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Advanced Precalculus: Geometry, Trigonometry and Exponentials

University of Padova via FutureLearn


Take your precalculus knowledge to the next level

This course is the second of two precalculus courses from the University of Padova, providing you with the advanced mathematical skills required to complete a first course in calculus.

You’ll get to grips with more challenging precalculus topics: plane and solid geometry; logarithms and exponentials; equalities and inequalities; and trigonometric functions and identities.

By the end of this course you’ll have gained the skills to support further mathematical studies.

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.

Ideally, you’ll have already taken the first course - Precalculus: the Mathematics of Numbers, Functions and Equations or be familiar with the topics covered in it, and have a basic knowledge of high school mathematics.

Taught by

Francis Clarke

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4.8 rating, based on 38 reviews

Start your review of Advanced Precalculus: Geometry, Trigonometry and Exponentials

  • Graham Divall

    Graham Divall completed this course, spending 25 hours a week on it and found the course difficulty to be hard.

    A very good course which I found, personally, difficult and demanding. A lot of fellow students appeared to have strong mathematical backgrounds and were probably familiar with many of the topics covered. I found a tendency for the videos to speak...
  • Anonymous
    this course will help me to understand better the calculus. the tutor who delivered the course explained the main points in detailed. The presentation of the course in graphical way helps me to deeply understand the trigonometric ratios, exponential and logarithmic functions well. Combination of the sines and cosines function that results in waves was very interesting part of the course. Introduction to the limits could be a better idea in pre-calculus.
  • Anonymous
    This Advanced Precalculus refreshed my memory of topics from long ago, and introduced some expanded aspects of the topics I had never before seen. At 72 years old, it is good to be challenged and to acquire new skills and understanding. Thank you for the wide variety of courses I have completed in maths, science, social studies, astronomy and medical topics.
  • Anonymous
    This course was really well explained and structured. The practical exercises were very helpful to consolidate learning and recorded sessions managed to cover exactly the right areas. Just a shame that some of the videos were out of sync and some text in the answers was hidden
  • Anonymous

    Anonymous completed this course.

    Initial Videos gave complete step by step guidance and clarity of the topic. Though challenging, but not impossible. The task questions were well set, kind of covering most of the concepts and the solving videos/pdf were helpful to mark our work or address my misconception or error. Thoroughly enjoyed working on them, reignited the passion in me for mathematics and also enabled me to replenish my subject knowledge.
  • Or Ka King
    This is very good topic as higher education programs. This is very interested in so many learner. This is very much famous topic.

    This is as follows as soon as possible.

    This is as very good in development at in-depth view's.

  • Anonymous

    Anonymous completed this course.

    This and the earlier precalculus course from the University of Padova are two of the best courses on FutureLearn, both challenging but enjoyable. They have a regular structure, the theory of each topic is discussed followed by practical examples of problem...
  • Anonymous
    Maths is for active engagement and this course is both engaging and varied in approach.

    The format is well balanced with ludid expositions, practical problem-solving demonstrations and post quiz comments and clarifications. Rather than a formulaic approach there were some unexpected twists and turns. There were also references to a wider field of Maths as well as a wider world.

    The course is suitable for any advanced student - post as well as pre-university, whether learning the material for the first time or in need of practice.
  • Minh Nguyen

    Minh Nguyen completed this course.

    Very demanding zciriculum and fun, and serious concentration is needed,. Was a little tool fast to take in 8-10 minutes per section of the course though, I had to play it some time more than once to capture all of the technical information and answers...
  • Anonymous
    This is an excellent course which I thoroughly enjoyed. The lecture videos are clear to understand and delivered with a sprinkling of dry humor. The chance to put into practice the content of the lectures in the 'Its Your Turn' lessons is both useful and fun, but at the same time challenging. Getting these problems right gives a real sense of achievement. I'd recommend this course to anyone wanting to learn the principles of maths.
  • Anonymous
    The course was challenging and a lot of fun. It was very well presented with difficult concepts rendered understandable.The educators interacted nicely with students and the atmosphere was pleasant. I particularly appreciated the ‘it’s your turn’ part which had some very well chosen exercises with indispensable workings well laid out.
  • Anonymous
    This is an excellent course! The video lectures, excercises and quiz - are all made such that you will remeber it for long time to come. There are many basic thngs that I learnt for the first time though I have been using it as habit.

    Maths can't be made easier than this....
  • Kevin Griffiths completed this course.

    Very enjoyable. All the tutors are knowledgable, enthusiastic and engaging. The structure of the course, with a lecture followed by worked examples which you are encouraged to try yourself, works really well. The pace is quite fast and some of the material...
  • Anonymous
    This was a very comprehensive and challenging course. A lot of examples and exercises to check the understanding of the material. Very good overall.
  • Anonymous

    Anonymous completed this course.

    This is not a course to rush through but taking the time will be worth it. I didn't have time to do the course properly so used it more as revision.

    The lectures are clear and things are quite well explained - I also appreciated how the lecturers showed their sense of humour and are happy to respond to comments and questions you might have. They're genuinely encouraging which was something I didn't expect.

    The notes aren't as great but do look up online maths textbooks for supplementary info!
  • Anonymous

    Anonymous completed this course.

    I thought the course was quite interesting. I thought the course would be about differentiation or integration but I was pleasantly surprised. I enjoyed most of it and thought it was a nice difficulty and I didn't find it so hard that I couldn't sleep at night. I quite liked that you were shown how to do all the questions in week 1 but a little disappointed that it didn't return for the future weeks. I especially liked it when Francis showed his humorous side. His circle joke was legendary.
  • Anonymous

    Anonymous completed this course.

    Inspiring course, urges to think about numbers and how it applies to surrounding environments. Currently I'm also studying bioinformatics, which I know this course will come into use. In the duration of this I also came to understand the relationship between math and art. Many of the equations presented in this course invoked visuals related to art, which helped me to understand the questions with greater clarity.
  • Andrew Starodubstev

    Andrew Starodubstev completed this course, spending 11 hours a week on it.

    Thank Francis, Alberto, Carlo, Francesco and Valentina so much! I have gained the knowledge of several new approaches to mathematics and having that new knowledge mathematics became even more beautiful. Everything is a mathematics! I downloaded videos and text materials to recall and refresh my understanding.
  • Ged Langosz

    Ged Langosz completed this course.

    One of the best Future Learn courses that I have done. I have signed up for over 40 courses so far, and this easily rates amounts the best.

    The course content was comprehensive. It set its target at the correct audience. The material is challenging but provides a correct in depth discussion of the subject.

    The material was presented in informative, friendly lectures which were easy to understand. This was backed up with extensive challenging exercises. The answer of these were provided in great detail.

    This course provides a solid grounding for any student who is about to start learning calculus.

    I thoroughly recommend it.
  • Anonymous

    Anonymous completed this course.

    A great deal of hard work was put into this MOOC, one of the most thorough (and demanding, but that is not a criticism) that I have done. All involved showed a love for their subject and the wish to share that. Excellent!

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