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AS Maths – Pure – Index Laws

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1A Slides (Courtesy of Owen134866)

Dr Frost Video

• 168 Multiply algebraic terms with powers Key Skill Video (GCSE)
• 169 Divide algebraic terms with powers Key Skill Video (GCSE)
• Whole Topic Video (Up to 2:09)

Bicen Maths Live Lesson

Algebraic Expressions 1 • Index Laws • P1 Ex1A • 🤖

Algebraic Expressions 2 • Index Laws, extra egs • P1 Ex1A • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 1-6

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

• 194a: Use laws of indices for multiplying powers with algebraic bases.
• 194c: Use laws of indices for dividing powers with algebraic bases.
• 194d: Multiply algebraic terms with powers.
• 194e: Divide algebraic terms with powers.
• 194f: Raise an algebraic term to the power of 0.
• 194g: Use laws of indices for raising a power to a power with an algebraic base.
• 194h: Simplify an expression using multiple index laws with a single algebraic variable.
• 194j: Raise an algebraic term to a positive integer power.
• 194l: Simplify an expression using multiple index laws with multiple algebraic variables.
• 194m: Split a fraction using index laws.
• 194n: Determine the unknown power in an expression involving index laws with positive indices given its algebraic equivalent.
• 358a: Express a power using a different base.
• 358b: Use change of base to form a linear formula.
• 358c: Use index laws and change of base to write as a single index.
• 358e: Change the subject of a formula by transforming to the same base.
• 194: Exam Practice: Algebraic index laws (basic)
• 358: Exam Practice: Expressing a power using a different base

Other Videos

Indices

Indices 1

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• martahidegkuti
  • Rules of Exponents✦

Worksheets

• kutasoftware Worksheets
  • Multiplication Property of Exponents
  • Division Property of Exponents
  • Powers of Products and Quotients
• MadAsMaths (T. Madas)
  • Indices Exam Questions✦ Q25, 29–32, 34, 36, 43–44, 47, 49, 53–55, 58–59 (difficulty 3–5 of 5)
  • Surd Exam Questions✦ Q46 (difficulty 3 of 5)
  • Indices Practice Number Indices Q8; Algebraic Indices Q1–5; Indicial Equations Q4–8 · questions only

• martahidegkuti.com Integer Exponents✦ (Sample Problems on Page 3)
• martahidegkuti.com Exponents 1 (Sample Problems on Page 9)

AS Maths – Pure – Negative and Fractional Indices

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

1D Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (From 2:09)

Bicen Maths Live Lesson

Algebraic Expressions 3 • Fractional and Negative Indices • P1 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 15-19

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

• 298a: Raise a whole number to a negative integer power.
• 298b: Raise a fraction to a negative integer power.
• 298d: Raise an algebraic term to a negative integer power.
• 298e: Write a fraction with an algebraic term on the denominator as a power of x
• 298f: Raise an algebraic fraction to a negative integer power.
• 394a: Raise a number to the power of one half.
• 394b: Raise a number to the power of a unit fraction.
• 394d: Raise a fraction to the power of a unit fraction.
• 394e: Raise a number to the power of a non-unit fraction.
• 394f: Raise a fraction to the power of a non-unit fraction.
• 394h: Raise a number to the power of a negative fraction.
• 394i: Raise a fraction to the power of a negative fraction.
• 394j: Raise an algebraic term to the power of a positive unit fraction.
• 394k: Raise an algebraic term to the power of any positive fraction.
• 394l: Raise an algebraic term to the power of a negative fraction.
• 394m: Raise an algebraic fraction to the power of a negative fraction.
• 394n: Write a power with a unit fractional index as a surd expression.
• 394o: Write a power with a non-unit fractional index as a surd expression.
• 394p: Write a surd expression in one variable as a power of that variable (or value).
• 394r: Simplify an algebraic fraction using index laws with negative and fractional powers and surd notation.
• 395a: Solve equations given in the form x^-1 = a
• 395b: Solve equations given in the form x^-a = b
• 395c: Solve equations given in the form x¹/a = b
• 395d: Solve equations given in the form x^a/b = c resulting in integer solutions.
• 395e: Solve equations given in the form x^a/b = c resulting in solutions in surd form.
• 395f: Solve equations given in the form x^-a/b = c
• 395g: Solve equations requiring rearrangement, leading to x^a=b where a is a fraction.
• 298: Exam Practice: Negative indices
• 394: Exam Practice: Fractional indices
• 395: Exam Practice: Solving equations involving negative and fractional powers and surds

Practice Questions

• Practise Questions

Other Videos

Fractional Indices

Indices 2

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• SRWhitehouse Indices Activity✦ (TES Account Required) 
• Standards Unit Using Indices✦
• SRWhitehouse
  • Exponential equations✦

Worksheets

• kutasoftware Worksheets
  • Radicals and Rational Exponents
  • Simplifying Rational Exponents
• MadAsMaths (T. Madas)
  • Equations Exam Questions I Q55 (difficulty 4 of 5)
  • Indices Exam Questions✦ Q1–13, 15–16, 18–23, 26–28, 33, 37, 39–40, 45, 48, 50–52, 61 (difficulty 2–5 of 5)
  • Surd Exam Questions✦ Q73, 80–81 (difficulty 4–5 of 5)
  • Indices Practice Number Indices Q1–7, 9; Algebraic Indices Q6–7; Indicial Equations Q1–3, 9 · questions only

• martahidegkuti.com Rational Exponents✦ (Practice Problems on Page 8)
• Jo Morgan Exponential Equations✦ (TES Account Required)

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.)
• Jethwa Topic Test (coming soon) and Starter Activities (p1-6)
• PMT
  • Solomon Indices Questions & Answers
  • OCR MEI Indices 1 PPQs & MS
  • OCR MEI Indices 2 PPQs & MS
• crashMATHS
  • End of topic test: Algebra II (indices & surds): Test✦

Worksheets

• Mathshelper (Jon Stone)
  • Indices Worksheet
• Maths Genie
  • Algebraic Expressions: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 1 Algebra and Functions: Worksheets · Unit Test
• Mathsaurus (Kevin Olding)
  • Surds and indices (exam questions)
• Physics & Maths Tutor
  • Surds and Indices: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• Madas Maths
  • Indices exam questions✦
• MadAsMaths (T. Madas)
  • Indices Exam Questions✦ Q56–57 (difficulty 5 of 5)

Activities

• NRICH (student problems)
  • Indices & Surds
• MEI
  • MEI teaching notes, misconceptions & prompts: Surds indices✦
• Underground Mathematics
  • Index issues✦
• AMSP (formerly FMSP)
  • Roots and indices maze✦