| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grades 10/11 - Geometry | 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 | 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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| 3 | 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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| 4 | 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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| 5 | 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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| 6 | 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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| 7 | 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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| 8 | 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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| 9 | 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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| 10 | 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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| 11 | 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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| 12 | 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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| 13 | Surface area | Surface Area of Pyramids | Info | Go |
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Objective: To calculate the surface area of pyramids |
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| 14 | 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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| 15 | 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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| 16 | Algebra - Basic | Equations Resulting from Substitution into Formulae | Info | Go |
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Objective: To solve equations created by substituting values into formulae |
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| 17 | Algebra - Basic | Changing the Subject of the Formula | Info | Go |
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Objective: To change the subject of algebraic formulae using equation-solving techniques |
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| 18 | 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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| 19 | 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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| 20 | 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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| 21 | 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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| 22 | 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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| 23 | 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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| 24 | 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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| 25 | 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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| 26 | 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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| 27 | 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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| 28 | 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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| 29 | 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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| 30 | 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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| 31 | 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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| 32 | 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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| 33 | 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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| 34 | 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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| 35 | Geometry part 3 | Midsegments | Info | Go |
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Objective: To determine midsegments, their length, slope and other properties |
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| 36 | Quadrilaterals | Quadrilaterals 1 | Info | Go |
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Objective: To recognise, name and describe the properties of quadrilaterals |
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| 37 | 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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| 38 | 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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| 39 | 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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| 40 | 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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| 41 | Quadrilaterals | Quadrilaterals 6 | Info | Go |
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Objective: To establish the properties of quadrilaterals in the number plane |
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| 42 | 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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| 43 | 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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| 44 | 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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| 45 | 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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| 46 | 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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| 47 | 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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| 48 | 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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| 49 | 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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| 50 | 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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| 51 | 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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| 52 | 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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| 53 | 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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| 54 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 55 | 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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| 56 | 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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| 57 | Logic | Mathematical induction | Info | Go |
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Objective: To use proof by mathematical induction |
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| 58 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | Info | Go |
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Objective: On completion of the lesson the student will be able to form related conditional statements. |
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| 59 | Matrices | Vectors | Info | Go |
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Objective: To use vectors to find resultant speeds and displacements |
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| 60 | Matrices - Linear systems | Number of Solutions | Info | Go |
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Objective: To determine solutions to systems of equations |
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| 61 | Matrices - Linear systems | Vector Addition in 2 and 3D | Info | Go |
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Objective: To represent, add, subtract and determine the direction of vectors |
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| 62 | Matrices - Linear systems | Optimal Solutions | Info | Go |
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Objective: To use linear programming to maximise or minimise an objective function |
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| 63 | 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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| 64 | 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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| 65 | Uniform motion | The Speed Formula | Info | Go |
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Objective: To calculate speed, distance or time using speed = distance/time |
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| 66 | Uniform motion | Using Subscripted Variables | Info | Go |
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Objective: To use subscripted variables to solve motion problems |
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| 67 | Uniform motion | Uniform Motion With Equal Distances | Info | Go |
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Objective: To solve motion problems where distances are equal |
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| 68 | Uniform motion | Uniform Motion Adding the Distances | Info | Go |
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Objective: To solve motion problems where total distance travelled is given |
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| 69 | Uniform motion | Uniform Motion With Unequal Distances or Time | Info | Go |
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Objective: To solve motion problems where either distance or time are different |
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| 70 | Uniform motion | Uniform Motion Problems Where the Rate is Constant | Info | Go |
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Objective: To solve miscellaneous motion problems where the rate is constant |
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| 71 | Uniform motion | Vertical Motion under gravity: Object Dropped from Rest | Info | Go |
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Objective: To calculate velocity, time and distance for vertically falling objects dropped from rest |
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| 72 | Uniform motion | Vertical Motion under gravity: Initial Velocity not Zero | Info | Go |
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Objective: To calculate velocity, time and distance for vertical motion with initial velocity not zero |
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| 73 | 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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| 74 | 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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| 75 | 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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| 76 | 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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| 77 | Pythagoras | Proofs of Pythagoras' Theorem | Info | Go |
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Objective: To examine and complete proofs of Pythagoras' Theorem |
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| 78 | 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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| 79 | 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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| 80 | 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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| 81 | 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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| 82 | 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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| 83 | 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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| 84 | 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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| 85 | 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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| 86 | Circle geometry part 2 | Theorem: The products of the intercepts of two intersecting chords are equal | Info | Go |
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Objective: To use the product of chord segments theorem to find chord interval lengths |
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| 87 | Circle geometry part 2 | Theorem - The relationship between the tangent and secant from the same point | Info | Go |
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Objective: To use the tangent square, secant product theorem to find segment lengths |
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| 88 | Circle geometry part 2 | Theorem - If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic. | Info | Go |
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Objective: To prove a quadrilateral is cyclic using the supplementary angles theorem. |
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| 89 | Circle geometry part 2 | Theorem - If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic. | Info | Go |
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Objective: To prove points concyclic if they form congruent angles from two other points. |
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| 90 | Circle geometry part 2 | Theorem - When circles touch, the line of the centres passes through the point of contact. | Info | Go |
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Objective: To use the collinearity of centres and the point of contact of two circles. |
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| 91 | Circle geometry part 2 | Theorem - Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points. | Info | Go |
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Objective: To find the centre of the circle passing through 3 given points. |
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| 92 | Co-ordinate geometry part 2 | Transformations: Reflections | Info | Go |
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Objective: To identify reflections and to use isometric properties of reflections |
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| 93 | 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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| 94 | 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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| 95 | 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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| 96 | 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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| 97 | Geometry transformations | The definition and concept of combined transformations resulting in an equivalent single transformation | Info | Go |
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Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations. |
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| 98 | Matrices | Matrices: basic concepts | Info | Go |
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Objective: To write and state the order of a matrix and to identify square matrices |
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| 99 | Matrices | Addition and Subtraction of Matrices | Info | Go |
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Objective: To add and subtract matrices |
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| 100 | Matrices | Scalar matrix: multiplication | Info | Go |
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Objective: To multiply a matrix by a scalar |
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| 101 | Matrices | Multiplication of one matrix by another matrix | Info | Go |
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Objective: To perform matrix multiplication and to recognise that AB is not equal to BA |
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| 102 | Matrices | Translation in the number plane | Info | Go |
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Objective: To use matrix addition to translate points |
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| 103 | Matrices | Translation by matrix multiplication | Info | Go |
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Objective: To transform points and objects by matrix multiplication |
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| 104 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | Info | Go |
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Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication |
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| 105 | Co-ordinate geometry part 1 | The Distance Formula | Info | Go |
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Objective: To use the distance formula to calculate the lengths of lines and distances |
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| 106 | Co-ordinate geometry part 1 | The Mid-Point Formula | Info | Go |
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Objective: To determine the mid-point of an interval using the mid-point formula |
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| 107 | Co-ordinate geometry part 1 | The Gradient | Info | Go |
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Objective: To find the gradient of a line given its angle of inclination or given rise and run |
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| 108 | Co-ordinate geometry part 1 | The Gradient Formula | Info | Go |
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Objective: To use the gradient formula to find the gradient of straight lines |
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| 109 | Co-ordinate geometry part 1 | The Straight Line | Info | Go |
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Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b |
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| 110 | Co-ordinate geometry part 1 | Lines Through the Origin | Info | Go |
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Objective: To state the equation of lines passing through the origin and to graph y = mx |
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| 111 | Co-ordinate geometry part 1 | General Form of a Line and the x and y Intercepts | Info | Go |
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Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area |
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| 112 | Co-ordinate geometry part 1 | Slope Intercept Form of a Line | Info | Go |
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Objective: To change equation to slope intercept form and graph it and to find equation given graph |
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| 113 | Co-ordinate geometry part 1 | Point Slope Form of a Line | Info | Go |
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Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1) |
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| 114 | Co-ordinate geometry part 2 | Two Point Formula: equation of a line which joins a pair of points | Info | Go |
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Objective: To find the equation of the line which joins a pair of points |
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| 115 | Co-ordinate geometry part 2 | Intercept form of a straight line: find the equation when given x and y | Info | Go |
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Objective: To find the equation of a line given the x-axis and y-axis intercepts |
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| 116 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | Info | Go |
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Objective: To change the standard form of a straight line equation to the y = mx + b form |
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| 117 | Co-ordinate geometry part 2 | Perpendicular Lines | Info | Go |
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Objective: To identify the equation of a line that is perpendicular to a given linear equation |
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| 118 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | Info | Go |
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Objective: To identify the graph which matches a given inequality |
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| 119 | Co-ordinate geometry part 2 | Perpendicular Distance | Info | Go |
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Objective: To calculate the perpendicular distance from a point to a line and between lines |
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| 120 | Co-ordinate geometry part 2 | Line through the intersection of two given lines | Info | Go |
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Objective: To determine the equation of a line passing through the intersection of two lines |
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| 121 | Co-ordinate geometry part 2 | Angles between two lines | Info | Go |
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Objective: To find the angle between two given straight lines |
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| 122 | Co-ordinate geometry part 2 | Internal and external division of an interval | Info | Go |
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Objective: To find the value of k given the interval AB is divided at point P in the ratio of k to some value |
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| 123 | Graphs part 1 | The Circle: to find radii of circles | Info | Go |
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Objective: To find radii of circles, centre (0, 0) using x^2 + y^2 = a^2 and write equations of circles |
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| 124 | Graphs part 1 | The semicircle: to select the equation given the semicircle and vice versa | Info | Go |
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Objective: To select the equation given a semicircle and vice versa |
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| 125 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | Info | Go |
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Objective: To describe properties of a parabola from its equation and sketch the parabola |
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| 126 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | Info | Go |
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Objective: To describe and sketch parabolas of the form y = x^2 + bx + c |
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| 127 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | Info | Go |
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Objective: To describe and sketch parabolas of the form y = (x - a)^2 |
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| 128 | Graphs part 1 | Graphing irrational roots | Info | Go |
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Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola |
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| 129 | Graphs part 1 | Solving Simultaneous Equations graphically | Info | Go |
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Objective: To solve simultaneous equations graphically |
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| 130 | Algebra - Quadratic equations | Introduction to Quadratic Equations | Info | Go |
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Objective: To find the solutions of quadratic equations presented as a product of factors |
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| 131 | Algebra - Quadratic equations | Solving Quadratic Equations with Factorisation | Info | Go |
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Objective: To solve quadratic equations requiring factorisation |
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| 132 | Algebra - Quadratic equations | Solving Quadratic Equations | Info | Go |
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Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 |
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| 133 | Algebra - Quadratic equations | Completing the square | Info | Go |
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Objective: To complete an incomplete square |
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| 134 | Algebra - Quadratic equations | Solving Quadratic Equations by Completing the Square | Info | Go |
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Objective: To solve quadratic equations by completing the square |
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| 135 | Algebra - Quadratic equations | The Quadratic Formula | Info | Go |
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Objective: To find the roots of a quadratic equation by using the quadratic formula |
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| 136 | Algebra - Quadratic equations | Problem solving with quadratic equations | Info | Go |
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Objective: To solve problems which require finding the roots of a quadratic equation |
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| 137 | Algebra - Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | Info | Go |
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Objective: To determine points of intersection of quadratic and linear equations |
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| 138 | Graphs part 2 | General equation of a circle: determine and graph the equation | Info | Go |
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Objective: To determine and graph the equation of a circle with radius a and centre (h,k) |
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| 139 | Exam | Exam - Grades 10/11 - Geometry | Info | Go |
|
Objective: Exam |
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