| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Self Assessment | Self Assessment - Grades 11 - 12: Geometry | Info | Go |
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Objective: Assessment |
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| 2 | Measurement - Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | Info | Go |
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Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height |
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| 3 | Measurement - Area | Finding the Area of a Triangle and Other Composite Shapes | Info | Go |
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Objective: To calculate the area of triangles and measure and calculate composite shape area |
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| 4 | Measurement - Volume | Introducing the Formula for Volume | Info | Go |
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Objective: To calculate the volume of rectangular prisms using V=l x b x h |
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| 5 | Measurement - Volume | Solving Problems about Volume Part 1 | Info | Go |
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Objective: To solve volume problems using same and mixed units of length |
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| 6 | Measurement - Volume | Solving Problems about Volume Part 2 | Info | Go |
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Objective: To solve volume problems involving larger objects |
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| 7 | Measurement - Advanced area | Area of a Trapezium | Info | Go |
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Objective: To calculate the area of trapezia using A=(h/2)(a+b) |
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| 8 | Measurement - Advanced area | Area of a Rhombus | Info | Go |
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Objective: To calculate the area of a rhombus using diagonal products |
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| 9 | Measurement - Advanced area | Area of a Circle | Info | Go |
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Objective: To calculate the area of circles and sectors and to solve circle problems |
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| 10 | Measurement - Advanced area | Area of Regular Polygons and Composite Figures | Info | Go |
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Objective: To calculate area of composite figures and solve problems using correct formulae |
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| 11 | Measurement - Advanced volume | Finding the volume of prisms | Info | Go |
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Objective: To calculate the volume of prisms using V=Ah and solve volume problems |
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| 12 | Measurement - Advanced volume | Volume of a Cylinder and Sphere | Info | Go |
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Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each |
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| 13 | Measurement - Advanced volume | Volume of Pyramids and Cones | Info | Go |
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Objective: To calculate the volumes of pyramids and cones |
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| 14 | Measurement - Advanced volume | Composite Solids | Info | Go |
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Objective: To calculate the volume of composite figures using appropriate formulae |
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| 15 | Surface area | Surface Area of a Cube/Rectangular Prism | Info | Go |
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Objective: To calculate the surface area of cubes and rectangular prisms |
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| 16 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | Info | Go |
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Objective: To calculate the surface area of triangular and trapezoidal prisms |
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| 17 | Surface area | Surface Area of a Cylinder and Sphere | Info | Go |
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Objective: To calculate the surface area of cylinders and spheres |
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| 18 | Surface area | Surface Area of Pyramids | Info | Go |
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Objective: To calculate the surface area of pyramids |
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| 19 | Surface area | Surface Area of Composite Solids | Info | Go |
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Objective: To calculate the surface area of composite solids |
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| 20 | Surface area | Surface area of composite solids | Info | Go |
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Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. |
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| 21 | Geometry part 1 | Measuring Angles | Info | Go |
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Objective: To use a protractor to measure angles and identify angles as acute, obtuse or reflex |
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| 22 | Geometry part 1 | Adjacent Angles | Info | Go |
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Objective: To recognise and calculate the size of adjacent angles |
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| 23 | Geometry part 1 | Complementary and Supplementary Angles | Info | Go |
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Objective: To recognise and calculate the size of complementary and supplementary angles |
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| 24 | Geometry part 1 | Vertically Opposite Angles | Info | Go |
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Objective: To determine values of pronumerals in vertically opposite angles |
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| 25 | Geometry part 1 | Angles at a Point | Info | Go |
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Objective: To use angles at a point to calculate unknown angles |
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| 26 | Geometry part 1 | Parallel Lines | Info | Go |
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Objective: To identify angle pairs and calculate angles formed by a transversal and parallel lines |
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| 27 | Geometry part 1 | Additional questions involving parallel lines | Info | Go |
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Objective: To determine angle magnitude for angles formed by parallel lines and transversals |
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| 28 | Geometry part 1 | Angle Sum of a Triangle | Info | Go |
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Objective: To use the angle sum for a triangle to calculate unknown angles |
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| 29 | Geometry part 1 | Exterior angle theorem | Info | Go |
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Objective: To use the external angle of a triangle theorem to calculate unknown angles |
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| 30 | Geometry part 1 | Special triangles | Info | Go |
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Objective: To use the properties of equilateral and isosceles triangles to calculate angle size |
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| 31 | Geometry part 1 | Quadrilaterals | Info | Go |
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Objective: To use the angle sum of a quadrilateral to calculate unknown angles |
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| 32 | Geometry part 1 | Geometric Constructions | Info | Go |
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Objective: To bisect a line, bisect an angle and construct a perpendicular using a compass and ruler |
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| 33 | Geometry part 3 | Points, Lines and Planes | Info | Go |
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Objective: To identify collinear points and coplanar lines and points in 2 and 3 dimensions |
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| 34 | Geometry part 3 | Angles | Info | Go |
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Objective: To label and classify angles and calculate pronumeral values within angles |
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| 35 | Geometry part 3 | Angle Bisector Construction and its Properties | Info | Go |
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Objective: To geometrically bisect angles and calculate angle size given bisection |
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| 36 | Geometry part 3 | Circumcenter and Incenter | Info | Go |
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Objective: To use properties of triangles, circles, circumcentres and incentres |
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| 37 | Geometry part 3 | Orthocentre and Centroids | Info | Go |
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Objective: To use properties of triangles, circles orthocentres and centroids |
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| 38 | Geometry part 3 | Midsegments | Info | Go |
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Objective: To determine midsegments, their length, slope and other properties |
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| 39 | Quadrilaterals | Quadrilaterals 1 | Info | Go |
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Objective: To recognise, name and describe the properties of quadrilaterals |
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| 40 | Quadrilaterals | Properties of Parallelograms - Opposite Angles Equal | Info | Go |
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Objective: To prove and use "Opposite angles of a parallelogram are congruent" |
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| 41 | Quadrilaterals | Properties of Parallelograms - Diagonals, Sides and Angles | Info | Go |
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Objective: To prove parallelogram properties and calculate unknown angles and lengths |
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| 42 | Quadrilaterals | The Parallelogram Umbrella | Info | Go |
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Objective: To prove properties of specific parallelograms and find angles and lengths |
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| 43 | Quadrilaterals | Properties of Trapezoids | Info | Go |
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Objective: To prove properties of trapezoids and find unknown lengths and angles |
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| 44 | Quadrilaterals | Quadrilaterals 6 | Info | Go |
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Objective: To establish the properties of quadrilaterals in the number plane |
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| 45 | Locus | Constructions and Loci 1: Transformations | Info | Go |
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Objective: To identify and use the locus of a point with simple constraints |
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| 46 | Locus | Constructions and Loci 2 | Info | Go |
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Objective: To identify and use the locus of a point with multiple constraints |
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| 47 | Geometry part 2 | More difficult exercises involving parallel lines | Info | Go |
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Objective: To determine the angles of geometric figures using known properties and theorems |
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| 48 | Geometry part 2 | Further difficult exercises involving formal reasoning | Info | Go |
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Objective: To determine formally angles of geometric figures using known properties and theorems |
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| 49 | Geometry part 2 | Angles of regular polygons | Info | Go |
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Objective: To calculate the internal and external angles of a polygon |
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| 50 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | Info | Go |
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Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS |
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| 51 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | Info | Go |
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Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS |
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| 52 | Geometry part 2 | Proofs and Congruent Triangles | Info | Go |
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Objective: To use congruency in formal proofs in order to determine unknown angles and sides |
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| 53 | Geometry part 2 | Similar Triangles | Info | Go |
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Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles |
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| 54 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | Info | Go |
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Objective: To determine unknown sides and angles of similar triangles |
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| 55 | Geometry part 2 | Examples involving overlapping triangles | Info | Go |
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Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles |
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| 56 | Geometry part 3 | The Triangle Inequality Theorem | Info | Go |
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Objective: To use the triangle inequality theorem to determine constructability of triangles |
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| 57 | Pythagoras | Pythagoras' Theorem: Finding the Hypotenuse | Info | Go |
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Objective: To calculate the length of a hypotenuse using Pythagoras' Theorem |
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| 58 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | Info | Go |
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Objective: To identify right triangles by using Pythagorean Triples or Pythagoras' Theorem |
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| 59 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | Info | Go |
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Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals |
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| 60 | Pythagoras | Calculating a Leg of a right-angled Triangle | Info | Go |
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Objective: To calculate the length of sides other than the hypotenuse using Pythagoras' Theorem |
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| 61 | Pythagoras | Proofs of Pythagoras' Theorem | Info | Go |
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Objective: To examine and complete proofs of Pythagoras' Theorem |
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| 62 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 63 | Logic | Disproof of Counter Example | Info | Go |
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Objective: To identify a statement as a counter example to disprove a statement |
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| 64 | Logic | Proof by Disproof of a Contradictory Statement | Info | Go |
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Objective: To prove that a statement is true by proving that the contradictory statement is false |
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| 65 | Logic | Mathematical induction | Info | Go |
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Objective: To use proof by mathematical induction |
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| 66 | Trigonometry part 1 | Trigonometric Ratios | Info | Go |
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Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle |
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| 67 | Trigonometry part 1 | Using the Calculator | Info | Go |
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Objective: To determine trigonometric ratios using a calculator |
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| 68 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | Info | Go |
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Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle |
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| 69 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | Info | Go |
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Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle |
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| 70 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | Info | Go |
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Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle |
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| 71 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | Info | Go |
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Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator |
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| 72 | Trigonometry part 1 | Bearings: The Compass | Info | Go |
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Objective: To change from true bearings to compass bearings and vice versa |
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| 73 | Trigonometry part 1 | Angles of Elevation and Depression | Info | Go |
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Objective: To identify and distinguish between angles of depression and elevation |
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| 74 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | Info | Go |
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Objective: To solve problems involving bearings and angles of elevation and depression |
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| 75 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | Info | Go |
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Objective: To find angles in right-angled triangles given trigonometric ratios |
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| 76 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | Info | Go |
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Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems |
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| 77 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | Info | Go |
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Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees |
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| 78 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | Info | Go |
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Objective: To complete the cosine rule to find a subject side for given triangles |
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| 79 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | Info | Go |
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Objective: To complete the cosine rule to find a subject angle for given triangles |
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| 80 | Trigonometry part 1 | The Sine Rule: Finding a Side | Info | Go |
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Objective: To find an unknown side of a triangle using the sine rule |
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| 81 | Trigonometry part 1 | The Sine Rule: Finding an Angle | Info | Go |
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Objective: To find an unknown angle of a triangle using the sine rule |
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| 82 | Trigonometry part 1 | The Sine Area Formula for a Triangle | Info | Go |
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Objective: To use the sine formula for the area of a triangle to calculate area |
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| 83 | Geometry transformations | Geometry Transformations without Matrices: Translation | Info | Go |
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Objective: To find the image of a point or object after a translation |
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| 84 | Geometry transformations | Geometry Transformations without Matrices: Rotation | Info | Go |
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Objective: To determine rotation angle and to perform prescribed rotations |
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| 85 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | Info | Go |
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Objective: To describe dilations and to calculate lengths and scale factors of dilated figures |
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| 86 | Geometry transformations | Geometry Transformations without Matrices: Mixed and Combined Transformations | Info | Go |
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Objective: To identify images produced by a given sequence of transformations |
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| 87 | Circle geometry part 1 | Theorem - Equal arcs subtend equal angles at the centre | Info | Go |
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Objective: To know that equal arcs on circles of equal radii subtend equal angles at the centre |
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| 88 | Circle geometry part 1 | Theorem - The perpendicular from the centre to a chord bisects the chord | Info | Go |
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Objective: To know that the perpendicular from the centre of a circle to a chord bisects the chord and to know that the line from the centre of a circle to the mid-point of a chord is perpendicular to the chord |
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| 89 | Circle geometry part 1 | Theorem - Equal chords in a circle are equidistant from the centre | Info | Go |
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Objective: To know that equal chords in equal circles are equidistant from the centres |
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| 90 | Circle geometry part 1 | Theorem - The angle at the centre is double the angle at the circumference | Info | Go |
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Objective: To know that the angle at the centre of a circle is double the angle at the circumference standing on the same arc |
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| 91 | Circle geometry part 1 | Theorem: Angles in the same segment of a circle are equal | Info | Go |
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Objective: To know that angles in the same segment of a circle are equal |
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| 92 | Circle geometry part 1 | Theorem: The angle of a semi-circle is a right angle | Info | Go |
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Objective: To know that the angle of a semi-circle is a right angle |
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| 93 | Circle geometry part 1 | Theorem: The opposite angles of a cyclic quadrilateral are supplementary | Info | Go |
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Objective: To know that the opposite angles of a cyclic quadrilateral are supplementary |
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| 94 | Circle geometry part 1 | Theorem - Exterior angle of cyclic quadrilateral equals interior opposite angles | Info | Go |
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Objective: To know that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle |
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| 95 | Circle geometry part 1 | Theorem - At the point of contact a tangent is perpendicular to the radius | Info | Go |
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Objective: To know that the tangent to a circle is perpendicular to the radius drawn to it |
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| 96 | Circle geometry part 1 | Theorem: Tangents to a circle from an external point are equal | Info | Go |
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Objective: To know that the tangents to a circle from an external point are equal |
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| 97 | Circle geometry part 1 | Theorem - Angle between a tangent and chord equals angle in alternate segment | Info | Go |
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Objective: To know that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment |
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| 98 | Exam | Exam - Grades 11 - 12: Geometry | Info | Go |
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Objective: Exam |
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