Algebraic Fractions

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A2 Maths – Pure – Multiplying and Dividing Algebraic Fractions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

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1B Slides (Courtesy of Owen134866)

Dr Frost Videos

Simplifying Algebraic Fractions (KS5)

Whole Topic Video ‘Simplify algebraic fractions by cancelling common factors.’

Multiplying & Dividing Algebraic Fractions (KS5)

Whole Topic Video ‘Multiply and divide algebraic fractions’

Bicen Maths Live Lesson

Partial Fractions 1 • Algebraic Fractions, all operations • P2 Ex1B/C • 🚀

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 12-14✦

Exam Practice

• Exam Practice: Simplify algebraic fractions by cancelling common factors. · Multiply and divide algebraic fractions.

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.
• 388a: Multiply algebraic fractions with single terms on the numerators and denominators.
• 388b: Divide algebraic fractions with single terms on the numerators and denominators.
• 388c: Multiply algebraic fractions with bracketed expressions on the numerators and denominators.
• 388d: Divide algebraic fractions with bracketed expressions on the numerators and denominators.
• 388e: Multiply algebraic fractions requiring prior simple factorisation.
• 388f: Divide algebraic fractions requiring prior simple factorisation.
• 388g: Multiply algebraic fractions requiring prior factorisation including monic quadratic expressions.
• 388h: Divide algebraic fractions requiring prior factorisation including monic quadratic expressions.
• 388i: Multiply algebraic fractions requiring prior factorisation, including non-monic quadratic expressions.
• 388j: Divide algebraic fractions requiring prior factorisation, including non-monic quadratic expressions.
• 387: Exam Practice: Simplifying single algebraic fractions by cancelling common factors
• 388: Exam Practice: Multiplying and dividing algebraic fractions

Further Practice

• Practise Questions: Simplify algebraic fractions by cancelling common factors. · Multiply and divide algebraic fractions.

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Naikermaths Algebraic Fractions PPQs✦ (Solutions✦)
• Solomon C3 Rational Expressions A✦ (Solutions✦) (p1)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Exam Questions Q19 (difficulty 3 of 5)
  • Algebraic Fractions Multiplication & Division Q1–3

A2 Maths – Pure – Adding and Subtracting Algebraic Fractions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

1C Slides (Courtesy of Owen134866)

Dr Frost Video

Adding & Subtracting Algebraic Fractions (KS5)

Whole Topic Video

Bicen Maths Live Lesson

Partial Fractions 1 • Algebraic Fractions, all operations • P2 Ex1B/C • 🚀

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 15-17✦

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

• 389a: Add and subtract algebraic fractions with integer denominators and single terms on the numerators.
• 389b: Add algebraic fractions with integer denominators and linear expressions on the numerators.
• 389c: Subtract algebraic fractions with integer denominators and linear expressions on the numerators.
• 389d: Add or subtract algebraic fractions with algebraic denominators made up of single terms.
• 389e: Add algebraic fractions with algebraic linear denominators.
• 389f: Subtract algebraic fractions with algebraic linear denominators.
• 389g: Add or subtract a mixture of fractional and non-fractional algebraic terms.
• 389h: Add and/or subtract three algebraic fractions all with different denominators. (not yet active)
• 389i: Add or subtract algebraic fractions with a factorised quadratic expression in one denominator.
• 389j: Combine multiplication or division of algebraic fractions with an addition or subtraction.
• 390a: Add or subtract algebraic fractions where non-quadratic factorising is required (changing one denominator).
• 390b: Add or subtract algebraic fractions where non-quadratic factorising is required (changing two denominators).
• 390c: Add or subtract algebraic fractions where quadratic factorising is required (changing one denominator).
• 390d: Add or subtract algebraic fractions where quadratic factorising is required (changing two denominators).
• 390e: Add or subtract three fractions requiring prior factorisation.
• 390f: Combine multiplication or division of algebraic fractions, requiring prior factorisation of the denominators, with an addition or subtraction.
• 389: Exam Practice: Adding and subtracting algebraic fractions (no factorisation of denominators required)
• 390: Exam Practice: Adding and subtracting algebraic fractions, requiring prior factorisation of the denominators

Further Practice

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions

Worksheets

• Jethwamaths Starter Activities (p3-4)
• Solomon C3 Rational Expressions A✦ (Solutions✦) (p2)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Exam Questions Q1–2, 5, 7, 16–17, 23–26, 29 (difficulty 2–4 of 5)
  • Algebraic Fractions Adding Algebraic Fractions Q2–10

A2 Maths – Pure – Introduction to Partial Fractions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

1D Slides (Courtesy of Owen134866)

Dr Frost Video

Partial Fractions (KS5)

Whole Topic Video (Up to 3:36)

Bicen Maths Live Lesson

Partial Fractions 2 • Simple Partial Fractions • P2 Ex1D • 🚀

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 18-21✦

Exam Practice

• Exam Practice (Last Q with squared denominator)

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

• 559a: Decompose a rational function into partial fractions: ax+b/(cx + d)(ex + f)
• 559b: Decompose a rational function into partial fractions: ax² + bx + c/(dx + e)(fx + g)(hx + i)
• 559: Exam Practice: Decompose rational expressions into partial fractions

Other Videos

Partial Fractions

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• alutwyche
  • Partial Fractions Codebreaker 1 & Solution
  • Partial Fractions Codebreaker 2 & Solution
  • Codebreakers
  • Codebreakers (2)
• Longman Cheshire (via Resourceaholic) Partial Fractions Fun Sheet✦ 
• Transum
  • Partial Fractions
• Ticktock Maths
  • Partial Fractions lesson (slides)

Worksheets

• Jethwamaths Starter Activities (p7-8)
• Mathshelper (Jon Stone)
  • Partial Fractions
• Physics & Maths Tutor
  • Partial Fractions: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Algebraic Fractions Partial Fractions Q1–6

A2 Maths – Pure – Repeated Factors in Partial Fractions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

1E Slides (Courtesy of Owen134866)

Dr Frost Video

Partial Fractions (KS5)

Whole Topic Video (From 3:36 to 7:16)

Bicen Maths Live Lesson

Partial Fractions 3 • Repeated Linear Factor in Denominator • P2 Ex1E • 🚀

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 22-24✦

Exam Practice

• Exam Practice (Last Q with squared denominator)

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

• 559c: Decompose a rational function with a repeated factor into partial fractions: ax² + bx + c/(dx + e)(fx + g)²
• 559: Exam Practice: Decompose rational expressions into partial fractions

Other Videos

Partial Fractions with a Repeated Factor

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwamaths Starter Activities (p5-6)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Exam Questions Q33–34 (difficulty 5 of 5)
  • Algebraic Fractions Partial Fractions Q7–10

A2 Maths – Pure – Algebraic Division in Partial Fractions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

1FG Slides (Courtesy of Owen134866)

Dr Frost Video

Partial Fractions (KS5)

Whole Topic Video (From to 7:16)

Bicen Maths Live Lesson

Partial Fractions 4 • Improper Fractions – without partial fractions • P2 Ex1F • 🚀

Partial Fractions 5 • Improper Partial Fractions • P2 Ex1G • 🚀

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 25-31✦

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

• 559d: Decompose a top-heavy rational function into partial fractions: ax²+bx+c/(dx + e)(fx + g)
• 559: Exam Practice: Decompose rational expressions into partial fractions

Further Practice

• Practise Questions

Other Videos

Partial Fractions with Improper Fractions

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Lots of Mixed Worksheets in the Whole Topic Resources Below
• Naiker Maths
  • Algebraic Division: Exam Qs 2005–11 · Mark scheme · Exam Qs 2012–17 · Mark scheme
• MadAsMaths (T. Madas)
  • Algebraic Fractions Exam Questions Q6, 8, 12, 18, 28 (difficulty 2–4 of 5)
  • Algebraic Fractions Algebraic Divisions Q1–6; Partial Fractions Q11–12
  • Polynomials Q4 (difficulty 3 of 5)

External Whole Topic Past Paper Style Questions (Covering All Proof)

• 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.)
• Jethwamaths Worksheet (p12-16), Topic Test (p1-4) & Starter Activities (p3-10)
• Naikermaths Algebraic Fractions PPQs✦ (Solutions✦)
• Solomon C4 Partial Fractions Worksheet A✦ (Answers✦), Worksheet B✦ (Answers✦)
• PMT PPQs by Topic – note most of these extend into Binomial Expansion or Integration
  • Edexcel Set 1, Set 2
  • OCR Partial Fractions
  • OCR MEI Set 1 (Answers), Set 2 (Answers), Set 3 (Answers)
  • Cheat Sheet
• Dr Frost Topic Test✦ (Teacher login required)

Other Whole Topic Resources

• Berwick Maths Diagnostic Questions
• kutasoftware Partial Fractions Worksheet

Activities

• NRICH (student problems)
  • Algebra & Functions
• Andy Lutwyche
  • Partial Codebreaker 3

Worksheets

• Maths Genie
  • Algebraic Methods: Questions · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Further algebra (exam questions)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Exam Questions Q27, 30 (difficulty 4 of 5)
• Dr Austin Maths
  • Simplifying Practice Grid (Word | PDF | Answers)