The way to improve your mathematical skills is to do lots of questions (then do some more!) You need to apply what you know and just reading your notes will not help you do that. Worked examples can be very helpful – particularly if you cover up the solution and try answering the question yourself first.
If you are looking for questions the following sites provide many for you.
Maths Centre (age 16+)
An extensive collection of very clear notes and other resources are available from the mathcentre. There are many very clearly worked examples, also exercises (with answers). Check the resource types, choosing Practice & Revision for example would lead you to this Calculus Refresher (under the Chain rule) which is a whole workbook of mixed calculus examples. mathtutor provides mathcentre resources conveniently structured as a course.
mathcentre – Maths Tutor
Just the Maths (age 18+)
Just the Maths by Tony Hobson is another extensive collection of notes which include numerous worked examples and also exercises to try (with answers). These notes are very useful for students in their last years at school and at university.
The Maths Teacher (age 11-17)
David Smith’s site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. GCSE (age 14-16, though many of these resources would be helpful for younger students also) and A-Level (age 16-18) lessons are available. For each topic not only is a video available but also a transcript and exercises with solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you.
Diagnostic Questions (Craig Barton & Simon Woodhead) (age 11 – 16+)
A totally brilliant site – thousands of multiple choice questions with your misconceptions anticipated. Try some diagnostic questions (all multiple choice) to check your understanding.
BBC Sites (ages 5 to 18)
All the BBC sites have quizzes and/or tests for you to try as well as notes and examples.
BBC Skillswise although aimed at adults, this site has information on basic Mathematics (and English) skills useful for any age.
BBC Bitesize KS1 (ages 5-7) BBC Bitesize KS2 (ages 7-11)
BBC Bitesize KS3 (ages 11-14) BBC GCSE Bitesize (ages 14 – 16)
BBC Higher Maths (age 17+)
CIMT, The Centre for Innovation in Mathematics Teaching
(age 5 – 18)
Scroll down this page
to see all the material available for students of all ages. The student texts include worked examples in every section. The texts also have exercises which are usually password protected. (Schools can obtain the password from CIMT). Note in particular the Interactive Material (examples with online checking of answers for Year 7
| Year 8
| Year 9
(have a look at the topics here which may be useful for slightly older students also).
If you choose the GCSE course material
for example and scroll down the page you will see all the pupil textbook chapters.
Trinity School have very helpful Mathematics resources
– many examples for you to try (answers included)
- Trinity School Nottingham – numerous questions and answers
WolframAlpha (age 5 upwards!)
If you are trying any exercises you can obviously check the answers given in the notes; remember that you can also check your answers with WolframAlpha. You could make up questions of your own and check the answers on WolframAlpha, for example suppose you want to make sure you can multiply out brackets – make up your own question (writing questions is actually a good way to check your understanding), for example multiply out (x+3)(x+2), write your answer, then check it on WolframAlpha. Perhaps some calculus? Differentiate sinxcosx wrt x.
On the subject of WolframAlpha, there are several slideshows on the WolframAlpha page on this blog to help you get used to the syntax.