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Applications of differentiation (new A level) - notes, examples, exercises and a homework/test

Applications of differentiation (new A level) - notes, examples, exercises and a homework/test

This 18-page resource covers all the uses/applications of differentiation as required for the new A level. In every section it contains examples to work through with your class followed by an exercise of questions for students to attempt themselves (answers included). The sections are: 1. Tangents and normals - finding the equations of tangents/normals to curves 2. Stationary points - finding them and determining their nature using first or second derivative 3. Smallest and largest values of a function - finding min&max value of f(x) in a set of values for x 4. Practical problems - using differentiation to find optimal solution to a problem in context This projectable and printable resource will save you having to write out or create any notes/examples when teaching this topic. It also increases how much you can get through in lessons as students don't have to copy notes/questions and can work directly onto spaces provided for solutions. You could also email/print some or all of this for students who have missed lessons or need additional notes/practice/revision. Also included is a 2-page assessment that can be used as a homework or test. Fully worked solutions to this assessment are provided.
langy74
6 GCSE/IGCSE maths worksheets (with solutions)

6 GCSE/IGCSE maths worksheets (with solutions)

6 GCSE/IGCSE maths worksheets on the following topics: standard form, expanding brackets and factorising, fractions and differentiation. Solutions are included. From https://placeformath.blogspot.com.cy/p/worksheet-shop.html
math_w
Graph Sketching Discussion Venn Diagram

Graph Sketching Discussion Venn Diagram

Students are to think of a graph that would fit in all the regions of the Venn diagram. Three categories are: 1. Graphs with only 1 stationary point 2. Graphs with a maximum 3. Graphs that go through the point (0,1) This is really useful as a discussion activity for where graphs cross the axes and for differentiation. A sample set of answers is included.
wtongue
Graph Sketching Warm Up

Graph Sketching Warm Up

This resource was designed for my Y12s to help them practise the skills needed to sketch graphs (quadratics and cubics). Generally the outer ring of questions requires some on the inner questions in order to complete.
wtongue
Differentiation rules worksheet (with solutions)

Differentiation rules worksheet (with solutions)

A worksheet on the following differentiations rules: constant function rule, power rule, addition rule, product rule, quotient rule, exponential function rule, natural logarithm function rule and chain rule. Detailed solutions are provided. From https://placeformath.blogspot.com.cy/p/worksheet-shop.html
math_w
Differentiation worksheet (with solutions)

Differentiation worksheet (with solutions)

A worksheet on elemetary differentiation. The exercises require use of the power rule and the addition rule. Solutions are included. Good for GCSE/IGCSE students. From https://placeformath.blogspot.com.cy/p/worksheet-shop.html
math_w
Algebra with Fractions basics - help for KS5 (or KS4)

Algebra with Fractions basics - help for KS5 (or KS4)

This question sheet is aimed at A Level students who are struggling to do simple algebraic manipulation where fractions are involved. For the most part these are not typical 'algebraic fractions' questions (e.g. adding algebraic fractions), but are more basic than that. For example, I have encountered students who are otherwise working at fairly high grades but are unable to differentiate, say, 3x/4 because they cannot see that it is equivalent to 3/4× x (and hence simply x multiplied by a constant). Another issue is that students quite often ‘simplify’ fractions by trying to cancel in invalid ways.
pand
A-Level Maths - Core 1 - Complete Notes

A-Level Maths - Core 1 - Complete Notes

10 pages of neatly handwritten notes on the whole syllabus of Pure Core 1 (AQA). I usually use these to give to my students if they struggle to take notes and concentrate at the same time. It also acts as a handy detailed syllabus/plan of study, as well as just a revision tool for students: Sections of the notes: 1 - Straight Lines 2 - Quadratics 3 - Surds 4 - Simultaneous Equations 5 - Inequalities 6 - Algebraic Division 7 - Cubic Graphs 8 - Circles 9 - Differentiation 10 - Integration * - With 2 pages of worked exam solutions to go with regular examples throughout. Please have a look at some of my free IB notes if you would like to see the style of notes I am offering here. Hopefully there are none, but please let me know if you do see any errors! Also, let me know if there is any interest in other A-Level modules!
jwmcrobert
A2 MATHEMATICS: APPLICATIONS OF IMPLICIT DIFFERENTIATION

A2 MATHEMATICS: APPLICATIONS OF IMPLICIT DIFFERENTIATION

Complete lesson which builds upon the introduction. Students will be shown how to use their expressions for the derivative function to find stationary points, name tangents and normals. The resource is fully differentiated, contains an exam question and a challenge. Answers are included.
Weltmeister7
A2 MATHEMATICS: INTRODUCTION TO IMPLICIT DIFFERENTIATION

A2 MATHEMATICS: INTRODUCTION TO IMPLICIT DIFFERENTIATION

Complete lesson that introduces students to the art of finding the derivative of a function defined implicitly. The powerpoint explains the difference between explict and implicit functions and then shows students how, by applying the chain rule, we can differentiate any expression. The lesson sheet that accompanies it is fully differentiated, contains an exam question and a challenge question. The answers are included.
Weltmeister7