Study Notes
Algebraic expressions consist of numbers and letters, known as variables, without equal signs. These variables can be substituted with different values to evaluate the expression.
- Algebraic Expression — a combination of numbers, variables, and operations without an equal sign. Example: 3x + 5
- Like Terms — terms in an expression that have the same variable raised to the same power. Example: 2a and 5a are like terms.
- Distributive Law — a method to expand expressions by multiplying each term inside a bracket by the term outside. Example: 2x(3x + y - 4z) = 6x^2 + 2xy - 8xz
Exam Tips
Key Definitions to Remember
- Algebraic expressions contain numbers, variables, and operations.
- Like terms have the same variable and power.
- The distributive law is used to expand expressions with brackets.
Common Confusions
- Mixing up like terms with unlike terms.
- Forgetting to apply the distributive law correctly.
Typical Exam Questions
- What is the value of 3x + 2z when x = 4 and z = -5? Answer: 2
- Simplify the expression 2a + 5a. Answer: 7a
- Expand and simplify (x−3)^2(2x+1). Answer: 2x^3 − 11x^2 + 12x + 9
What Examiners Usually Test
- Ability to substitute values into expressions.
- Simplifying expressions by combining like terms.
- Expanding expressions using the distributive law.