Algebraic Expressions

Year 1 / ASYear 2 / A-Level All Boards (AQA, Edexcel, OCR, WJEC, CCEA) AQA

A-Level Mathematics revision: Algebraic Expressions. Learning objectives, key points, worked examples and practice questions across AQA, Edexcel, OCR, WJEC and CCEA.

Exam Board:

📌 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: xᵃ x xᵇ = xᵃ⁺ᵇ, xᵃ ÷ xᵇ = xᵃ⁻ᵇ, (xᵃ)ᵇ = xᵃᵇ, x⁰ = 1, x⁻ᵃ = 1/xᵃ

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)

🎯 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

💡 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

❓ Practice Questions

Questions:

Expand and simplify (3x - 2)(x + 4) - (x - 1)^2
Factorise completely: 6x^2 + 13x + 6
Simplify: (x^3 - 8)/(x^2 - 4)
Divide 2x^3 - 5x^2 + 3x - 1 by (x - 2) using polynomial division
Given f(x) = x^3 - 6x^2 + 11x - 6, show (x-1) is a factor and factorise fully
Simplify: (2x^2y⁻^3)^3 ÷ (4x⁻¹y^2)^2

🎬 Video Resources

Algebraic Expressions - Overview -- YouTube Search
Algebraic Expressions - Exam Questions -- YouTube Search

📄 Past Papers & Exam Resources

AQA A-Level Mathematics - Algebraic Expressions -- AQA
Edexcel A-Level Mathematics - Algebraic Expressions -- Edexcel
OCR A-Level Mathematics - Algebraic Expressions -- OCR

🔗 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

📚 Lesson Plan (50 minutes)

Starter (5 min): Recall prior knowledge of algebraic expressions with quick questions.
Teaching (15 min): Work through each of the learning objectives, explaining principles step by step.
Key points review (5 min): Revisit the key points together, confirming understanding.
Worked example (10 min): Model the example question: Simplify fully: (2x^2 + 3x - 2)/(x + 2) - (x^2 - 4)/(x - 2). Solution: Factorise: (2x-1)(x+2)/(x+2) - (x-2)(x+2)/(x-2) = (2x-1) - (x+2) = x - 3
Practice (10 min): Students attempt the practice questions independently; circulate and support.
Plenary (5 min): Review answers and address misconceptions.

🏠 Homework

Expand and simplify (3x - 2)(x + 4) - (x - 1)^2
Factorise completely: 6x^2 + 13x + 6
Simplify: (x^3 - 8)/(x^2 - 4)
Divide 2x^3 - 5x^2 + 3x - 1 by (x - 2) using polynomial division
Given f(x) = x^3 - 6x^2 + 11x - 6, show (x-1) is a factor and factorise fully
Simplify: (2x^2y⁻^3)^3 ÷ (4x⁻¹y^2)^2

🧾 Assessment

Check practice answers against the model answer; use the built-in practice questions as formative assessment.

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