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Differentiation Tangents and Normals Part 2

Differentiation Tangents and Normals Part 2

This worksheet contains some demanding questions on tangents and normals, suitable for more able students. Detailed typed answers are provided to every question. I hope you find it useful. You can get more free worksheets on many topics, mix and match, with detailed step-by-step solutions at http://www.onemathsquestions.com
joezhou
Differentiation 1 - Tangents and normals

Differentiation 1 - Tangents and normals

Two worksheets on tangents and normals, starts off standard, the difficulty increases, later questions can be challenging. As always, detailed solutions are provided to every question. I hope you find it useful. You can get more free worksheets on many topics, mix and match, with detailed step-by-step solutions at http://www.onemathsquestions.com
joezhou
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