Study Notes
Algebraic expressions involve manipulating mathematical phrases using variables and constants. Key concepts include index laws, expanding brackets, factorising, negative and fractional indices, surds, and rationalising denominators.
- Index laws — rules used to simplify powers of the same base. Example: Add, multiply, or subtract the indices.
- Expanding brackets — multiplying each term in one expression by each term in another. Example: (a + b)(c + d) = ac + ad + bc + bd.
- Factorising — writing an expression as a product of its factors. Example: x^2 + 5x + 6 = (x + 2)(x + 3).
- Negative and fractional indices — indices that are negative or fractions, applying the same laws. Example: x^(-1) = 1/x, x^(1/2) = √x.
- Surds — square roots of numbers that cannot be simplified into whole numbers. Example: √2, √3.
- Rationalising denominators — converting a surd in the denominator to a rational number. Example: 1/√2 = √2/2.
Exam Tips
Key Definitions to Remember
- Index laws: rules for simplifying powers.
- Expanding brackets: multiplying terms across expressions.
- Factorising: expressing as a product of factors.
- Surds: non-simplifiable square roots.
- Rationalising denominators: making denominators rational.
Common Confusions
- Mixing up the rules for adding and multiplying indices.
- Forgetting to collect like terms after expanding brackets.
- Confusing factorising with expanding.
- Misapplying the rules for rationalising denominators.
Typical Exam Questions
- How do you expand (x + 3)(x - 2)? Answer: x^2 + x - 6
- What is the factorised form of x^2 + 5x + 6? Answer: (x + 2)(x + 3)
- Simplify 1/√3. Answer: √3/3
What Examiners Usually Test
- Ability to apply index laws correctly.
- Skill in expanding and simplifying expressions.
- Proficiency in factorising quadratic expressions.
- Understanding of surds and rationalising denominators.