Overview
Get an introduction to precalculus fundamentals
This course is the first of two precalculus courses from the University of Padova that will provide you with an introduction to the fundamental mathematical skills required to complete your first course in calculus.
You will learn the basic precalculus required for college or undergraduate-level studies, including factoring and division, sets and set operations, reasoning and proofs, functions and graphs, and equations and inequalities.
On this online precalculus course, you will gain the foundation to support further mathematical studies and improve your use of maths in everyday life.
This course is for anyone who wants to brush up on their basic mathematical skills, particularly students in the last year of high school, or at the beginning of undergraduate studies, who intend to take a first course in calculus.
Syllabus
- Numbers
- Presentation of the course
- Integers
- Rational numbers
- Real numbers
- Absolute value
- An induction proof
- It’s quiz time!
- Test yourself
- Functions
- The function concept
- The graph of a function
- Integer powers
- Roots and radicals
- Simplifying radicals
- Rational powers
- It’s quiz time
- Test yourself
- Algebra
- Polynomial and identities
- Roots of polynomials
- Quadratic polynomials
- Polynomial division
- Finding roots
- Binomial coefficients
- It’s quiz time
- Test yourself
- Equations
- Introduction: types of equations
- Equivalence
- Polynomial equations
- Equations involving a radical
- Equations with several radicals
- Equations with absolute values
- Equations in several variables
- It’s quiz time
- Test yourself
- Inequalities
- General principles
- The quadratic case
- Polynomial inequalities
- Inequalities with radicals
- Inequalities with absolute values
- Lines in the plane
- Systems of linear inequalities
- It’s quiz time
- Test yourself
- Revision Test