Prior Content: GCSE/IGCSE Surds
Previous Section: Indices
Next Section: Expanding & Factorising
Contents
- Whole Topic Notes
- 1E Surds Introduction
- 1F Rationalising Surds
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Download Full Topic Slides
- Textbook Notes as PPTs (Courtesy of Owen134866)
Full Notes to Accompany Slides
Dr Frost
- Dr Frost Algebraic Expressions Section
- Dr Frost Algebraic Expressions Slides
- Blank Notes to Follow Slides Word Doc & PDF Surds Only (Courtesy of King’s Chester Maths Department)
- Blank Notes to Follow Slides Word Doc & PDF Whole Chapter Notes (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
Notes
- Physics & Maths Tutor
- Ch.1 Algebraic Expressions: Cheat sheet
1E Surds Introduction
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
- Whole Topic Video (Up to 6:34)
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 334a: Simplify a surd.
- 334b: Simplify a multiple of a surd.
- 334d: Simplify a surd of a fraction or mixed number.
- 335a: Multiply two surds or a surd and a non-surd.
- 335b: Square a surd.
- 335c: Multiply multiples of surds.
- 335d: Square a multiple of a surd.
- 335e: Multiply two surds that require simplifying.
- 335f: Raise a surd to a positive integer power greater than 2.
- 335g: Divide two surds.
- 335h: Divide two surds that require simplifying.
- 335i: Multiply or divide surds with algebra.
- 336a: Add or subtract surds with the same root.
- 336b: Add or subtract surds that require simplifying.
- 336c: Reason about the sum, difference and product of a mixture of rational and irrational numbers.
- 337a: Expand a single bracket with surds.
- 337b: Expand a single bracket with surds, where simplification of surds is required.
- 337c: Expand two brackets involving surds given in the form (a+√b)(c+√b)
- 337d: Expand two brackets with surds, where simplification of surds is required.
- 337e: Expand two brackets involving multiples of surds.
- 337f: Square a bracket involving surds.
- 337g: Multiply three brackets involving surds.
- 337h: Compare coefficients of surds and non-surds to determine values of variables.
- 334: Exam Practice: Simplifying surds
- 335: Exam Practice: Multiplying and dividing surds
- 336: Exam Practice: Adding and subtracting surds
- 337: Exam Practice: Expanding brackets with surds
Other resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Berwick Maths Diagnostic Questions
- Susan Wall True or False Surds Activity✦
- Standards Unit Manipulating Surds✦
- The Chalkface
- Surds Investigation: PDF · PowerPoint
- Khan Academy
- Quiz (Tricky Qs on Following Quiz)
Worksheets
- Jethwa Maths Starter Activities (p9-12)
- kutasoftware Worksheets
- MathedUp
- MadAsMaths (T. Madas)
- Surd Exam Questions✦ Q1–2, 4–8, 10–11, 13, 15, 19, 22–23, 26–27, 29, 31–32, 41–43, 48–49, 51, 53, 57–61, 64–65, 69, 72, 76, 79, 82, 88 (difficulty 2–5 of 5)
- Surds Q1–3, 6–23 · questions only
1F Rationalising Surds
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Dr Frost Video
- Whole Topic Video (From 6:34)
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Exam Practice
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 392a: Rationalise the denominator of a fraction given in the form fraca√b
- 392b: Rationalise the denominator of a fraction given in the form fracab√c
- 392c: Rationalise the denominator of a fraction given in the form fraca√b and where subsequent simplification is required.
- 392d: Rationalise the denominator of a fraction given in the form fraca√bc√d
- 392e: Simplify expressions given in the form fraca + √b√c
- 392f: Rationalise the denominator of a fraction to subsequently add or subtract surds.
- 392g: Solve equations given in the form (a√b)x = c or (a√b)x = c√d
- 392h: Simplify ≤ft(fraca√bright)n where n is large.
- 393a: Rationalise the denominator of a fraction given in the form fracab + √c
- 393b: Rationalise the denominator of a fraction given in the form fraca√bc + √d
- 393c: Rationalise the denominator of a fraction given in the form fraca√b + √c or fraca√b√c + √d
- 393d: Rationalise the denominator of a fraction given in the form fracab + c√d or fraca√bc + d√e
- 393e: Rationalise the denominator of a fraction given in the form fraca + √bc + √b
- 393f: Rationalise the denominator of a fraction given in the form fraca+√bc+√d, where simplification of a surd is required.
- 393g: Rationalise the denominator of a fraction given in the form fraca + b√cd + e√c
- 393h: Rationalise the denominator of a fraction given in the form fraca+b√cd+e√f, where simplification is required.
- 393i: Rationalise the denominator of a fraction where either the numerator or the denominator is squared.
- 393j: Solve equations given in the form x(a + b√c) = d or x(a + b√c) = d+e√f
- 393k: Solve equations with surds and unknowns on both sides.
- 392: Exam Practice: Rationalising the denominator where the denominator consists of a single surd term
- 393: Exam Practice: Rationalising the denominator where the denominator consists of a surd and a second term
Other resources
Other Videos
Courtesy of Maths Genie
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Berwick Maths Diagnostic Questions
- MEI Surds Arithmagons✦
- Underground Mathematics Ab-surd!✦ / Scary Sum✦ / Nested surds✦
- Khan Academy
- Quiz (Tricky Qs on Following Quiz)
Worksheets
- Jethwa Maths Starter Activities (p13-14)
- kutasoftware Worksheets
- MadAsMaths (T. Madas)
- Indices Exam Questions✦ Q9, 12, 21, 23, 27, 33 (difficulty 3 of 5)
- Surd Exam Questions✦ Q3, 9, 12, 14, 16–18, 20–21, 24–25, 28, 30, 33–40, 44–45, 47, 50, 52, 54, 56, 62–63, 68, 78, 83, 86, 91 (difficulty 2–5 of 5)
- Surds Q4–5, 24–34 · questions only
Whole Topic Summary Resources (Including Past Paper Questions)
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 Maths Topic Test (p1-3) Covering Indices & Surds
- Mathsaurus Surds & Indices Mixed Exam Board PPQs
- PMT
- crashMATHS
- End of topic test: Algebra II (indices & surds): Test✦
Worksheets
- Mathshelper (Jon Stone)
- Physics & Maths Tutor
- Surds and Indices: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
- Madas Maths
- Dr Oliver Mathematics
- MadAsMaths (T. Madas)
- Surd Exam Questions✦ Q66–67, 71, 74, 77, 84, 87, 89–90, 92 (difficulty 5 of 5)
Activities
- NRICH (student problems)
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.