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 ...
Basic Concepts

Algebraic Expressions and Equations

What Are Algebraic Expressions?

Algebraic expressions combine numbers, variables (like \( x \) or \( y \)), and operations. They're like math sentences that describe relationships or patterns.

  • Expressions have no equals sign, just a combination of terms (like \( 2x + 5 \)).
  • Equations have an equals sign and can be solved for a variable (like \( 2x + 5 = 11 \)).

Solving Equations

To solve equations, you'll use inverse operations to isolate the variable. Always aim to get your variable alone on one side of the equation.

Applying to Life

Solving equations helps you figure out unknowns, like what score you need on your next test to get an A, or how many hours you need to work to afford something you want.

Checking Solutions

Plug your answer back in to check that it makes both sides of the equation equal!

Examples

  • Solving \( 3x - 2 = 10 \) gives \( x = 4 \).

  • Simplifying \( 2(x + 3) = 2x + 6 \).

In a Nutshell

Algebra is about working with variables and solving for unknowns.

Key Terms

Variable
A symbol representing a number in an expression or equation.
Equation
A mathematical statement showing two expressions are equal.
Expression
A mathematical phrase combining numbers, variables, and operations.
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Ratios, Proportions, and Percents