1. Resources Home
  2. Whole School
  3. Mathematics
  4. Advanced pure
  5. Roots of polynomials
Cubics: Expanding and factorising

Cubics: Expanding and factorising

With factorising and removing brackets of cubics being new to the GCSE specifications last year I have introduced these two lesson to my class teaching. Starting with removal of brackets students are able to extend from the two brackets situation to the three brackets. The following lesson looks at the more complicated factorising a cubic. Initially starting with the first factor given style of question before looking at factorising with no hint given. Worksheets are given for both lessons which could be used in class or as a piece of homework.
sjcooper
IB Maths HL - Complete Notes

IB Maths HL - Complete Notes

Complete notes, without any option topics, just the main topics 1 to 6 This is a collection of all of the notes I have written for my IB Maths HL class. They are handwritten, concise notes, covering the whole course in 77 pages. Topic 1 - Algebra - 21 Pages Topic 2 - Functions - 10 Pages Topic 3 - Trigonometry - 6 Pages Topic 4 - Vectors - 10 Pages Topic 5 - Statistics & Probability - 10 Pages Topic 6 - Calculus - 20 Pages If you would like to see what you would be getting, you can download Topic 1 of IB SL or IB Math Studies for free. I hope you enjoy, and please ‘follow’, as I will be uploading other IB resources soon.
jwmcrobert
Surds topic

Surds topic

4 full lessons 1 homework lesson 1 - introduction to surds lesson 2 - simplifying surds lesson 3 - rationalising the denominator lesson 4 - conjugate rationalising the denominator Please review and follow For more resources: https://www.tes.com/teaching-resources/shop/osmith25
osmith25
Conjugate rationalising the denominator lesson

Conjugate rationalising the denominator lesson

Lesson includes Title, date, objective, success criteria, key words Starter Discussion task Definitions and examples AfL quick fire questions AfL true or false AfL misconceptions questions Chilli challenge questions Accessible for lower ability and challenge high ability Plenary FUSE Please leave a review For more resources: https://www.tes.com/teaching-resources/shop/osmith25
osmith25
Using Quadratic formula

Using Quadratic formula

A powerpoint introducing using the quadratic formula to solve quadratic equations. A worksheet for students to create their own equations to solve. Students roll dice to choose coefficients, then write the equation in their books and solve. No solutions due to huge amount of possible questions. Need dice for lesson
cmlk20
Edexcel Further Core Pure AS

Edexcel Further Core Pure AS

These notes and examples contain everything you need to deliver the new Edexcel Further Core Pure AS content. There are 6 student booklets and 6 teacher booklets containing detailed solutions to all examples.
Omega
Edexcel Further Core Pure AS Topic 2: Further Algebra

Edexcel Further Core Pure AS Topic 2: Further Algebra

These notes and examples are designed for the delivery of the new Edexcel A Level Further Maths Linear Specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload. Each topic is available as a separate purchase, or you can download the entire set covering all the the Core Pure AS content. To purchase the complete set of notes for the Core Pure AS content, click here: [https://www.tes.com/teaching-resource/edexcel-further-core-pure-as-11890483]
Omega
Curve sketching and trig formulae and revision notes

Curve sketching and trig formulae and revision notes

Revision notes with formulae. Can be used for revision or as a formulae sheet. Includes: Standard graphs with descriptions. Continuous and discontinuous functions Finding maxima and minima Division of polynomials Converting between degrees and radians, including common angles in degrees and radians Arc lengths, sectors and segments Sine and cosine rule Double angled and half angled formula
Chris11494
Edexcel New Maths A Level year 1 complete notes

Edexcel New Maths A Level year 1 complete notes

These notes and examples cover all of the content for the new linear Edexcel maths A Level: pure maths, statistics and mechanics. Answers are included to all worked examples. There are 12 pure maths booklets, 4 mechanics booklets and 7 statistics booklets, provided everything you need to teach the new specification.
Omega
Algebra: Remainder Theorem + Worksheet - perfect for AS Level

Algebra: Remainder Theorem + Worksheet - perfect for AS Level

This is a whole lesson on the different aspects of learning the remainder theorem. 27 slides + worksheet. The lesson includes: A starter linking to solving quadratics and factorising Learning objectives key words 2 AFL activities around the key words (avoids confusion when doing exam questions) quick few examples and activities on factorising (reminder only) Method One: Long Division (1 example and 1 question) Method Two: Introspection (2 examples and 1 question) - my preferred method as I think it makes why it works much clearer and builds a better understanding. WORKSHEET with ANSWERS! Plenary - 3 questions that can fully factorise. NOTE: Feel free to browse my shop for more excellent free and premium lessons and as always please RATE and FEEDACK, thank you!
ajf43
Geometric Sequence Worksheets

Geometric Sequence Worksheets

These are two worksheets on geometric sequence, each question has full step by step solutions. I hope you find these useful. You can get more free worksheets on many topics, mix and match, with detailed step-by-step solutions at our website link on the worksheets
joezhou
Binomial Theorem, Partial Fractions, Complex Numbers

Binomial Theorem, Partial Fractions, Complex Numbers

Three homeworks and a set of extended questions on the topics of Expansions with the Binomial Theorem Using Partial Fractions Complex Numbers, operations, polynomials, Argand diagrams and De Moivres Theorem All provided with comprehensive solutions
dh2119
Partial Fractions

Partial Fractions

Differentiated A level lesson plan and presentation to help students understand Partial Fractions. Starter, task, assessment and plenary for the lesson
Edustem1
Notes and Examples for Edexcel A Level Maths Year 1 Topic 7: Further Algebra

Notes and Examples for Edexcel A Level Maths Year 1 Topic 7: Further Algebra

These notes and examples are designed for the delivery of the new Edexcel A Level Maths Linear Specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload. Each topic is available as a separate purchase, or you can download the entire set covering all the the Year 1 pure maths content. To purchase all year 1 pure topics, click here: https://www.tes.com/teaching-resource/notes-and-examples-for-a-level-maths-year-1-pure-11821867 To purchase the complete notes for the entire year 1 syllabus (pure, statistics, mechanics), including large data set activities, click here: https://www.tes.com/teaching-resource/edexcel-new-maths-a-level-year-1-complete-notes-11872425
Omega
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2012"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2012"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2012 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Sketching Quartic Graphs table

Sketching Quartic Graphs table

A table which helps pupils to sketch quartic graphs. Some questions where pupils are required to work backwards, such as using the graph to work out equation.
FawziyahR
40 slide Powerpoint Advanced Higher Maths Complex Numbers Argand Diagrams Worked Solutions

40 slide Powerpoint Advanced Higher Maths Complex Numbers Argand Diagrams Worked Solutions

40 slide Powerpoint for Advanced Higher Maths Unit 2: Complex Numbers. There is a brief revision of the basics of Complex numbers followed by a series of questions. The 24 questions (many of them multi-part) require the construction of Argand Diagrams, use of the quadratic formula, polynomial long division, and simultaneous equations. There are fully worked solutions (including diagrams) for complex number topics relating to: Equating Real and Imaginary Parts; Finding square, cube, fourth, fifth and sixth roots of complex numbers (including unity) and plotting them on an Argand diagram; Verifying and finding roots of complex number polynomials; Expanding and simplifying complex numbers using the Binomial Theorem and De Moivre’s Theorem; Interpreting geometrically loci in the complex plane; Conversions between polar and rectangular forms; Complex Conjugates; Exponential Form; Trigonometric identities, substitutions and simplification. The questions are grouped in approximate order of difficulty and to match the usual order of progress through this topic. *Animated workings come up line by line on mouse clicks.*
biggles1230
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2013"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2013"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2013 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2014"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2014"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2014 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2015"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2015"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2015 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2016"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2016"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2016 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Algebraic methods Edexcel A-level Year 1/AS Pearson Ch 7

Algebraic methods Edexcel A-level Year 1/AS Pearson Ch 7

Presentation covering the whole of chapter 2 (4-6hrs) from the Pearson Edexcel Pure Mathematics Year 1/AS book. Includes examples (for the proof examples there are only questions, I worked through these with the students on the board) and notes for; Algebraic fractions Dividing polynomials The factor Theorem Mathematical proof Methods of proof Suitable for the new A-Level specification year 1 or AS-level. Also suitable for able GCSE students. Presentation designed to be used as teaching aid for entire block of lessons. Opportunities for students to work through examples on whiteboards, and notes on key points. All learning objectives included and maintained throughout the presentation. Editable for you to select you own questions or add consolidation work. OTHER CHAPTERS AVAILABLE
domgosli
Solving Quadratic Equations

Solving Quadratic Equations

These three worksheets combined have 180 quadratic equations. On the first page of 'Solving Quadratic Equations 1' the equations are organised by type of factorising: Highest Common Factor, Difference of Two Squares and Product-Sum Method. On the second page, the same three types have been mixed up, and students need to identify which type of factorising to use. 'Solving Quadratic Equations 2' and 'Solving Quadratic Equations 3' are more difficult, and can be used as a differentiated task either done in class or set for homework. 'Solving Quadratic Equations 3' is targeting students who are aiming for a grade 9. All three worksheets have answers. For your convenience, the Word files are included.
mathsmuscateer
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
Partial Fractions Codebreaker 3

Partial Fractions Codebreaker 3

The usual terrible joke revealed having dealt with partial fractions with mixed numbers (a remainder) and partial fractions with (x+n)^2 on the denominator.
alutwyche
Binomial Expansion Worksheets

Binomial Expansion Worksheets

This worksheet bundle contains questions on binomial expansion for positive integer power index n. Detailed typed answers are provided to every question. I hope you find it useful. You can get more worksheets on many topics, mix and match, with detailed step-by-step solutions at http://www.onemathsquestions.com
joezhou
Graphs and transformations Edexcel A-level Year 1/AS Pearson Ch 4

Graphs and transformations Edexcel A-level Year 1/AS Pearson Ch 4

Presentation covering the whole of chapter 4 (6-8hrs) from the Pearson edexcel Pure Mathematics Year 1/AS book. Includes examples and notes for: Cubic graphs Quartic graphs Reciprocal graphs Points of intersection Graph transformations Translating graphs Stretching graphs Transforming functions Suitable for the new A-Level specification year 1 or AS-level. Also suitable for able GCSE students. Presentation designed to be used as teaching aid for entire block of lessons. Opportunities for students to work through examples on whiteboards, and notes on key points. All learning objectives included and maintained throughout the presentation. Editable for you to select you own questions or add consolidation work. OTHER CHAPTERS AVAILABLE
domgosli
Roots of Quadratics- Sum and Products

Roots of Quadratics- Sum and Products

Aimed at KS5 pupils and pupils doing further maths IGCSE full lesson with ppt and worksheets (worksheets are from SRWhitehouse thanks for posting them as the work set in the PPT relates to Edexcel IGCSE Further Pure Maths text book) PPt has full worked examples, starter on finding the descriminant and finding how many roots a quadratic has). Introduces the roots and sums and products. Opportunity for group discussion with full work examples. (amended one slide 03/11)
commuter
Curve Sketching

Curve Sketching

A full lesson on sketching cubics, quartics and reciprocal functions. Incorporates the use of GeoGebra and the Casio fx-991EX Classwiz. Please do leave feedback! Thank you.
cparkinson3
IB Maths HL - Topic 2 Functions - Notes

IB Maths HL - Topic 2 Functions - Notes

Handwritten notes that I made for my HL students on Topic 2 in the IB - Functions. It includes: 2.1 - Concepts (Domain, range, composite, inverse, domain restriction, odd/even functions) 2.2 - Graph Features (Intercepts, asymptotes, absolute value graphs) 2.3 - Transformations 2.4 - Rational, Log, Exp. graphs 2.5 - Polynomials (+ factor and remainder theorem) 2.6 - Quadratics (+ sum and product of roots for quad. and poly.) 2.7 - Inequalities If you are an HL teacher (or student) and you found these helpful, please 'follow' me, then you will see as soon as I get around to uploading the remaining topics of the HL course (Feb/March/April 2018).
jwmcrobert
Algebra: Cubic Graphs & Factor Theorem (+ resources) - perfect for higher tier & AS level

Algebra: Cubic Graphs & Factor Theorem (+ resources) - perfect for higher tier & AS level

This is a whole lesson. 20 slides + resources. It starts looking at drawing cubic graphs, before quickly moving on to looking at sketching them and developing the understanding and skills to do so. It looks at working out the key points needed and using the factor theorem and factorising in order to do so. The lesson comes with a starter, several little MWB activities, worksheet, excellent teaching slides, a handout of all the different graphs and plenary. NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!
ajf43
Lesson on Remainder Theorem and Factor Theorem

Lesson on Remainder Theorem and Factor Theorem

This is lesson on remainder and factor theorems. The bundle contains both the lesson presentations with 'overlay animations', where steps are reviewed one at a time. There is also an accompanying presenter view pdf for teachers for each lesson ppt. The documents are prepared meticulously with LaTeX, I hope you find these useful. In addition, you can get unlimited number of high quality practice questions and solutions for both lessons on my website: www.onemathsquestions.com. They are under topics "Polynomial Division". You can generate the worksheets yourself, and each question will come with a set of very detailed step by step solutions, set out in exactly the same way as the lesson presentation examples. Hope you find these useful, and if you have any comments or suggestions, please feel free to contact me through TES or my website. Best wishes, Joe
joezhou
Algebra: Quadratic Graphs BUNDLE (3 Lessons) - ideal for years 10 - 12

Algebra: Quadratic Graphs BUNDLE (3 Lessons) - ideal for years 10 - 12

This is a three lesson sequence of lessons on quadratic graphs, with the first two containing the material needed for GCSE and the third lesson the additional material needed for AS-Level. 1. Introduction 2. Gradients and Other Problems 3. Further Problems NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!
ajf43
Algebra: Quadratic Graphs 2 - Gradients & Other Problems (+ resources)

Algebra: Quadratic Graphs 2 - Gradients & Other Problems (+ resources)

This is second of two whole lessons on teaching the various aspects of quadratic graphs containing the various aspects introduced with the new 9-1 GCSE syllabus. The first lesson being the introduction is important to go through before this lesson and this builds on it by looking at problems involving the gradient. 14 slides. This lesson is available with two other lessons on quadratic graphs as a three-lesson bundle and a reduction and is highly recommended as an excellent sequence of lessons. NOTE: Feel free to browse my shop for more free and premium resources! As always please RATE and FEEDBACK (comments good or bad) thank you!
ajf43
Lesson on Simultaneous Equations where one equation is linear and one quadratic

Lesson on Simultaneous Equations where one equation is linear and one quadratic

This is lesson on solving simultaneous equations where one equation is linear and the other is quadratic. The bundle contains both the lesson presentations with 'overlay animations', where steps are reviewed one at a time. There is also an accompanying presenter view pdf for teachers for each lesson ppt. The documents are prepared meticulously with LaTeX, I hope you find these useful. In addition, you can get unlimited number of high quality practice questions and solutions for both lessons on my website: www.onemathsquestions.com. They are under topics "Simultaneous Eqn Linear Quad". You can generate the worksheets yourself, and each question will come with a set of very detailed step by step solutions, set out in exactly the same way as the lesson presentation examples. Hope you find these useful, and if you have any comments or suggestions, please feel free to contact me through TES or my website. Best wishes, Joe
joezhou
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
AS Level 2017 Mathematics Lesson 23 and 24 Curve Sketching

AS Level 2017 Mathematics Lesson 23 and 24 Curve Sketching

Two lessons which slowly take students through the basics of curve sketching. The powerpoints show students how to get a hold of the shape of each curve (quadratic, cubic, quartic, reciprocal), the role the sign of the dominant terms plays and the effect of repeated roots (tangency). The powerpoints contain a starter of basic material in the A level course so far and the worksheets are fully differentiated. One of these can easily be used with KS4, the other should only be used for high achievers
Weltmeister7
Logarithm Questions Part 2

Logarithm Questions Part 2

These are worksheets on logarithms, worksheets 3 and 4, containing more demanding log equations. 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