PSAT Math

A comprehensive guide to mastering the math concepts tested on the PSAT, including real-world applications and testing strategies.

Numbers and OperationsAlgebraic Expressions and EquationsRatios, Proportions, and Percents
Linear and Quadratic FunctionsSystems of Equations and InequalitiesData Analysis and Probability
Budgeting and Personal FinanceUnit Conversions and MeasurementAnalyzing Real-World Graphs and Surveys
Smart Guessing and EliminationTime Management and Pacing
Numbers and Operatio...Algebraic Expression...Ratios, Proportions,...Linear and Quadratic...Systems of Equations...Data Analysis and Pr...Budgeting and Person...Unit Conversions and...Analyzing Real-World...Smart Guessing and E...Time Management and ...
Advanced Topics

Linear and Quadratic Functions

Linear Functions

A linear function creates a straight line when graphed. Its general form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  • Slope tells you how steep the line is.
  • Y-intercept is where the line crosses the y-axis.

Quadratic Functions

Quadratic functions have the form \( y = ax^2 + bx + c \). Their graph is a parabola (U-shaped curve). Quadratics often model things that rise and fall, like the path of a basketball.

Real-World Applications

Linear functions can model earning money per hour, while quadratics model things like the distance a car travels when braking.

Solving Equations

You can solve linear equations by isolating \( x \). For quadratics, methods include factoring, using the quadratic formula, or completing the square.

Key Formula

\[y = mx + b\]

Examples

  • The equation \( y = 2x + 1 \) represents a line with slope 2 and y-intercept 1.

  • Using \( y = x^2 \), plugging in \( x = 3 \) gives \( y = 9 \).

In a Nutshell

Linear and quadratic functions describe and predict patterns and changes in the world around us.

Key Terms

Function
A relationship where each input has exactly one output.
Slope
A measure of the steepness of a line.
Quadratic
An expression or equation including a variable squared.
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Systems of Equations and Inequalities