Study Notes
Algebraic expressions are combinations of numbers, letters, and operations without equal signs. The letters are variables that can represent different numerical values.
- Algebraic Expression — a mathematical phrase involving numbers, variables, and operations. Example: 3x + 5
- Variable — a symbol used to represent a number in expressions or equations. Example: In 2x + 3, x is the variable.
- Like Terms — terms in an expression that have the same variables raised to the same power. Example: 2a and 5a are like terms.
- Expanding — using the distributive law to multiply terms outside a bracket with each term inside the bracket. Example: 2x(3x + y) = 6x^2 + 2xy
Exam Tips
Key Definitions to Remember
- An algebraic expression contains numbers, variables, and operations without an equal sign.
- Variables are symbols that can represent different values.
- Like terms have the same variables raised to the same power.
Common Confusions
- Mixing up like terms with unlike terms.
- Forgetting to apply the distributive law correctly when expanding expressions.
Typical Exam Questions
- What is the value of 3x + 2z when x = 4 and z = -5? Answer: 2
- Simplify the expression: a + 3b - 4a - 8b. Answer: -3a - 5b
- Expand and simplify: (x-3)^2(2x+1). Answer: 2x^3 - 11x^2 + 12x + 9
What Examiners Usually Test
- Ability to simplify expressions by combining like terms.
- Skill in expanding expressions using the distributive law.
- Understanding of substituting values into expressions to evaluate them.