Go |
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Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. |
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| 12 | Algebraic expressions | Simplifying algebraic expressions: multiplication | Info | Go |
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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. |
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| 13 | Algebraic expressions | Simplifying algebraic expressions: division | Info | Go |
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Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. |
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| 14 | Algebraic expressions | Expanding algebraic expressions: multiplication | Info | Go |
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Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. |
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| 15 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | Info | Go |
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Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. |
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| 16 | Algebraic expressions | Expanding and simplifying algebraic expressions | Info | Go |
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Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. |
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| 17 | Algebraic equations | Solving two step equations | Info | Go |
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Objective: On completion of the lesson the student will be able to solve two step equations. |
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| 18 | Algebraic equations | Solving equations containing binomial expressions | Info | Go |
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Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
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| 19 | Algebraic equations | Equations involving grouping symbols. | Info | Go |
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Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
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| 20 | Algebraic equations | Equations involving fractions. | Info | Go |
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Objective: On completion of the lesson the student will know how to solve equations using fractions. |
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| 21 | Algebra- formulae | Equations resulting from substitution into formulae. | Info | Go |
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Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. |
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| 22 | Algebra- formulae | Changing the subject of the formula. | Info | Go |
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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. |
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| 23 | Scientific notation | Scientific notation with larger numbers | Info | Go |
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Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. |
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| 24 | Scientific notation | Scientific notation with small numbers | Info | Go |
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Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. |
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| 25 | Scientific notation | Changing scientific notation to numerals | Info | Go |
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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. |
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| 26 | Significant figures | Significant figures | Info | Go |
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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. |
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| 27 | Simultaneous equns | Simultaneous equations | Info | Go |
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Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. |
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| 28 | Simultaneous equns | Elimination method | Info | Go |
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Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. |
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| 29 | Simultaneous equns | Elimination method part 2 | Info | Go |
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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. |
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| 30 | Simultaneous equns | Applications of simultaneous equations | Info | Go |
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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. |
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| 31 | Coordinate Geometry-gradient | Gradient | Info | Go |
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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. |
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| 32 | Coordinate Geometry-gradient | Gradient formula. | Info | Go |
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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. |
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| 33 | Coordinate Geometry-straight line | The straight line. | Info | Go |
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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. |
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| 34 | Coordinate Geometry-slope, etc. | Lines through the origin. | Info | Go |
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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. |
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| 35 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | Info | Go |
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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. |
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| 36 | Coordinate Geometry-intercept | Slope intercept form of a line. | Info | Go |
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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. |
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| 37 | Coordinate Geometry-point slope | Point slope form of a line | Info | Go |
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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. |
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| 38 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. | Info | Go |
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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. |
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| 39 | Co-ordinate Geometry-Intercept form | Intercept form of a straight line: find the equation when given x and y | Info | Go |
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Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. |
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| 40 | Co-ordinate Geometry-Parallel lines equations | Parallel lines: identify equation of a line parallel to another | Info | Go |
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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. |
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| 41 | Time zones | Time zones | Info | Go |
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Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. |
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| 42 | Similar triangles | Similar triangles | Info | Go |
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Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. |
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| 43 | Similar triangles | Using similar triangles to calculate lengths | Info | Go |
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Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. |
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| 44 | Pythagoras | Find the hypotenuse | Info | Go |
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Objective: On completion of this lesson the student will be able to use Pythagoras' Theorem to calculate the length of the hypotenuse. |
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| 45 | Pythagoras | Pythagorean triples | Info | Go |
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Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. |
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| 46 | Pythagoras | Find the hypotenuse Part 2 | Info | Go |
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Objective: On completion of this lesson the student will be able to use Pythagoras' Theorem to calculate the length of the hypotenuse using decimals and surds. |
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| 47 | Pythagoras | Calculating a leg of a right-angled triangle | Info | Go |
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Objective: On completion of this lesson the student will be able to use Pythagoras' Theorem to calculate the length of one of the shorter sides of a right triangle. |
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| 48 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | Info | Go |
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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. |
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| 49 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | Info | Go |
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Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. |
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| 50 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | Info | Go |
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Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. |
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| 51 | Coordinate geometry | Solve by graphing | Info | Go |
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Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. |
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| 52 | Graphing binomials | Binomial products. | Info | Go |
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Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. |
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| 53 | Graphing binomials | Binomial products with negative multiplier | Info | Go |
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Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products. |
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| 54 | Graphing binomials | Binomial products [non-monic]. | Info | Go |
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Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. |
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| 55 | Squaring binomial | Squaring a binomial. [monic] | Info | Go |
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Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. |
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| 56 | Squaring binomial | Squaring a binomial [non-monic]. | Info | Go |
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Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. |
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| 57 | Factorising | Expansions leading to the difference of two squares | Info | Go |
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Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. |
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| 58 | Algebraic expressions-products | Products in simplification of algebraic expressions | Info | Go |
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Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. |
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| 59 | Algebraic expressions-larger expansions | Algebraic Expressions - Larger expansions. | Info | Go |
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Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. |
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| 60 | Algebra-highest common factor | Highest common factor. | Info | Go |
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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. |
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| 61 | Factors by grouping | Factors by grouping. | Info | Go |
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Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. |
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| 62 | Difference of 2 squares | Difference of two squares | Info | Go |
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Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. |
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| 63 | Common fact and diff | Common factor and the difference of two squares | Info | Go |
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Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. |
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| 64 | Quadratic trinomials | Quadratic trinomials [monic] - Case 1. | Info | Go |
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Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. |
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| 65 | Factorising quads | Factorising quadratic trinomials [monic] - Case 2. | Info | Go |
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Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. |
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| 66 | Factorising quads | Factorising quadratic trinomials [monic] - Case 3. | Info | Go |
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Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. |
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| 67 | Factorising quads | Factorising quadratic trinomials [monic] - Case 4. | Info | Go |
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Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. |
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| 68 | Factorising quads | Factorisation of non-monic quadratic trinomials | Info | Go |
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Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. |
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| 69 | Factorising quads | Factorisation of non-monic quadratic trinomials - moon method | Info | Go |
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Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. |
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| 70 | Trigonometry-ratios | Trigonometric ratios. | Info | Go |
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Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op |
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| 71 | Trigonometry-ratios | Using the calculator. | Info | Go |
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Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. |
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| 72 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | Info | Go |
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Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. |
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| 73 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | Info | Go |
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Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. |
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| 74 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | Info | Go |
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Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. |
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| 75 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | Info | Go |
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Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. |
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| 76 | Trigonometry-elevation | Angles of elevation and depression. | Info | Go |
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Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. |
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| 77 | Trigonometry-practical | Trigonometric ratios in practical situations. | Info | Go |
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Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. |
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| 78 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | Info | Go |
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Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. |
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| 79 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | Info | Go |
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Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. |
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| 80 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. - exact ratios. | Info | Go |
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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. |
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| 81 | Exam | Exam - Grade 11 - Mathematics Applied 3/4 | Info | Go |
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Objective: Exam |
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