AdelaideX: MathTrackX: Polynomials, Functions and Graphs

• Algebra and arithmetic
• Basic vocabulary for sets of real numbers
• Basic concepts of functions
• Understanding and graphing polynomials
• Mathematical problem solving

Week 1: Numbers

• Distinguish between integers, rational numbers and real numbers
• Simplify expressions involving integers, fractions and/or real numbers
• Apply basic rules of arithmetic to solve problems (both theoretical and practical in nature) involving integers, fractions and/or real numbers
• Demonstrate use of the four basic inequalities to manipulate and solve simple problems.

Week 2: Linear functions and their graphs

• Identify and plot points in the coordinate plane
• Understand a function as something that takes a number as input and returns another number as output
• Determine the slope and y-intercept of a linear relationship based on its equation
• Plot the graph of a linear function
• Determine the linear function corresponding to a given graph of a line in the coordinate plane
• Solve linear equations in the context of both theoretical and practical problems.

Week 3: Polynomials and their graphs

• Identify a polynomial and determine its basic properties
• Solve problems of a theoretical or practical nature involving quadratics
• Graph polynomials and identify basic properties from their graphs including the location of roots, turning points and points of inflection
• Perform simple manipulation of polynomials with degree greater than two and solve problems involving special cases that can be reduced to solving a quadratic.

Week 4: Functions and graphs

• Understand the concept of a function and be able to identify when a given relation constitutes a valid function
• Understand and be able to identify the domain and range of functions, either from their definition or from a graph
• Be able to identify fundamental properties of a function from its graph (including its sign, where it is increasing or decreasing, etc.)
• Understand the concept of continuity and be able to identify whether a function is continuous
• Be able to construct functions via the sum, multiplication and/or composition of existing functions.

Week 5: Assessment

There is a timed exam.