| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grade 9-12 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 | Space | Recognise and name prisms according to spatial properties | Info | Go |
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Objective: To name prisms according to the shape of the base |
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| 3 | Space | Recognise and name pyramids according to spatial properties | Info | Go |
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Objective: To name pyramids according to the shape of the base |
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| 4 | Space | Recognise nets for prisms, pyramids, cubes and cones | Info | Go |
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Objective: To match a net with a solid and determine whether a given net forms a solid |
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| 5 | Space | Viewing 3-D Shapes | Info | Go |
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Objective: To recognise what a solid looks like when viewed from a given direction |
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| 6 | 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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| 7 | 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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| 8 | 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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| 9 | 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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| 10 | 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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| 11 | 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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| 12 | 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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| 13 | 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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| 14 | 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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| 15 | 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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| 16 | 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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| 17 | 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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| 18 | 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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| 19 | 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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| 20 | 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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| 21 | 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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| 22 | 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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| 23 | Geometry part 3 | Midsegments | Info | Go |
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Objective: To determine midsegments, their length, slope and other properties |
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| 24 | Quadrilaterals | Quadrilaterals 1 | Info | Go |
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Objective: To recognise, name and describe the properties of quadrilaterals |
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| 25 | 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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| 26 | 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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| 27 | 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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| 28 | 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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| 29 | Quadrilaterals | Quadrilaterals 6 | Info | Go |
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Objective: To establish the properties of quadrilaterals in the number plane |
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| 30 | 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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| 31 | 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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| 32 | 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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| 33 | 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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| 34 | 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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| 35 | 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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| 36 | 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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| 37 | 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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| 38 | 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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| 39 | 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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| 40 | 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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| 41 | 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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| 42 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 43 | 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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| 44 | 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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| 45 | 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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| 46 | 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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| 47 | Matrices | Addition and Subtraction of Matrices | Info | Go |
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Objective: To add and subtract matrices |
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| 48 | Matrices | Scalar matrix: multiplication | Info | Go |
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Objective: To multiply a matrix by a scalar |
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| 49 | 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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| 50 | Matrices | Translation in the number plane | Info | Go |
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Objective: To use matrix addition to translate points |
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| 51 | Matrices | Translation by matrix multiplication | Info | Go |
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Objective: To transform points and objects by matrix multiplication |
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| 52 | 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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| 53 | 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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| 54 | 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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| 55 | 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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| 56 | 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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| 57 | 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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| 58 | 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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| 59 | 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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| 60 | 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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| 61 | 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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| 62 | 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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| 63 | 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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| 64 | 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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| 65 | 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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| 66 | 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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| 67 | 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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| 68 | 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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| 69 | 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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| 70 | 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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| 71 | 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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| 72 | 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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| 73 | 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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| 74 | Pythagoras | Proofs of Pythagoras' Theorem | Info | Go |
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Objective: To examine and complete proofs of Pythagoras' Theorem |
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| 75 | Matrices | Vectors | Info | Go |
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Objective: To use vectors to find resultant speeds and displacements |
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| 76 | Matrices - Linear systems | Number of Solutions | Info | Go |
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Objective: To determine solutions to systems of equations |
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| 77 | 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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| 78 | 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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| 79 | Matrices - Linear systems | Linear Systems with Matrices | Info | Go |
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Objective: To identify and describe matrices and perform row operations in matrices |
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| 80 | 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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| 81 | 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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| 82 | 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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| 83 | 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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| 84 | 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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| 85 | 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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| 86 | 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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| 87 | 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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| 88 | 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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| 89 | 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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| 90 | 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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| 91 | 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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| 92 | 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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| 93 | 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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| 94 | 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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| 95 | 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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| 96 | 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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| 97 | 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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| 98 | 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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| 99 | 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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| 100 | 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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| 101 | 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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| 102 | 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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| 103 | 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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| 104 | 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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| 105 | 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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| 106 | 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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| 107 | 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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| 108 | 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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| 109 | 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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| 110 | 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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| 111 | 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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| 112 | 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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| 113 | 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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| 114 | 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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| 115 | Surface area | Surface Area of Pyramids | Info | Go |
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Objective: To calculate the surface area of pyramids |
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| 116 | 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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| 117 | 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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| 118 | 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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| 119 | Trigonometry part 1 | Using the Calculator | Info | Go |
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Objective: To determine trigonometric ratios using a calculator |
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| 120 | 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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| 121 | 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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| 122 | 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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| 123 | 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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| 124 | 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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| 125 | 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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| 126 | 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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| 127 | 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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| 128 | 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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| 129 | 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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| 130 | 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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| 131 | 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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| 132 | 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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| 133 | 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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| 134 | 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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| 135 | Trigonometry part 2 | Reciprocal Ratios | Info | Go |
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Objective: To find the trigonometric ratios for a given right-angled triangle |
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| 136 | Trigonometry part 2 | Complementary Angle Results | Info | Go |
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Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality |
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| 137 | Trigonometry part 2 | Trigonometric Identities | Info | Go |
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Objective: To simplify expressions using trigonometric equalities |
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| 138 | Trigonometry part 2 | Angles of Any Magnitude | Info | Go |
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Objective: To assign angles to quadrants and to find trigonometric values for angles |
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| 139 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | Info | Go |
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Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees |
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| 140 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | Info | Go |
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Objective: To recognise the sine curve and explore shifts of phase and amplitude |
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| 141 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | Info | Go |
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Objective: To recognise the cosine curve and explore shifts of phase and amplitude |
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| 142 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | Info | Go |
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Objective: To recognise the tangent curve and explore shifts of phase and amplitude |
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| 143 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | Info | Go |
|
Objective: To graph the primary trigonometric functions and their inverses |
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| 144 | Trigonometry part 2 | Using One Trig. Ratio to Find Another | Info | Go |
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Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier. |
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| 145 | Trigonometry part 2 | Solving Trigonometric Equations - Type I | Info | Go |
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Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. |
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| 146 | Trigonometry part 2 | Solving Trigonometric Equations - Type II | Info | Go |
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Objective: To solve trigonometric equations for angles from 0 to 360 degrees. |
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| 147 | Trigonometry part 2 | Solving Trigonometric Equations - Type III | Info | Go |
|
Objective: To solve trigonometric equations using tan? = sin?/cos?. |
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| 148 | Exam | Exam - Grade 9-12 Geometry | Info | Go |
|
Objective: Exam |
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