You have selected NT Year 12 Applied 5: Optimisation

# TOPIC TITLE +/-
40 Absolute value equations Absolute value equations Info Go

Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio

See the sample lesson in action here

Close

18 Co-ordinate Geometry-Inequalities Inequalities on the number plane. Info Go

Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.

See the sample lesson in action here

Close

16 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y Info Go

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.

See the sample lesson in action here

Close

17 Co-ordinate Geometry-Parallel lines equations Parallel lines: identify equation of a line parallel to another Info Go

Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.

See the sample lesson in action here

Close

15 Co-ordinate Geometry-Two point formula Two point formula: equation of a line which joins a pair of points. Info Go

Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.

See the sample lesson in action here

Close

44 Conic sections Introduction to conic sections and their general equation Info Go

Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation.

See the sample lesson in action here

Close

45 Conic sections The parabola x. = 4ay Info Go

Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.

See the sample lesson in action here

Close

46 Conic sections Circles Info Go

Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.

See the sample lesson in action here

Close

47 Conic sections Ellipses Info Go

Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.

See the sample lesson in action here

Close

48 Conic sections Hyperbola Info Go

Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.

See the sample lesson in action here

Close

27 Coordinate geometry Solve by graphing Info Go

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.

See the sample lesson in action here

Close

6 Coordinate Geometry-intercept Slope intercept form of a line. Info Go

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.

See the sample lesson in action here

Close

7 Coordinate Geometry-point slope Point slope form of a line Info Go

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.

See the sample lesson in action here

Close

5 Coordinate Geometry-slope, etc. Lines through the origin. Info Go

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.

See the sample lesson in action here

Close

4 Coordinate Geometry-straight line The straight line. Info Go

Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.

See the sample lesson in action here

Close

90 Exam Exam - Year 12 Applied 5: Optimisation Info Go

Objective: Exam

See the sample lesson in action here

Close

42 Exponential function The exponential function. Info Go

Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.

See the sample lesson in action here

Close

8 Functions Definition, domain and range Info Go

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.

See the sample lesson in action here

Close

9 Functions Notation and evaluations Info Go

Objective: On completion of the lesson the student will be understand different notations for functions.

See the sample lesson in action here

Close

10 Functions More on domain and range Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.

See the sample lesson in action here

Close

11 Functions Domain and range from graphical representations Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.

See the sample lesson in action here

Close

12 Functions Evaluating and graphing piecewise functions Info Go

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.

See the sample lesson in action here

Close

13 Functions Functions combinations Info Go

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.

See the sample lesson in action here

Close

14 Functions Composition of functions Info Go

Objective: On completion of the lesson the student will understand composition of functions or a function of a function.

See the sample lesson in action here

Close

49 Functions Definition, domain and range Info Go

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.

See the sample lesson in action here

Close

50 Functions Notation and evaluations Info Go

Objective: On completion of the lesson the student will be understand different notations for functions.

See the sample lesson in action here

Close

51 Functions More on domain and range Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.

See the sample lesson in action here

Close

52 Functions Domain and range from graphical representations Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.

See the sample lesson in action here

Close

53 Functions Evaluating and graphing piecewise functions Info Go

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.

See the sample lesson in action here

Close

54 Functions Functions combinations Info Go

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.

See the sample lesson in action here

Close

55 Functions Composition of functions Info Go

Objective: On completion of the lesson the student will understand composition of functions or a function of a function.

See the sample lesson in action here

Close

56 Functions Inverse functions Info Go

Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.

See the sample lesson in action here

Close

57 Functions Rational functions Part 1 Info Go

Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.

See the sample lesson in action here

Close

58 Functions Rational functions Part 2 Info Go

Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.

See the sample lesson in action here

Close

24 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c. Info Go

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.

See the sample lesson in action here

Close

25 Functions and graphs Graphing perfect squares: y=(a-x) squared Info Go

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.

See the sample lesson in action here

Close

23 Geometry-parabola The parabola: to describe properties of a parabola from its equation Info Go

Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.

See the sample lesson in action here

Close

26 Graphing roots Graphing irrational roots Info Go

Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.

See the sample lesson in action here

Close

39 Graphing-cubic curves Graphing cubic curves Info Go

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.

See the sample lesson in action here

Close

37 Graphing-polynomials Graphing complex polynomials: quadratics with no real roots Info Go

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.

See the sample lesson in action here

Close

38 Graphing-polynomials General equation of a circle: determine and graph the equation Info Go

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student's skills in logic and reasoning.

See the sample lesson in action here

Close

36 Linear systems Optimal solutions (Stage 2) Info Go

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.

See the sample lesson in action here

Close

86 Linear systems Optimal solutions (Stage 2) Info Go

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.

See the sample lesson in action here

Close

87 Linear systems Linear systems with matrices (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.

See the sample lesson in action here

Close

88 Linear systems Row-echelon form (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.

See the sample lesson in action here

Close

89 Linear systems Gauss Jordan elimination method (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.

See the sample lesson in action here

Close

43 Log functions Logarithmic functions. Info Go

Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit

See the sample lesson in action here

Close

76 Matrices Basic concepts Info Go

Objective: On completion of the lesson the student will have had an introduction to matrices

See the sample lesson in action here

Close

77 Matrices Addition and subtraction of matrices Info Go

Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations.

See the sample lesson in action here

Close

78 Matrices Scalar matrix multiplication Info Go

Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.

See the sample lesson in action here

Close

79 Matrices Multiplication of one matrix by another matrix Info Go

Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.

See the sample lesson in action here

Close

80 Matrices Translation in the number plane Info Go

Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.

See the sample lesson in action here

Close

81 Matrices Translation by matrix multiplication Info Go

Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.

See the sample lesson in action here

Close

73 Polar coordinates Plotting polar coordinates and converting polar to rectangular Info Go

Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.

See the sample lesson in action here

Close

74 Polar coordinates Converting rectangular coordinates to polar form Info Go

Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.

See the sample lesson in action here

Close

75 Polar coordinates Write and graph points in polar form with negative vectors (Stage 2) Info Go

Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.

See the sample lesson in action here

Close

59 Pythagoras Find the hypotenuse Info Go

Objective: On completion of this lesson the student will be able to use Pythagoras' Theorem to calculate the length of the hypotenuse.

See the sample lesson in action here

Close

60 Pythagoras Pythagorean triples Info Go

Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.

See the sample lesson in action here

Close

61 Pythagoras Find the hypotenuse Part 2 Info Go

Objective: On completion of this lesson the student will be able to use Pythagoras' Theorem to calculate the length of the hypotenuse using decimals and surds.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will understand simple quadratic equations.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.

See the sample lesson in action here

Close

31 Quadratic equations Completing the square Info Go

Objective: On completion of the lesson the student will understand the process of completing the square.

See the sample lesson in action here

Close

32 Quadratic equations Solving quadratic equations by completing the square Info Go

Objective: On completion of the lesson the student will understand the reasoning behind completing the square.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will be familiar with the quadratic formula.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.

See the sample lesson in action here

Close

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..

See the sample lesson in action here

Close

41 Rect.hyperbola The rectangular hyperbola. Info Go

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.

See the sample lesson in action here

Close

84 Simultaneous equations Number of solutions (Stage 2) Info Go

Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.

See the sample lesson in action here

Close

19 Simultaneous equns Simultaneous equations Info Go

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.

See the sample lesson in action here

Close

20 Simultaneous equns Elimination method Info Go

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.

See the sample lesson in action here

Close

21 Simultaneous equns Elimination method part 2 Info Go

Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.

See the sample lesson in action here

Close

22 Simultaneous equns Applications of simultaneous equations Info Go

Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.

See the sample lesson in action here

Close

1 Study Plan Study plan - Year 12 Applied 5: Optimisation Info Go

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.

See the sample lesson in action here

Close

82 Transformations Special transformations - reflections, rotations and enlargements. Info Go

Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.

See the sample lesson in action here

Close

72 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle. Info Go

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.

See the sample lesson in action here

Close

68 Trigonometry-compass Bearings - the compass. Info Go

Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.

See the sample lesson in action here

Close

69 Trigonometry-elevation Angles of elevation and depression. Info Go

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.

See the sample lesson in action here

Close

70 Trigonometry-practical Trigonometric ratios in practical situations. Info Go

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.

See the sample lesson in action here

Close

62 Trigonometry-ratios Trigonometric ratios. Info Go

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op

See the sample lesson in action here

Close

63 Trigonometry-ratios Using the calculator. Info Go

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.

See the sample lesson in action here

Close

64 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 1 Sine]. Info Go

Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.

See the sample lesson in action here

Close

65 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. Info Go

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.

See the sample lesson in action here

Close

66 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. Info Go

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

See the sample lesson in action here

Close

67 Trigonometry-ratios Unknown in the denominator. [Case 4]. Info Go

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.

See the sample lesson in action here

Close

71 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio. Info Go

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.

See the sample lesson in action here

Close

83 Vectors Vectors Info Go

Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.

See the sample lesson in action here

Close

85 Vectors 2 vector addition in 2 and 3D (stage 2) Info Go

Objective: On completion of the lesson the student will understand and use component forms for vector resolution.

See the sample lesson in action here

Close