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University of Adelaide

MathTrackX: Polynomials, Functions and Graphs

University of Adelaide via edX

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Overview

This course is part one of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

This course will lay down the foundations of basic mathematical vocabulary and play a role in communicating key concepts throughout the MathTrackX Program. A central concept underpinning this course is the mathematical concept of function. Functions occur throughout mathematics and an understanding of them is essential.

Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will introduce functions, the algebra of numbers & polynomials and sets of numbers and intervals of the real number line.

Join us as we provide opportunities to develop your skills and confidence in these mathematical functions.

Syllabus

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.

Taught by

Dr Daniel Stevenson, Dr David Butler, Dr Brendan Harding, Dr Melissa Humphries and Nicholas Crouch

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Reviews

4.3 rating at edX based on 9 ratings

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