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Precalculus: the Mathematics of Numbers, Functions and Equations

University of Padova via FutureLearn


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.


  • 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

Taught by

Francis Clarke



4.8 rating, based on 48 Class Central reviews

4.6 rating at FutureLearn based on 28 ratings

Start your review of Precalculus: the Mathematics of Numbers, Functions and Equations

  • Anonymous
    I am new to MOOC and am both humbled and honoured that such esteemed professionals would provide a course like this, gratis, to anyone in the world with a computer and access to the internet. The team behind it should be justifiably proud of their e…
  • Anonymous
    The course is well structured and organized with topics fine-tuned for the students which want to refresh their already good knowledge from the high school. I highly recommend it.
  • Anonymous
    Interesting course on Precalculus (Numbers, Functions, Equations and Inequalities) with a focus on depth rather than breadth. Proofs were touched on as well. The format was great as well, there were a few (5-7) concepts for each week's topic. Each c…
  • Robert John Humphries
    I have rated this course 5 stars, although there have been times when when I was so frustrated that that I would have said otherwise. The nature of the instruction seems to be very university oriented. By that I mean the lecture component which give…
  • Anonymous
    I did not like this class. In my opinion I did not learn anything. The expiations were unhelpful, and I disliked that not all the problems were solved in a video even though there was a pdf of the answers it would have been nice to have all of the problems in a video. I would not recommend this class.
  • Anonymous
    excellent course, with detailed explanations, thorough notations and terminology, paced well.

    I like the explanatory video, examples are well explained and questions to practice give enough material to deepen the understanding.
    Thank you!
  • Mike Lewis
    A very well-presented course which lived up to all its claims. The presentations were clear and easy to understand, and the instructors all had an easy-going and personable style (I would especially mention Francis Clark in this regard - a really good teacher). My only problem was that the course required a lot more of my time than I expected, and I had to rush through the final segments in order to finish in time.

    I'm happy to recommend this course to anyone who needs to prepare for a more advanced maths class or who (like me) simply wants to recapture what was learned (and forgotten) long ago. But make sure you have enough time in your schedule to complete all the segments.
  • Anonymous
    This was an excellent in depth course of all the concepts which are necessary before one can move on to logarithmic functions and solid geometry. The material is presented in a very compact way so I would recommend watching each video several times. The exercises and their solutions are fascinating.
  • Anonymous
    Very important course. It helps you learn and covers all calculus material in a very good way. It taught me alot with a well organized videos and important notes.
  • Anonymous
    Excellent course, I highly appreciate the methodology, first the theoretical explanation and second the exercises, both in video or in pdf. I recommend to everybody that needs a refresh of the topic, or just to revise or check the syllabus in order to learn the next course. The explanations are very easy to understand, excellent work¡
  • Anonymous
    I thought the course was well presented and well structured. Providing a pdf copy of the key points from the presentations was much appreciated, as was the follow-up worked examples. I've completed several on-line courses, and this one was one of the best. Congratulations to everyone involved in the preparation and presentation.
  • Anonymous
    many thanks to Francis and his team for this excellent course. It took me much longer than I initially thought but it was really enjoyable. I will definitely join your next course and look forward seeing you in Padova in my retirement. Keep safe, Jurgen
  • Anonymous
    This was a great course. I had not done any advanced mathematics for several years and this gave a good introduction and reminder of older topics as well as introducing successfully newer ones. Nice bit of humour as well
  • Anonymous
    An excellent course for those wanting to brush up and revise their knowledge. I found the course very helpful.

    Notwithstanding the above, this course is not for the novice looking for an introduction to mathematics.
  • Anonymous
    I loved the way you helped students develop their thinking abilities in resolving maths.

    There's no need to keep things that we don't understand and can't explain. Thanks to all of you
  • Anonymous
    I loved the course, some things helped me as a review, there were also new things that I learned, that I knew about them but now I understood them better.
  • Anonymous
    The course il very well explained and there is plenty of material to test yourself and understand your point of weakness and strength
  • Anonymous
    Great course , great instructors ! Easy and interesting to follow. Provides a good refresher to existing knowledge.
  • Anonymous
    The MOOC was incredibly interesting and fun. The activities weren't too difficult but not too easy that they didn't require thinking. The lecturers were some of the best, as they were informative, clear and engaging. Also, the questions in the comments would always be answered. I especially enjoyed the comedy show between the 2 researchers. I would recommend this to anyone that has or is doing their A-levels or equivalent qualifications as a reminder.
  • Anonymous
    Taken this course to refresh my knowledge before getting into Calculus and Algorithms afterwards. It is great, straight to the point. If you are looking for deep understanding it is good to solve all the examples and go along all the practice videos. If you're like me just refreshing already established but slightly blurred knowledge, it will be enough to just go through the lectures. They are very explanatory.

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