Page 1: Mathematical Concepts and Formulas
This page covers essential mathematical concepts including linear equations, statistics, quadratic equations, and exponential rules. The content is structured to provide a comprehensive understanding of these fundamental topics.
Linear Equations Section:
The page begins with an exploration of linear equations, emphasizing slope concepts and solution types.
Definition: Linear equations with identical slopes are parallel lines, represented by equations like y = 2x + 3 and y = 2x - 1.
Example: Two parallel lines are shown with equations y = 2x + 3 and y = 2x - 1, demonstrating the "same slope" concept.
Statistical Measures Section:
The text continues with detailed explanations of key statistical measures.
Vocabulary: Mean - the average calculated by dividing the sum of values by the number of values
Vocabulary: Range - the difference between the largest and smallest values in a dataset
Vocabulary: Median - the middle value when data is arranged in order
Vocabulary: Mode - the most frequently occurring value in a dataset
Quadratic Equations Section:
The section on quadratic equations focuses on solution types and the discriminant.
Highlight: The quadratic formula x = -b ± √(b²-4ac)/2a is used to find solutions
Example: The discriminant b²-4ac determines the number of solutions:
- Positive discriminant: two solutions
- Zero discriminant: one solution
- Negative discriminant: no solutions
Percentage Calculations:
The page includes practical applications of percentage calculations.
Example: To calculate a 5% decrease from 100:
- Subtract: 100 - 5 = 95%
- Convert to decimal: 95 ÷ 100 = 0.95
Exponent Rules Section:
The final section covers rules and calculations of exponents in math.
Definition: Key exponent rules include:
- When multiplying like bases, add exponents (a² × a³ = a⁵)
- When dividing like bases, subtract exponents (a⁴ ÷ a² = a²)
- Power to a power: multiply exponents ((a²)³ = a⁶)
- Any number to the zero power equals 1 (a⁰ = 1)
