# Advanced pure teaching resources: Further functions

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

#### 1-9 GCSE EXAM PAPER ON COMPOSITE AND INVERSE FUNCTIONS

A GCSE paper made up of differentiated questions on composite and inverse functions. This is a 1 hour activity.Step-by-step worked solutions are provided. The questions get harder as you go along.
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#### Algebra Bundle 20% off

A bundle of my algebra premium resources, Algebraic Fractions, Compositie Functions, Iterations, Equations of Linear Graphs,, Substitution, Roots and Turning Points.All fully differentiated and suitable for new curriculum with plenty of problem solving, reasoning ect. Soltions for all tasks included.
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#### Piecewise and Absolute Value Functions Matching Game

This is a matching activity. The students are given 6 of each of the following: table of values, absolute value functions, piecewise functions, and graphs. They have to make 6 matching sets (table of values, absolute value function, piecewise function and a graph). 4 pages total.Answer key is included.

#### Composite Functions

A series of lessons (2-3) on finding and solving equations of composite functions. It gives the pupils plenty of opportunity to become familiar with the notation of f(x) ect and using this to substitute numbers into an expression. It then gives pupils the chance to find fg(x) ect and then moves onto solving equations suh as fg(x) = gf(x). There are also problem solving tasks to develop pupils learning.All tasks are differentiated, 2-4 levels for each task to make it accessible to all pupils but also to stretch the more able. All tasks have full solutions to it is easy to peer and self assess during the lesson. The lesson includes reasoning and problem solving tasks which ensure that this is suitable for the 9-1 GCSE curriculum. I have used this lesson and pupils were engaged yet challenged.
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#### A level maths - 1st year

Selection of presentations that cover most of the 1st year pure maths in the A level maths course
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#### A level maths - 2nd year

Selection of presentations that cover most of the 2nd year pure maths in the A level maths course
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#### Further maths A level

Presentations that covers areas of the further maths A level units
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#### Mathematics of Finance

Mathematics of Finance is one of the topic which is covered during Mathematics lectures and seminars in order to enhance students knowledge.During this Lecture and Seminar we are covering following subtopics (Agenda):- Indices and logarithms and their rules- Exponential functions- Applications of exponential functions- Limit and continuity of functions In this File you will find:- 1 Mathematics of Finance Lecture Power Point Presentation 28 Slides- 1 Seminar Plan - 19 Seminar Activities with full answer list for studentsAll covered materials are taught for bachelor level students Level 3.Please write your comments once you purchase this lesson in order to have some suggestions for further improvements of teaching materials.
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#### Derivative of Univariable Functions

Derivative of Univariable Functions is one of the topic which is covered during Mathematics lectures and seminars in order to enhance students knowledge.During this Lecture and Seminar we are covering following subtopics (Agenda):- Meaning of derivatives- Differentiation rules of univariate functions - Applications of derivativesIn this File you will find:- 1 Derivative of Univariable Functions Lecture Power Point Presentation 28 Slides- 1 Seminar Plan - 19 Seminar Activities with full answer list for studentsAll covered materials are taught for bachelor level students Level 3.Please write your comments once you purchase this lesson in order to have some suggestions for further improvements of teaching materials.
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#### Multivariable Functions

Multivariable Functions is one of the topic which is covered during Mathematics lectures and seminars in order to enhance students knowledge.During this Lecture and Seminar we are covering following subtopics (Agenda):- Space Rn- Multivariable functions and their properties- Applications of multivariable functionsIn this File you will find:- 1 Multivariable Functions Lecture Power Point Presentation - 1 Seminar Plan - 21 Seminar Activities with full answer list for studentsAll covered materials are taught for bachelor level students Level 3.Please write your comments once you purchase this lesson in order to have some suggestions for further improvements of teaching materials.

#### Roots and Turning Points

A series of lessons (2-3) on finding the roots and turning points equations. It recaps the skills required such as solving, factorising and completing the square on a quadratic and then develops these skills to find roots and turning points of an equation. There are plenty of reasoning tasks suitable for the new curriculum and this stretches the more able to understand the properties of graphs. There are also algebraic questions and links it to sketching graphs.All tasks are differentiated to 3 or 4 levels to allow the skill to be practiced and then to stretch and challenge the more able. All tasks have either worked solutions or typed solutions so that the pupils can self mark. This has been used with top set year 11, all pupils engaged and made good progress.
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#### VCE Mathematical Methods Unit 3 Functions and Graphs

Set of lesson plans (presentations) wit carefully selected examples , class activities, assessment, TI Nspire handouts.

#### Limits 1 – Circuit Training

Limits 1 – Circuit TrainingWork out the problem in the cell #1. To advance in the circuit, find your answer and mark that cell #2. Work out that problem and then find your answer again. Continue working in this manner until you complete the circuit.There are 24 problems in this product.All answers are included.My students love doing these activities.Thank you for checking my resources.

#### 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.

#### Functions

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) Higher Tier syllabus. The 36 questions in this booklet can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. Calculators are not allowed for the questions in this booklet.Topics covered in this booklet are: evaluating f(x) for given values of x, finding x for given values of f(x), composite functions, inverse functions and applying transformations to graphs and functions.This booklet has excellent examples of questions of the new topics in the reformed GCSE Mathematics (9-1) curriculum.
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#### Geometry: Trigonometry (Trig) 8 lesson bundle - perfect for GCSE/IGCSE

Lesson (1 - 3) - very detailed look at what I call basic Trig (soh,cah,toa) Lesson 4 - sine rule Lesson 5 - Cosine rule Lesson 6 - Trig area rule Lesson (7 -8) - trig graphs ... there is quite a lot of A-Level (C1) material involved, however, additional A-Level material (C2-C4) will be uploaded separately. This is perfect for covering ALL aspects of the KS4 curriculum, whether iGCSE or GCSE. NOTE: Feel free to browse my shop for more excellent free and premium resources, and as always please rate and feedback, thanks.
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#### Plotting Rational Functions

A large selection of presentations and activities that show the learners how to sketch rational functions. It includes intercepts, asymptotes and also looks at substituting small and large values of x so students can collect all the data needed to sketch the graphs.Also includes finding the min/max point on a graph without using calculusSMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.
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#### 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.

#### Modelling exponential growth and decay.

Modelling exponential growth and decay. Effective use of technology. Carefully chosen examples with full solutions. The zipped file contains student handout, teacher handout and tns file.

Suitable for Years 10/11/12/12. Add Maths and A level Maths.Plenty of practice questions on Functions.

#### Geometry: Trig Graphs 2 - Further Trig Graphs (+ matching activity)

This is designed to be the second lesson on trigonometric graphs looking at the amplitude and period as well as equivalent values. This comes with an excellent matching activity, as well as questions on the slide, excellent teaching slides, lesson objectives, a starter an plenary. I normally at a KS4 level, whether GCSE/ iGCSE over two lessons, with additional lessons needed for different modules at A-Level. I will again look to upload additional lessons in the future. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thanks.

#### Geometry: Trig Graphs 1 - Drawing basic trig graphs

This is designed as a first lesson or introduction to trig graphs. It is pretty extensive with 27 slides, lots of little activities and animation. I often follow this lesson up with the 'Spaghetti Lesson' and will look to upload this at some point. I normally at a KS4 level, whether GCSE/ iGCSE over two lessons, with additional lessons needed for different modules at A-Level. I will again look to upload additional lessons in the future. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thanks.
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#### International Baccalaureate Standard Level bundle

All my published IB Standard Level resources including full revision package at a discounted price.

#### Implicit and Parametric functions

A pair of presentations that explain what Implicit and Parametric functions are and how you can differentiate them. Presentations have detailed explanations and clear worked examples of exam style questions.SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.
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#### C3 / C4 revision package! Super discount!

A super package of C3 / C4 revision files with thousands of questions. Includes trigonometric relations, vectors, integrals (how do you work them out?) and mixed questions with extra topics, at a discounted price!

#### Inverse Function, Range, Domain and Composite Functions

A selection of presentations that shows learners how to find the inverse of a function. The presentations also clearly explains the range and domain of a function. The composite functions presentation starts basic explaining how to use function notation and then leads onto more complicated examples and questions for learners to attempt. Also includes a range and domain jigsaw for students to use to create a poster. SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.

#### Modulus Fuction

This large presentation introduces the modulus function and its graph. It covers how to sketch a modulus graph and also has questions for students to do. It then moves into solving modulus functions both algebraically and using the graphs. SMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.
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#### C4 mark scheme bundle

This bundle includes all of the C4 worksheet mark schemes, if you purchase all of the mark schemes together they will be discounted by 50%.
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#### C4 binomial expansion mark scheme

**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 worksheet mark scheme with examination style questions on the topic Binomial Expansion. Each question has the value of marks it is worth on the right hand side. The worksheet can be used as homework, in-class or even an assessment.
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#### C4 parametric equations mark scheme

**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 worksheet mark scheme with examination style questions on the topic Parametric Equations. Each question has the value of marks it is worth on the right hand side. The worksheet can be used as homework, in-class or even an assessment.