amazon.co.ukAlgebraic Expressions
A-Level Mathematics revision: Algebraic Expressions. Learning objectives, key points, worked examples and practice questions across AQA, Edexcel, OCR, WJEC and CCEA.
π Key Points
Key Fact: Collecting like terms: only terms with identical variables and powers can be combined
Key Fact: Expanding brackets: multiply each term inside by the term outside (FOIL for double brackets)
Key Fact: Difference of two squares: a^2 - b^2 = (a + b)(a - b)
Key Fact: Perfect square trinomials: a^2 +/- 2ab + b^2 = (a +/- b)^2
Key Fact: Factorising by grouping: pair terms to extract common factors
Key Fact: Algebraic fractions: factorise numerator and denominator first, then cancel common factors
Key Fact: Index laws: xα΅ x xα΅ = xα΅βΊα΅, xα΅ Γ· xα΅ = xα΅β»α΅, (xα΅)α΅ = xα΅α΅, xβ° = 1, xβ»α΅ = 1/xα΅
Key Fact: Polynomial long division: dividend = divisor x quotient + remainder
Key Fact: Factor theorem: if f(a) = 0 then (x - a) is a factor of f(x)
π― Learning Objectives
- Simplify algebraic expressions by collecting like terms
- Expand single and double brackets using distributive law
- Factorise quadratic expressions including difference of two squares
- Manipulate algebraic fractions with numerical and algebraic denominators
- Apply index laws to simplify expressions with powers
- Use the factor theorem and remainder theorem for polynomial division
π‘ Worked Example
Exam-Style Question
Question: Simplify fully: (2x^2 + 3x - 2)/(x + 2) - (x^2 - 4)/(x - 2)
Model Answer:
Factorise: (2x-1)(x+2)/(x+2) - (x-2)(x+2)/(x-2) = (2x-1) - (x+2) = x - 3
β Practice Questions
Model answers are being added progressively - questions marked ✗ don't have one yet. Cross-check with your teacher or the official mark scheme.
Questions:
- Expand and simplify (3x - 2)(x + 4) - (x - 1)^2✗ answer coming soon
- Factorise completely: 6x^2 + 13x + 6✗ answer coming soon
- Simplify: (x^3 - 8)/(x^2 - 4)✗ answer coming soon
- Divide 2x^3 - 5x^2 + 3x - 1 by (x - 2) using polynomial division✗ answer coming soon
- Given f(x) = x^3 - 6x^2 + 11x - 6, show (x-1) is a factor and factorise fully✗ answer coming soon
- Simplify: (2x^2yβ»^3)^3 Γ· (4xβ»ΒΉy^2)^2✗ answer coming soon
π¬ Video Resources
- Algebraic Expressions - Overview -- YouTube Search
- Algebraic Expressions - Exam Questions -- YouTube Search
π Past Papers & Exam Resources
π Further Reading & Resources
- Physics & Maths Tutor - Algebraic Expressions -- Free notes, worksheets, and past paper questions by topic
- Dr Frost Maths - Algebraic Expressions -- Free resources, slides, and interactive questions
- BBC Bitesize - Algebraic Expressions -- BBC Bitesize revision resources