Math Flashcards
Circle Equation (Not Centered at the Origin)
Formula: 
 is the center, and  is the radius.
Trigonometric Ratios
Formulas: , , 
Use: For right triangles.
Angle of Elevation and Depression
Concept:
- Angle of Elevation: Angle from the horizontal line of sight looking upward.
- Angle of Depression: Angle from the horizontal line of sight looking downward.
Quadratic Formula
Formula: 
Explanation: Solves quadratic equations .
Discriminant of a Quadratic
Formula: 
Explanation:
- : Two real and distinct roots.
- : One real, repeated root.
- : Two complex roots.
Sine and Cosine Rules
Sine Rule: , Cosine Rule: 
Use: For non-right triangles.
Area of a Triangle (Heron’s Formula)
Formula:
1. Given base and height: 
2. Heron’s formula:
- First, find .
- Then, .
Remainder Theorem
Concept:
- Remainder Theorem: The remainder when a polynomial  is divided by  is .
Standard Deviation (Single Variable Data)
Formula:
1. 
- Where  = standard deviation,  = each value,  = mean, and  = number of values.
2. Use: Measures data spread from the mean.
Interquartile Range (IQR)
Formula: 
Explanation: Measures the spread of the middle 50% of data points.
Scatter Plot and Line of Best Fit
Concept:
- Scatter Plot: A graph showing the relationship between two variables.
- Line of Best Fit: A straight line that best represents the data trend.
Polynomial Long Division
Concept:
- Process: Use division steps to divide polynomials, reducing powers of x step-by-step. The remainder is the final value after completing all divisions.
Transformations of a Parabola
Concepts:
- Vertical Shift:  (up or down by ).
- Horizontal Shift:  (left or right by ).
- Reflection:  (flips over the x-axis).
Standard Form of a Circle
Formula: 
Explanation: Circle with center  and radius .
Basic Sine and Cosine Graphs
Sine:  (starts at 0, peaks at , 0 at , min at , back to 0 at ).
Cosine:  (starts at 1, 0 at , min at , 0 at , back to 1 at ).
