Binomial Expansion

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AS Maths – Pure – Pascal's Triangle

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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8A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Binomial Expansion 1 • Small Powers using Pascal’s Triangle • P1 Ex8A • 🤖

Binomial Expansion 2 • Single Term in Expansion (Small Powers) • P1 Ex8A • 🤖

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 1-10✦

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

• 501a: Expand (x + b)ⁿ, where n is a positive integer up to 6, using Pascal’s triangle.
• 501b: Expand (x – b)ⁿ, where n is a positive integer up to 6, using Pascal’s triangle.
• 501: Exam Practice: Binomial expansion of (a + bx)ⁿ where n is a positive integer

Other Videos

Expanding Brackets using Pascal's Triangle

Corbett Maths Expanding Brackets Using Pascal’s Triangle

The Binomial Expansion

Courtesy of Maths Genie (Up to 4:57)

What came first? Pascal's triangle or the Binomial Expansion?

WW Why does Pascal’s Triangle appear in the Binomial Expansion?

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Dr Austin Maths
  • Expanding Brackets and Pascal’s (Word | PDF | Answers)
• Corbettmaths
  • Expanding Brackets (Pascal’s Triangle) Practice Questions & Solutions
• Pascal’s Triangle✦

AS Maths – Pure – Factorial Notation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

8B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Binomial Expansion 3 • Factorial and Choose Functions • P1 Ex8B • 🤖

Binomial Expansion 4 • Exploring ‘n choose r’ function • P1 Ex8B • 🤖

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 11-15✦

Extra Questions

• Dr Frost Questions (Only 1 Question – repeated in 8D)

Key Skills

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

• 501d: Understand the choose function and calculate values using it. (not yet active)
• 637a: Use the factorial function to get the number of arrangements of objects. (not yet active)
• 637e: Use a single application of a choose function. (not yet active)
• 501: Exam Practice: Binomial expansion of (a + bx)ⁿ where n is a positive integer
• 637: Exam Practice: Permutations and Combinations

Other Videos

The Binomial Expansion

Courtesy of Maths Genie (From 4:57 to 6:01)

Enrichment Video

Zero Factorial – Numberphile

Numberphile: Zero Factorial

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwa Maths Starter Activities (p1-2)
• Longman Cheshire Fun Sheet: Factorials✦
• MadAsMaths (T. Madas)
  • Binomial Expansions Exam Questions Q68, 72, 76 (difficulty 5 of 5)

AS Maths – Pure – Binomial Expansion

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

8C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Binomial Expansion 5 • Why are Pascal’s and Binomial Coefficient linked? • P1 Ex8C • 🤖

Binomial Expansion 6 • Higher Powers using Binomial Coefficients • P1 Ex8C • 🤖

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 16-19✦

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

• 501c: Expand (ax ± b)ⁿ, where n is a positive integer up to 6, using Pascal’s triangle.
• 501e: Find the first few terms of the expansion of (ax + b)ⁿ, with n>6, using the choose function.
• 501f: Find the first few terms of the expansion of (ax – b)ⁿ, with n>6, using the choose function.
• 501h: Expand (ax ± b)ⁿ for positive integers n, where b is fractional.
• 501i: Expand (a + bx)ⁿ for positive integers n, where b is algebraic.
• 501: Exam Practice: Binomial expansion of (a + bx)ⁿ where n is a positive integer

Other Videos

The Binomial Expansion

Courtesy of Maths Genie (From 6:01)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Joe Berwick via variationtheory.com Binomial Expansion✦
• Andy Lutwyche
  • Pascal’s Triangle To Investigation

Worksheets

• Colmanweb.com Binomial Expansions Progression✦
• MadAsMaths (T. Madas)
  • Binomial Expansions Exam Questions Q1–5, 12, 17, 24, 27–28, 33, 37, 42, 50, 53, 64, 66 (difficulty 2–4 of 5)
  • Binomial Expansions Practice Q1–6, 8

AS Maths – Pure – Solving Binomial Problems

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

8D Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Binomial Expansion 7 • Single Term in Expansion (Higher Powers) • P1 Ex8D • 🤖

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 20-23✦

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

• 501g: Determine the value of a coefficient in a binomial expansion with a positive integer power.
• 501j: Use a binomial expansion to reason about terms in the expansion of (a + bx)ⁿ (c + dx)
• 501l: Reason about the b and n in (a + bx)ⁿ given known coefficients of terms in the binomial expansion.
• 501m: Use a relationship between the coefficients of terms in a binomial expansion to determine an unknown constant. (not yet active)
• 501n: Reason about or determine terms of a binomial expansion where one of the terms in the binomial is a reciprocal. (not yet active)
• 501o: Determine terms of a trinomial expansion using a substitution. (not yet active)
• 501: Exam Practice: Binomial expansion of (a + bx)ⁿ where n is a positive integer

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• danwalker Binomial Expansion Lock Game✦ (TES Account Required)
• Underground Mathematics Which Power of x Has the Greatest Coefficient?
• Andy Lutwyche
  • Codebreaker
• Math = Love (Sarah Carter)
  • Add Em Up activity
• Transum
  • Binomial Theorem
• Interactive Maths
  • Scaffolded Binomial Expansion: Generator
• Goal Free Problems
  • A-Level Sequences & Series set Q6, Q7, Q8, Q10

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Crack the Code (Word | PDF | Answers)
• Jethwa Maths Starter Activities (p5-8)
• kutasoftware Worksheets
  • The Binomial Theorem
• MadAsMaths (T. Madas)
  • Binomial Expansions Exam Questions Q6–10, 14, 16, 18–20, 22–23, 26, 29–32, 36, 38–39, 43–44, 46–49, 51–52, 54–63, 65, 67, 73–75 (difficulty 2–5 of 5)
  • Binomial Expansions Practice Q9
  • Indices Exam Questions✦ Q60 (difficulty 5 of 5)

AS Maths – Pure – Binomial Estimation

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

8E Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Binomial Expansion 8 • Estimating Powers • P1 Ex8E • 🤖

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 24-26✦

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

• 501k: Use a binomial expansion to estimate the value of kⁿ
• 501: Exam Practice: Binomial expansion of (a + bx)ⁿ where n is a positive integer

Practice Questions

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Actvities

• The Chalk Face Excel Interactive Binomial Expansion
• Underground Mathematics Approximating task

Worksheets

• Jethwa Maths Starter Activities (p3-4)
• MadAsMaths (T. Madas)
  • Binomial Expansions Exam Questions Q11, 13, 15, 21, 25, 34–35, 40–41, 45 (difficulty 2–3 of 5)

Whole Topic Videos

Binomial Expansion 9 • Exam Questions • P1 Ex8 ExamQs • 🤖

Bicen Maths Exam Questions

External Whole Topic Past Paper Style Questions

• Jethwa Maths Worksheet, Topic Test & Starter Activities
• Dr Frost Topic Test✦ (Teacher Log in Required)
• Mathsaurus Mixed Exam Board PPQs
• Naiker Maths Exam Qs (2005-2011)✦ & MS✦
• MEI Binomial Topic Test✦
• PMT
  • Summary Binomial Expansion PPQs
  • Edexcel C2 Set 1 Binomial Expansion PPQs (Old Spec)
  • Edexcel C2 Set 2 Binomial Expansion PPQs (Old Spec)
  • OCR C2 Set 1 Binomial Theorem PPQs & Solutions (Old Spec)
  • OCR MEI Binomial Expansion PPQs & MS (Old Spec)
  • Summary Cheat Sheet
• Transum
  • Exam-style questions: Binomial Theorem

Worksheets

• Mathshelper (Jon Stone)
  • Binomial Expansion
• MathedUp
  • Binomial expansion: Questions · Challenge · Answers
• Maths Genie
  • The Binomial Expansion: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 1 Binomial Expansion: Worksheets · Unit Test
• Physics & Maths Tutor
  • Binomial Expansion: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• SRWhitehouse
  • Binomial expansion worksheets✦
• Dr Oliver Mathematics
  • Binomial expansion questions✦ (solutions✦)
• MadAsMaths (T. Madas)
  • Binomial Expansions Exam Questions Q70–71 (difficulty 5 of 5)
• Dr Austin Maths
  • Estimation Practice Grid (Word | PDF✦ | Answers✦)
  • Using Pascal's Triangle Practice Strips (Word | PDF | Answers)
  • Practice Grid (Word | PDF | Answers)
  • More Practice Grid (Word | PDF | Answers)
  • Finding Coefficients Practice Strips (Word | PDF | Answers)

Activities

• NRICH (student problems)
  • Sequences & Series
• The Chalkface
  • Binomial Expansion: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
• MEI
  • MEI teaching notes, misconceptions & prompts: Binomial expansion✦
• Andy Lutwyche
  • Codebreakers
  • Erica's Errors On Binomial Expansion 2, 3
  • Erica’s Errors