Polynomials

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Word Doc (Polynomials Only)

Word Doc (Whole Chapter)

PDF (Polynomials Only)

PDF (Whole Chapter)

AS Maths – Pure – Algebraic Fractions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

7A Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video

Bicen Maths Live Lesson

Factor Theorem 1 • Simplifying Algebraic Fractions • P1 Ex7A • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 1-5✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 387b: Simplify algebraic fractions where factorising out a common term in one of the numerator or denominator is required.
• 387c: Simplify algebraic fractions where factorising out a common term in both the numerator and denominator is required.
• 387d: Simplify algebraic fractions where factorisation of a simple quadratic on the numerator or denominator is required.
• 387e: Simplify algebraic fractions where factorisation of a simple quadratic on both the numerator and denominator is required.
• 387f: Simplify algebraic fractions where factorisation of a non-monic quadratic expression on the numerator or denominator is required.
• 387g: Simplify algebraic fractions where factorisation of a non-monic quadratic expression on both the numerator and denominator is required.
• 387h: Simplify algebraic fractions where one factorised term is a negative of another.
• 387: Exam Practice: Simplifying single algebraic fractions by cancelling common factors

Practice Questions

• Practise Questions

Other Videos

Simplifying Algebraic Fractions

Courtesy of Maths Genie (Some Multiplication & Division too)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Underground Maths Functions Builder II✦

Worksheets

• The Chalk Face Algebraic Fractions
• kutasoftware Worksheets
  • Simplifying Rational Expressions
• MadAsMaths (T. Madas)
  • Algebraic Fractions Exam Questions Q9, 20 (difficulty 3 of 5)
  • Algebraic Fractions Simplifying Rational Expressions Q1–7

AS Maths – Pure – Dividing Polynomials

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

7B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Factor Theorem 2 • Long Division • P1 Ex7B • 🤖

Factor Theorem 3 • Polynomial/Algebraic Division • P1 Ex7B • 🤖

Factor Theorem 4 • Division with 0 as x or x^2 coefficient • P1 Ex7B • 🤖

Factor Theorem 5 • Quadratic Divisors • P1 Ex7B • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 6-12✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 497a: Determine a factor from algebraic division of a quadratic or cubic expression, given another factor (no zero coefficients).
• 497b: Determine a factor from algebraic division of a cubic expression with zero coefficients, given another factor.
• 497c: Determine a factor from algebraic division of a polynomial of degree >3 given another factor.
• 497d: Determine the quotient and remainder from an algebraic division (no zero coefficients).
• 497e: Determine the quotient and remainder from an algebraic division (with zero coefficients).
• 497f: Determine the quotient and remainder for a division by a quadratic expression.
• 497g: Turn a top-heavy algebraic fraction into a form involving a quotient and remainder.
• 497h: Determine the original function given the divisor, quotient and remainder.
• 499a: Determine the remainder when a polynomial is divided by a linear expression. (not yet active)
• 499b: Use the remainder theorem to find an unknown coefficient. (not yet active)
• 499c: Use the remainder theorem to find two unknown coefficients. (not yet active)
• 497: Exam Practice: Algebraic division
• 499: Exam Practice: The remainder theorem

Practice Questions

• Practise Questions

Other Videos

Algebraic Long Division

Dividing Polynomials using the Grid Method

Courtesy of Maths Genie

Algebraic Long Division – Corbettmaths

Corbett Maths Algebraic Long Division

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Polynomial Division (Extends into Remainder Theorem)

Activities

• Berwick Maths Diagnostic Questions
• Longman Cheshire Fun Sheet: Algebraic division✦
• ayoob Dividing Polynomials (Not by Long Division)✦ (TES Account Required) 
• Underground Maths Divide It Up✦
• Andy Lutwyche
  • Codebreaker – (Dividing)
• Math = Love (Sarah Carter)
  • Box Method Division puzzles
  • Box Method Division Activity
  • Box Method Division Foldable
• Transum
  • Polynomial Division
• thewessens.net Classroom Apps
  • Polynomial Division with Exploding Dots (a visual alternative to long division)

Worksheets

• Jethwa Maths Starter Activity (p3-4)
• kutasoftware Worksheets
  • Dividing Polynomials
  • Dividing Polynomial Functions
• Mathshelper (Jon Stone)
  • Polynomial Division
• MadAsMaths (T. Madas)
  • Cubic Sketching✦ Q13–14
  • Polynomials Exam Questions (Intro) Q9, 14–15, 19–20, 28, 31–33, 41, 48, 51, 54–55, 57, 59–60, 63 (difficulty 2–4 of 5)
  • Polynomials Q1, 3, 6, 11–12 (difficulty 2–4 of 5)
• Starting Points Maths
  • Polynomial Division Using Exploding Dots (by Kieran McConville) · PDF

AS Maths – Pure – Factor Theorem

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

7C Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video

Bicen Maths Live Lesson

Factor Theorem 6 • The Factor Theorem • P1 Ex7C • 🤖

Factor Theorem 7 • Factorising using Factor Theorem • P1 Ex7C • 🤖

Factor Theorem 8 • Finding Unknown Coefficients using the Factor Theorem • P1 Ex7C • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 13-17✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 498a: Determine whether a linear expression is a factor of a polynomial.
• 498b: Determine a factor of a polynomial using the factor theorem.
• 498c: Factorise a cubic when one of the factors is known.
• 498d: Factorise a cubic expression using the factor theorem, where a factor is not known.
• 498e: Use the factor theorem to find a unknown coefficient.
• 498f: Use the factor theorem to find two unknown coefficients.
• 498g: Factorise the sum and difference of two cubes.
• 500a: Solve cubic equations given in the form x³ + bx² + cx = 0, solvable by factorisation.
• 500b: Solve cubic equations given in the form ax³ + bx² + cx = 0, solvable by factorisation.
• 500c: Solve cubic equations using the factor theorem, given one of the roots.
• 500d: Solve cubic equations given in the form x³ + bx² + cx +d = 0, solvable by factorisation.
• 500e: Solve cubic equations given in the form ax³ + bx² + cx +d= 0, solvable by factorisation.
• 500f: Solve cubic equations with only one rational solution.
• 500g: Show that a cubic has one real solution only. (not yet active)
• 498: Exam Practice: The factor theorem
• 500: Exam Practice: Solving cubic equations

Practice Questions

• Practise Questions

Videos & Other Multimedia

Factor Theorem – Corbettmaths

Corbett Maths Factor Theorem

Dividing Polynomials using the Grid Method

Courtesy of Maths Genie (From 4:21)

Rational Root Theorem – Rational Zero Theorem – for Polynomials

Radford Mathematics Rational Root Theorem

The Method No One Taught You – Finding the Tangent to a Curve

The Method No One Taught You – Finding the Tangent to a Curve by Dr Barker (Using the Remainder Theorem)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Mathematics Assessment Project Representing Polynomials✦ (strong links to sketching cubics and transformations, a good true or false section)
• Susan Wall, MEI Factor Theorem Activities✦ Similar to Above)
• Standards Unit Factorising Cubics✦
• Joe Berwick via variationtheory.com Polynomial Division and the Factor Theorem✦
• Andy Lutwyche
  • Cubics Codebreaker
• Goal Free Problems
  • A-Level Algebra & Coordinate Geometry set Q7, Q30

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Fill In The Blanks (Word | PDF | Answers)
• Corbettmaths
  • Factor Theorem Practice Questions & Solutions
• Jethwa Maths Starter Activity (p7-8)
• kutasoftware Worksheets
  • Graphs, Real Zeros, and End Behavior (Sketching Graphs but requires Factor Theorem to help Factorise)
  • Factors and Zeros
  • The Remainder Theorem (Q7-14)
  • The Rational Root Theorem (Really good to use at start before deciding what to ‘try’)
  • More on Factors, Zeros, and Dividing (Not Q15)
• Mathshelper (Jon Stone)
  • Factor & Remainder Theorem
  • Factor Theorem Cubic Solving
• Maths Genie
  • The Factor Theorem: Questions · Solutions · Lesson · Topic page
• Physics & Maths Tutor
  • Factor Theorem: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• Dr Oliver Mathematics
  • Factors questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Cubic Sketching✦ Q15–19
  • Cubics Exam Questions✦ Q3, 5, 10, 12–13, 15, 20 (difficulty 3–4 of 5)
  • Equations Exam Questions I Q28, 43 (difficulty 3–4 of 5)
  • Identities Q24, 26 (difficulty 4 of 5)
  • Polynomials Exam Questions (Intro) Q2–5, 8, 10–13, 17–18, 21–27, 29–30, 34–40, 42–47, 49–50, 53, 56, 58, 61–62, 64, 66 (difficulty 2–4 of 5)
  • Polynomials Practice (Intro) Factorizing Polynomials Q1–15; Solving Polynomial Equations Q1–3
  • Polynomials Q2, 5, 7, 9 (difficulty 3–4 of 5)
• Starting Points Maths
  • Cubic Polynomials: Factorise and Sketch (by Mr Cooke)

Whole Topic Videos

Factor Theorem 9 • Exam Q • P1 Ex7C • 🤖

Bicen Maths Exam Questions

Worksheets

• SRWhitehouse Factor and Remainder Theorem✦ (TES Account Required) Selection of Worksheets Covering the Whole Chapter (Minus Proof)
• MathedUp
  • Polynomial functions: Questions · Challenge · Answers
• Maths Genie
  • Algebraic Methods: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 1 Algebra and Functions: Worksheets · Unit Test
• MME
  • C1 Polynomials: Questions | Answers
• Joe Berwick (BerwickMaths)
  • Algebraic methods worksheets✦
• MadAsMaths (T. Madas)
  • Polynomials Exam Questions (Intro) Q65, 67 (difficulty 4–5 of 5)
• Dr Austin Maths
  • Algebraic Methods Revision Practice Grid (Word | PDF | Answers)
  • Algebraic Division Sort It Out (Word | PDF | Answers)
  • Using the Factor Theorem Match-Up (Word | PDF | Answers)
  • Harder Factor Theorem Practice Strips (Word | PDF | Answers)
  • Factorising Cubics Name the Film (Word | PDF | Answers)

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Dr Frost Worksheet in Next Section (Proof)
• Mathsaurus Mixed Exam Board PPQs
• Naiker Maths Exam Qs (2005-2011)✦ & MS✦
• PMT
  • Summary Remainder & Factor Theorem PPQs
  • AQA C1 Polynomials PPQs
  • Edexcel C2 Set 1 Remainder and Factor Theorem PPQs (Old Spec)
  • Edexcel C2 Set 2 Algebra & Functions PPQs (Old Spec)
  • OCR C2 Set 1 Factor & Remainder Theorem PPQs & Solutions (Old Spec)
  • OCR C2 Set 1 Factor & Remainder Theorem PPQs (Old Spec)
  • OCR MEI Factor & Remainder Theorems 1 PPQs & MS (Old Spec)
  • OCR MEI Factor & Remainder Theorems 2 PPQs & MS (Old Spec)
  • Summary Cheat Sheet

Activities

• NRICH (student problems)
  • Polynomials
• Andy Lutwyche
  • Erica's Errors On Algebraic Methods
  • Erica's Errors On Algebraic Methods 2