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Differentiation

Differentiation

16 Powerpoints presentation for the following topics: Limits and convergence Basic rules for derivative The equations of tangent and normal lines Basic rules of derivatives The derivative of e^x and the derivative of ln x The product rule The quotient rule The chain rule for composite functions The second derivative and higher order derivatives Rate of change Velocity and acceleration functions Relative and global extrema Concavity Sketching a graph Optimisation problems
oralhurt
Summary / revision of basic differentiation

Summary / revision of basic differentiation

The powerpoint presentation revises all the knowledge/skills required for basic differentiation - finding gradients, stationary points and their nature, tangents and normals, increasing and decreasing functions. The accompanying document mirrors the presentation and is meant to be completed by the students by themselves or as you work through the presentation - the document then serves as a revision sheet for the whole topic of differentiation. Note that these resources were created specifically for the Level 2 Further Maths course but they would still work well for a summary of the methods for basic differentiation.
langy74
Set of resources to teach and practise differentiation

Set of resources to teach and practise differentiation

These resources are a great way to help introduce the skills and knowledge for basic differentiation. For each aspect of differentiation there are explanations and examples to go through with your class and then exercises with lots of questions for your students to attempt on their own. There is several lessons worth of work here and a really useful revision presentation and sheet. Note that these resources were created specifically for the Level 2 Further Maths course so only covers the differentiation of functions with positive integers powers. However, this may make it ideal for some groups where you want them to focus on the process/method for each type of question and not get bogged down with negative or fractional powers.
langy74
Worksheets on increasing / decreasing functions and sketching graphs

Worksheets on increasing / decreasing functions and sketching graphs

The first worksheet has an introduction and explanation about increasing/decreasing functions, a few examples to work through as a class and then an exercise with 11 questions for students to complete. Answers to the exercise are included. The second worksheet gives students some practice at using differentiation to help sketch graphs. There are a couple of examples to go through with your class and then an exercise with 7 questions. Solutions are provided. Note that this resource was designed specifically for the Level 2 Further Maths qualification, so only covers differentiating functions with positive integer powers such as y=5x^3-4x+2, but can still be used an introduction to the general method of increasing/decreasing functions and sketching.
langy74
Worksheets to practise finding stationary points and their nature

Worksheets to practise finding stationary points and their nature

The first worksheet introduces the method for finding the point(s) on a curve with a particular gradient. There are a few examples to work through as a class and then 16 questions for students to attempt. The second worksheet focuses on finding stationary points. Again, it explains the method, has a few examples to work through as a class and then 20 questions for students to complete. The worksheet then has a section that can be used to explain how to determine the nature of a stationary point by considering the gradient of the curve just before/after the point. There are some examples to do as a class and then 8 questions for students to complete. The final worksheet can be used to explain and practise using the second derivative for determining the nature of stationary points. Answers to all exercises are included. Note that this resource was designed specifically for the Level 2 Further Maths qualification, so only covers differentiating functions with positive integer powers such as y=5x^3-4x+2, but can still be used an introduction to the general method of finding stationary points on a curve.
langy74
Worksheet to practise finding the equation of a tangent/normal to a curve

Worksheet to practise finding the equation of a tangent/normal to a curve

This worksheet starts with a refresher of the 2 methods to find the equation of a straight line if we know its gradient and a point it passes through. The next section is on finding tangents. There is an introduction with an explanation of the method, a couple of examples to work through as a class, and then 15 questions for students to do themselves. The next section is on finding normals. Again, there is an introduction with an explanation of the method, a couple of examples to work through as a class, and then 10 questions for students to do themselves. All answers to the students questions are included. Note that this resource was designed specifically for the Level 2 Further Maths qualification, so only covers differentiating functions with positive integer powers such as y=5x^3-4x+2, but can still be used an introduction to the general method of finding tangents and normals to a curve.
langy74
Introduction to differentiation and finding the gradient of a curve

Introduction to differentiation and finding the gradient of a curve

The presentation and accompanying worksheet introduces the topic of differentiation by considering the gradients of progressively smaller chords that are used to estimate the gradient of the curve/tangent at the point. Students use this method to find the gradient at some points on the y=x^2 curve and then on the y=x^3 curve - from these results they should be able to guess at generalising the method for differentiating x^n and then ax^n. This presentation and worksheet take a while to work through so this may take up a whole lesson. The worksheet starts by reminding students how to differentiate and what dy/dx represents. In section A there are 18 examples of finding dy/dx to work through as a class, and then 30 questions for students to complete on their own. In section B there are a few examples of finding the gradient of a curve at a given point (to do as a class), then 10 questions for students to complete on their own. All answers are provided for the students' questions. Note that this resource was designed specifically for the Level 2 Further Maths qualification, so only covers differentiating functions with positive integer powers such as y=5x^3-4x+2, but can still be used an introduction to differentiation in general.
langy74
Clumsy Clive On Differentiation

Clumsy Clive On Differentiation

Clive is tackling a new topic on the GCSE curriculum, but predicatably is struggling. Four questions getting increasingly difficult requiring you to check as Clive has made mistakes. These will hopefully generate discussion in class.
alutwyche