Differentiation For JC Students: FREE Summary Sheet & Questions

No one likes differentiation – or do they? If you are a JC student, you probably already learnt differentiation and you may be overwhelmed with the amount of new ‘rules’ in A Level differentiation compared to secondary school differentiation. So many students whine and struggle with differentiation because it CAN be quite complicated to grasp every single concept well.

Truth be told, there is no easy way out to study for differentiation. But being systematic and consistent helps! Differentiation is one of those topics where it helps to really have a checklist of concepts and question types, and you just need to go through everything, building up your confidence until you achieve mastery.

Of course, having a great H2 Math tutor can immensely benefit you as well, as their clear explanations can help you comprehend the concepts better.

So, without further ado, here’s our very quick overview of the topics and concepts you need for A Level differentiation!

1. What is differentiation?

As you do more differentiation questions, you might come a point where you have lost the plot – what am I doing? What is differentiation, anyway?

In short, differentiation gives you the derivative (dy/dx) which is the rate of change of f(x) with respect to x. Geometrically, the derivative of a function is also the gradient of the function’s tangent at any given point.

That is why you would see differentiation in application questions relating to rate, like kinematics.

2. How to do differentiation?

Most of your math lessons would focus on this – how to differentiate various types of functions. Beginners would start with basic algebraic functions, and for A Level H2 Math you would need to know how to differentiate functions including trigonometric, exponential, logarithmic expressions.

It’s easy to forget or lose track or which ones you know – so it is good to refer to a summary checklist and do practices which target one concept at a time. Once you are more or less familiar with the individual skills, you can then attempt quizzes which mix the concepts to build up your confidence and speed of recall.

We have a handy summary of all the must-know techniques for differentiation in the downloadable guide below!

3. Applications of differentiation

We briefly mentioned applications of differentiation – mostly scenarios relating to rate. The thing about application questions is that you need to know what to do without the question telling you explicitly. For example, the question may ask you to find the rate, and you need to know that it means you have to do differentiation.

Also: context is important! An added step to application questions is checking that your answer makes sense for that scenario given in the question. For example, in some scenarios you cannot possibly have a negative value as your answer – in that case, you need to make sure your answer is positive.

4. Higher-order derivatives

A second derivative is basically what you get when you differentiate a function twice. First, you find the derivative of the function, then you differentiate that derivative to get the second derivative. The second derivative is the rate of change of the first derivative.

In terms of kinematics in physics, you can think of the first derivative as speed, and the second derivative as velocity. However, you could also go on and perform more higher-order derivatives like finding the third, fourth, or fifth derivatives.

5. Integration and differentiation

If there is an ‘opposite’ to differentiation, it would be integration. Although they are different ‘topics’, integration and differentiation are closely related and you will often find multi-part questions that combine these concepts.

As such, it is crucial to understand the relation between integration and differentiation, and be ready to tackle questions that involve both concepts.

Master differentiation with Math Tutors at Future Academy

Having issue with differentiation or other big topics like trigonometry is a big red flag for your math grades. Depending on where you are in your understanding, it can take quite a lot of time and effort to get up to speed with the complexities of the topic. Fortunately, our JC tuition teachers can be a great help in getting you organised with summarised notes, worksheets matched to your level, and effective explanations for students just like you!

Simply check our timetable to find a suitable class timing for yourself – or request a new class timing. We can’t wait to help you achieve your math goals!

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