# Advanced pure teaching resources: Integration

Resources and ideas for mathematics, advanced pure, integration, written by teachers to support teaching and learning

#### Integration Lesson Presentation

A PowerPoint designed to be used with a class that can answer the many questions asked in an introduction to indefinite, definite integration and deciding on the integration required to find many areas underneath or between curves. Good to present to a class who have 'show me' boards. Useful either as an introduction or as a revision.

#### VCE Specialist Mathematics 3&4 Differential Equations

Drawing slope fields, solving differential equations using TI Nspire CAS and Euler's method.

#### Trigonometric identities and equations handout

a summary of all the trigonometric identities, equations and formulae needed for A-level maths, including integration and differentiation, laid out in a easy to read reference sheet. Also includes a display revision sheet on differentiating and integrating sin and cos.

#### A2 Maths OCR C4 exam question by topic workbook - first order differential equations

Exam questions, mark schemes and answer space, for the topic of 'first order differential equations', from papers from June 2015 - Jan 2009. Format enables students to keep all work relating to this topic in one place.

#### OCR MEI notes (C3, C4 and M1)

Summary of OCR MEI A level Mathematics units, C3, C4 and M1.

#### IB and A level maths revision, C4 integration, volumes of revolution

Four challenging exam-like questions with fully worked out solutions for A level and IB students who want to test their knowledge of volumes of revolution (C4 Integration).In each question, a solid of revolution has to be subtracted from or added to the integral. The curve in one question is described by parametric equations. Another question uses trigonometric functions. The problem of finding the radius and height of cone/cylinder, is addressed in the solutions.

#### Core 2 (Edexcel) Revision

Here is my power point trying to structure questions for C2 from past papers. I have split the paper into 9 sections and tried to group questions together. All solutions are given at a click. For use by giving to pupils and leaving them to it, or working through topics as a class. Every question from 2006-present. Also works extremely well on iPads.

#### Core 1 (Edexcel) Revision

Here is my power point trying to structure questions for C1 from past papers. I have split the paper into 11 sections and tried to group questions together. All solutions are given at a click. For use by giving to pupils and leaving them to it, or working through topics as a class. Every question from 2006-present. Also works extremely well on iPads.

#### Integration of Trig Functions - Matching Pairs Memory Game

Test your students recall and memory with this great matching pairs memory game. Three different games all on one PowerPoint test integration of trig functions including sin x, cos x, tan x, plus variants of sec x, cosec x, cot x, etc. Great for revision with the whole class or individually.

#### A level Maths: Integration worksheets

Revision and using Partial Fractions

#### Calculus Definite Integrals: Volume of Solids

This AB calculus packet includes notes, examples, and 2 practice tests (with solutions and illustrations). In addition to the disk and washer methods, geometric cross sections and the shell (or cylinder) method are discussed. To preview content, try the mathplane sites. Thanks for visiting. We appreciate your support!

#### A level Maths C2: Definite Integration worksheet

Including to find areas

#### Maths for Engineers - Calculus

Presentation that introduces both differentiation and integration. It shows the students how to solve calculus problems using polynomial, trigonometric and exponential functions.

#### Further Pure 2 powerpoints

A set of powerpoints covering all topics in FP2. Examples labelled WB correspond to the separately attached 'Workbook' (I give this as a single booklet so pupils have a clear model answer to each topic). References to Exercises are from the Pearson Edexcel FP2 textbook. Mistakes on complex numbers now corrected.

#### Integration by parts

A complete .ppt file that covers integration by parts method including whiteboards activities based on differentiation and integration prior learning, treasure hunt activity, examples on integration by parts and exam questions.

#### Mathematics Core 3 C3 and Core 4 C4 Lessons

Mathematics Core 3 C3 and Core 4 C4 LessonsThis is a set of lessons for A2 Core Mathematics. The resources includes Powerpoints.Powerpoint include:Learning objectivesQuestions on the topicImportant information written in red boxes to scaffold learning.Topics:FunctionsTrigonometryExponentials and LogarithmsProduct RuleQuotient RuleDifferentiation and Integration of Trigonometry Roots to equations (staircase and cobweb diagrams)Integration using the chain ruleIntegration using the rule of LogarithmsIntegration by Substitution Integration by PartsMid ordinate rule and Simpsons RuleExpansion formulaAlgebraPartial FractionsApplications of Partial FractionsImplicit differentiation Tangents and normalsParametric Equation and Differentiation Exponential Growth and DecayDifferential EquationsVectorsI hope you enjoy these lessons, they can be used in the following ways:To deliver a course with reduced planning but not reducing quality of the lesson.As a basis for an observation lesson to save time preparing resources.To give to students for out of lesson learning.To support teachers who are new to this topic, again to reduce planning time.As a bases for your own lessons where you can include exam questions to each presentation.As an activity where the questions can be printed and cut out.

#### A Level Mathematics Matching Pairs Bundle

A collection of matching pairs for Higher GCSE or A Level. Can be used as whole class starters or revision exercise

#### Matching Pairs Integration of Polynomials

Matching pairs activity, built in PowerPoint, for use as a starter or revision activity with the whole class

#### Matching Pairs - Find the Differential

Great quick starter (in PowerPoint) to either introduce students to integration as a reverse of differentiation or as a revision tool. Useful as a whole class activity.

#### Integration of sine and cosine functions

Power Point presentation, 11 slides, Explaining how to find the indefinite integral of the sine, and cosine functions and how to evaluate the definite integral of the same functions; use some examples to show how to integrate trigonometric functions, based on Mathematics IB Standard level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7Olb1FMa3hMZ1Bva0E/view?usp=sharing

#### A level maths revision jigsaw

Jigsaw covers calculus, quadratics, coordinate geometry and many other first year A level topics. All 4 sheets can be cut up and then the learners can reassemble them to make a geometric shape.

#### Further Integration Test HL Mathematics

IB HL Mathematics Test on further integration with applications.

#### A level checklists for students

A collection of checklist for students to use, covering the Edexcel AS/A2 Mathematics specification: Core 1, Core 2, Core 3, Core 4 Mechanics 1, Mechanics 2 Statistics 1, Statistics 2 **updated Core 1 Checklist - tidied up format a little.

#### Integration questions and full solutions for whole topic C1,C2,C3,C4 and partial fractions

In class notes and solutions on Integration covers C1,C2C3,C4 (includes integration by substitution, partial fractions, by parts, form f'(x)/f(x) etc...)

#### C4 Integration Revision Guide Edexcel

This is a 12 page revision guide to C4 integration (Edexcel). It is useful once the chapter has been taught and to help the students prepare for the exam and revise this challenging topic. There are sections on Integration by inspection, substitution, parts, parametric integration, volumes of revolution and differential equations. Each section has revision notes, worked examples and questions to try. There are answers at the back.

#### Matching Pairs - Find the Differential

A great resources to use with your class. Either use it as an introduction to integration or as a revision of differentiation.

#### AP Calculus Visualizing The Fundamental Theorem of Calculus Study Guide

This calculus study guide will helps students differentiate between the height of a function, the average height of the function, the slope of a tangent line, the slope of a secant line, the area under a curve, and the change in height between two points. Students will compare these six characteristics of a function using an original function as well as it's antiderivative function.There are 16 total problems where students can draw in the visuals themselves. An answer key is also included. This study guide is great to help students understand the Fundamental Theorem of Calculus for the AP Calculus exam.

#### Areas under graphs

Suitable for Higher Tier GCSE Mathematics or Further Mathematics, this resource introduces students to a small variety of methods for working out areas underneath graphs. Starting with the counting of squares method, it introduces the Trapezium Rule and others. A chart at the end allows students to record the different estimates they have in order to compare methods, and it concludes with a few thoughts about real-world applications and the basis for integral calculus.

#### AP Calculus Memorization Packet

AP Calculus Memorization Packet has tables, graphs, definitions, explanations, and examples for just about every topic covered on the AP Calculus AB test. This study guide is always being updated and organized to be more clear and to help students. A general understanding of the topics and concepts is necessary for this study guide to be of use. A lot of information is packed into six pages, organized by topics. The topics include: derivatives, applications of derivatives, integrals, application of integrals, limits, and parent functions.

#### CIE Pure 3 - Integration PPQs with worked solutions

Here is a collection of past paper questions with detailed worked solutions on integration (substitution; by parts; by inspection etc) for the CIE P3 A-Level Mathematics course. Ideal for testing or independent practise for your pupils.Please leave a review and I will send you one free resource of your choice.