Summary
In Algebra, you learn to solve problems using equations and expressions, manipulate algebraic fractions, and understand sequences and graphs.
- Simplification — combining like terms to make an expression simpler. Example: 3f + 4f - 2f simplifies to 5f.
- Factorisation — expressing an expression as a product of its factors. Example: x^2 - 2x can be factorised to x(x - 2).
- Rearranging Formulas — changing the subject of a formula. Example: Making r the subject in p = 4r - 3t gives r = (p + 3t)/4.
- Sequences — a set of numbers in a specific order, often defined by a rule. Example: The sequence 3, 7, 11, 15,... has a common difference of 4.
- Graphs — visual representations of equations, often used to find solutions graphically. Example: The graph of y = 8 + 7x - x^2 is a parabola.
Exam Tips
Key Definitions to Remember
- Simplification: Combining like terms.
- Factorisation: Expressing as a product of factors.
- Rearranging Formulas: Changing the subject of a formula.
Common Confusions
- Mixing up terms when simplifying expressions.
- Forgetting to apply the distributive property correctly when expanding brackets.
Typical Exam Questions
- Simplify 3f + 4f - 2f? Answer: 5f
- Make r the subject of p = 4r - 3t? Answer: r = (p + 3t)/4
- Find the next term in the sequence 3, 7, 11, 15,...? Answer: 19
What Examiners Usually Test
- Ability to simplify and factorise expressions accurately.
- Skill in rearranging formulas to make a different variable the subject.
- Understanding of sequences and ability to find the nth term.
- Competence in plotting and interpreting graphs to solve equations.