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Online Course

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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4.7 rating, based on 34 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

    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...
  • 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

    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.
  • 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!
  • 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...
  • 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
    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.
  • Anonymous

    Anonymous completed this course.

    Very nice course, was DEFINITELY challenging b/c of the CONSTANT set theory notation. But omg, after a while it just clicked and I could understand it. I guess b/c i was exposed so long to it. Especailly compared to other courses online, I would definitely say this is prob the hardest, maybe not the MOST thorough, but its proofs are rigorous as math should be, and is definitely a taste of what REAL math is, if you know what I mean. Thank you for the great time!! and Good Luck all :D
  • 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.

    Francis's teaching was excellent, clear easy to understand and rigorous. I found the other course tutors unclear and difficult to understand at times and although their working was correct they did seem to overcomplicate explanations and often used a slightly different notation to Francis, so I did find this a bit confusing. I am disappointed that the course has come to an end. I do hope that there will be more courses like this in future as I have really enjoyed it..
  • Anonymous

    Anonymous completed this course.

    A very thorough course well presented with worked solutions to help if in difficulty.
    Any comments posing questions are answered very quickly by course staff, I think they must work shifts to give such immediate responses, the most attentive monitoring of all the courses that I have done. I am just sorry that owing to other commitments I fell behind on this particular course, very rare for me not to complete a course. I shall probably sign up when it is re-run.
  • 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

    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.
  • Ivana Babkova

    Ivana Babkova completed this course.

    I appreciate a highly professional instruction, plenty of problems of varied difficulty to solve accompanied by a detailed solution of the problems both in videos and in pdf files, interesting applications of presented mathematical concepts, lots of quizes that prepare
    students for the tests, the support of the educators in answering students' questions.
    Taking part in the course was a great adventure.
  • Anonymous

    Anonymous completed this course.

    This is a very enjoyable, yet very serious course covering lots of different areas of Mathematics.
    Concepts are clear & concise. Excellent examples are used to enhance understanding & plenty of practise questions are given.
    This is a course for someone with a good knowledge of Mathematics who wishes to extend their knowledge & skill base in this subject.
    A thoroughly enjoyable & deep course of study.
  • Anonymous

    Anonymous completed this course.

    I love both PreCalculus and Advanced PreCalculus offered by you. My suggestion is that it will be better if Francis uses focus-directrix definition of conic section when deriving the canonical equation of ellipse, parabola, and hyperbola since it is much easier to understand. Other than that, I can safely say that this is the most impressive PreCalculus course that I have ever taken in my life.
  • 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.
  • 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.

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