The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
Section 1 Notes - Finding gradients, tangents and normals
Section 2 Notes - Increasing/decreasing functions, stationary points and derivative graphs
Section 3 Notes - Negative/fractional indices and applications
Section 4 Notes - Applied problems and differentiation from first principles
Use the following resources when directed in order to build up the fundamental skills to make the most of your classroom learning.
Log in to your Edpuzzle account and watch the two laws of indices assignment videos. (You can sign in using Google; just make sure you are logged in to your DSFC account.)
Please complete levels 1-3 of the laws of indices quizzes below (you will not be able to complete levels 4-5 yet) - click the icon in the top-right corner to open in a new window for increased readability.
Please complete and mark the exam questions below before completing the Google Form review question.
Differentiation EQs 1 - attach photos of your work onto the Google Classroom post
See Google Classroom assignment post for Google Form review question
If you are unsure about any of this work, please use the rest of the resources on this page or contact your teacher to fully develop your understanding on the topic before your next lesson.
Task 1: Complete and mark the worksheet 'Differentiation with coordinate geometry exam questions' - attach photos of your working to the remote learning Google Classroom post.
Task 2: Work through tasks 1.1 and 1.2 of The Calculus Project phase 1 below - see phase 1 instructions.
Task 3: Complete and mark the worksheet 'Sketching gradient functions' (based on The Calculus Project tasks) - attach photos of your working to the remote learning Google Classroom post. If you get stuck, please watch this video for some additional worked examples.
Task 4: See Google Classroom post for Google Form review question.
If you are unsure about any of this work, please use the rest of the resources on this page or contact your teacher to fully develop your understanding on the topic before your next lesson.
The following resources are designed to independently develop your geometric appreciation of A-level calculus alongside the classroom teaching. This is the most important part of A-level Maths, so it is vital you have a good understanding of it all!
Explore the independent GeoGebra resources through the link to the right (as with most sites, it is best to use a browser other than Internet Explorer to access this).
Use the document below to help direct your investigations:
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
In particular, 'The Essence of Calculus' video series is dotted throughout the relevant topic pages in A-level Maths and Further Maths, or you can find the full playlist here. These videos demonstrate a deeper cut of some of the most important ideas within A-level, so they are well worth a watch!
Introduction - Differentiation from first principles
Playlist 1 - Differentiation from first principles
Playlist 2 - Differentiation with polynomials, fractions and indices
Playlist 3 - Applications of differentiation
[These playlists are extended further in the Y13 section: Differentiation]
Open the simulation here to explore the derivative graphs of different functions.
Can you predict what they will look like before showing the answer?
Extra fun! The Essence of Calculus - Derivatives:
The Essence of Calculus - Geometric rates of change (up to 12:35 focuses on Y12 content, with the last part of the video moving into Y13 content):
The Essence of Calculus - Higher order derivatives:
Time for a history lesson...
Explore the derivative graphs of different functions.
Can you predict what they will look like before showing the answer?