This page has a variety of tasks designed for practise and revision. Practice questions are an important part consolidating students' understanding of a concept. They can be found from numerous sources and the following is not intended as a 'fix all' solution. Most teachers appreciate that questions gathered from numerous different sources make the best diet!
Below are links to a series of focussed worksheets for this topic. The worksheets consist largely of 'Practise Questions' but most finish with more open ended questions to extend. Ultimately, students need to be able to answer questions from a variety of topics and contexts, but often it is necessary to spend some time focussing on particular skills whilst still in the process of learning them. The worksheets are clearly titled according to the particular sub-topic and come complete with answers.
Concept of Calculus - Practise using the concept and terminology associated with functions. answers
Differentiating puzzle - This is one of the well known 'Tarsia' puzzles that is ideal for engaging students in practising how to differentiate expressions including negative indices. It is quite challenging so some clues at the ready might be useful. Here are the solutions.
This is a series of 'Fill in the Gaps' notes that I have created to help students keep useful records of the course. The rationale is explained in more detail on the 'Exams and Revision pages. Essentially the aim is bridge the gap between Students making their own notes on a blank canvas and being given detailed notes that they did not create.
1 - Concept 1 - Syllabus ref 7.1, Calculus as rate of change
2 - Differentiating Polynomials Syllabus ref 7.2, applying the general formula with positive and negative indices.
3-Gradients, tangents and normals Syllabus ref 7.3, exploring the process behind finding gradients, tangents and normals at a given point. Students are given the elements of the process jumbled up and asked to put them together in a coherent manner. In doing so they will have to revisit all of the key ideas.
4 Increasing and Decreasing functions (New 7.4, Previous 7.4)
5 - f'(x) = 0 Syllabus reference 7.5 about recognising and finding the points on a function where the gradient = 0.
6 - Optimisation Optimisation problems (New 7.6, Previous 7.5)
IB style questions
Here are some exam style questions on the topic of Calculus for students to practice with.
Errors - an appeal to users!
Few are infallible and we have all experienced frustration in finding errors in shiny new textbooks that we have just paid lots of money for! The advantage of online resources should be that as soon as errors are found they can be pointed out and corrected! When you find errors, please accept my apologies for the inevitable frustration it can cause but please also tell me as soon as you can on email@example.com so that I can correct it as soon as possible! Thank you!