Comprehensive Guide to Digital SAT Math

Algebra

A domain focusing on linear equations, systems of equations, and linear functions.

Slope-Intercept Form

The equation of a line expressed as y = mx + b, where m is the slope and b is the y-intercept.

Linear Equations

Equations that create a straight line when graphed, describing the relationship between two variables.

Linear Inequalities

Similar to linear equations but use inequality signs (>, <, ≥, ≤) instead of an equal sign.

Systems of Linear Equations

A set of two or more equations with the same variables that can be solved simultaneously.

One Solution

Occurs in systems of linear equations when lines intersect at exactly one point.

No Solution

Results from systems of linear equations when lines are parallel and have the same slope but different y-intercepts.

Infinitely Many Solutions

Occurs when two linear equations represent the same line, sharing both slope and y-intercept.

Quadratic Functions

Functions represented as y = ax² + bx + c, producing a U-shaped curve called a parabola.

Discriminant

The value b² - 4ac in a quadratic equation that indicates the number of real solutions.

Exponential Functions

Functions that model growth or decay, defined as y = a(1 ± r)ⁿ, where a is the initial amount.

Mean (Average)

The sum of a list of numbers divided by the count of numbers in that list.

Median

The middle number in a sorted list; if even, it is the average of the two middle numbers.

Standard Deviation

A measure indicating how spread out values are in a data set from the mean.

Pythagorean Theorem

A formula, a² + b² = c², used to determine the lengths of sides in right triangles.

SOH CAH TOA

A mnemonic for remembering the definitions of sine, cosine, and tangent in trigonometry.

Circle Equation

The formula (x - h)² + (y - k)² = r², used to represent a circle graphically.

Arc Length

The distance along the circumference of a circle, calculated as L = 2πr(θ/360) for degrees or L = rθ for radians.

Volume of Prisms

Calculated as Volume = Area of Base × Height.

Percentage Change Formula

Percentage Change = ((New Value - Old Value) / Old Value) × 100.

Ratios

Comparisons of two quantities expressed as a fraction or with a colon.

Proportions

Equations that state that two ratios are equivalent.

Quadratic Formula

A formula used to find the solutions of a quadratic equation, given by x = (-b ± √(b² - 4ac)) / 2a.

Linear Functions

Functions that graph as straight lines in the coordinate plane.

Rate of Change

The ratio describing how one quantity changes in relation to another; represented by the slope in a linear function.

x-Intercept

The point where a graph intersects the x-axis, occurring where y = 0.

y-Intercept

The point where a graph intersects the y-axis, occurring where x = 0.

Vertex of a Parabola

The highest or lowest point of a parabola, represented in vertex form as (h, k).

Probability

A measure of the likelihood that an event will occur, calculated as the ratio of desired outcomes to total outcomes.

Residual

The difference between the observed value and the predicted value from a regression line.

Complementary Angles

Two angles whose sum is 90 degrees.

Solid Line

Indicates a linear inequality where the endpoints are included in the solution set (≥ or ≤).

Dashed Line

Indicates a linear inequality where the endpoints are not included in the solution set (> or <).

Exponential Growth

Occurs when a quantity increases by a constant factor over equal time intervals.

Exponential Decay

Occurs when a quantity decreases by a constant factor over equal intervals.

Domain

The set of possible input values (x-values) for a function.

Range

The set of possible output values (y-values) for a function.

Intercepts

The points where a graph intersects the axes, including x-intercepts and y-intercepts.

Statistics

The branch of mathematics dealing with data collection, analysis, interpretation, presentation, and organization.

Mode

The number that appears most frequently in a data set.

Volume of Cylinders

Calculated as Volume = πr²h, where r is the radius and h is the height.

Volume of Cones

Calculated as Volume = (1/3)πr²h, where r is the radius and h is the height.

Box Plot

A visual representation of data that shows its minimum, first quartile, median, third quartile, and maximum.

Line of Best Fit

A straight line that best represents the data points on a scatter plot, used for making predictions.

Graphing a Quadratic

Involves identifying the vertex, intercepts, and direction of the parabola.

Comparing Linear Functions

Involves analyzing slopes and intercepts to determine relationships.