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Topic 4 – Functions and Graphs Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Topic 4 – Functions & Graphs
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Functions Definition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
3 Functions Notation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
4 Functions More on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
5 Functions Domain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
6 Functions Evaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
7 Functions Functions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
8 Functions Composition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
9 Functions and graphs Graphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
10 Graphing roots Graphing irrational roots
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.
11 Coordinate geometry Solve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
12 Functions Inverse functions
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.
13 Functions Rational functions Part 1
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.
14 Functions Rational functions Part 2
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.
15 Functions Parametric equations (Stage 2)
Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range.
16 Functions Polynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.
17 Functions Parametric functions (Stage 2)
Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.
18 Exponential function The exponential function.
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.
19 Log functions Logarithmic functions.
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
20 Trigonometry-ratios Trigonometric ratios.
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
21 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
22 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].
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.
23 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
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.
24 Trigonometry-ratios Unknown in the denominator. [Case 4].
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.
25 Trigonometry-compass Bearings – the compass.
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.
26 Trigonometry-elevation Angles of elevation and depression.
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.
27 Trigonometry-practical Trigonometric ratios in practical situations.
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.
28 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio.
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.
29 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle.
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.
30 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
31 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
32 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
33 Trigonometry-sine rule The sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
34 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
35 Trigonometry-areas The area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
36 Coordinate Geometry-gradient Gradient
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.
37 Coordinate Geometry-gradient Gradient formula.
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.
38 Coordinate Geometry-straight line The straight line.
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.
39 Coordinate Geometry-slope, etc. Lines through the origin.
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.
40 Coordinate Geometry-equation of line General form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
41 Coordinate Geometry-intercept Slope intercept form of a line.
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.
42 Coordinate Geometry-point slope Point slope form of a line
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.
43 Exam Exam – Topic 4 – Functions & Graphs
Objective: Exam