SAT Math: Heart of Algebra Flashcards

Created by

@EasygoingAgate6318

Study Notes

Intersections and Solutions

Two intersecting lines correspond to one solution.
Parallel lines indicate no solution exists.
Identical lines lead to infinitely many solutions.

Absolute Values

The absolute value of any number is always nonnegative.

System of Equations Insights

A false statement like 0=1 while solving indicates there are no solutions.
Two approaches to find the number of solutions in a system: graph the lines or attempt to solve them to see if a contradiction arises.

Systems of Equations Example

For the given equations 3s-2t=a and -15s+bt=-7, if there are infinitely many solutions, the equations must be identical, meaning coefficients must match when one equation is multiplied by a constant. This leads to b=10 and a=7/5.

Line Geometry

When two lines have defined (non-vertical) slopes, they are parallel if their slopes are identical, and perpendicular if the product of their slopes equals -1.

Linear Equations and Functions

A linear equation establishes a relationship between two variables that creates a straight line when graphed.
A system of linear equations comprises multiple linear equations with the same number of variables, dealt with simultaneously.
Linear functions are characterized by their straight line graphs represented as y=f(x)=a+bx, where x is independent and y is dependent.

Mathematical Definitions

An expression lacks an equals sign and represents a value.
An equation includes an equals sign, defining a specific relationship.
An inequality describes the value(s) that a variable can assume, illustrating the mathematical relationship without strict equality.
A function uniquely connects the value of one variable to one or more other variables through a defined process.

Description

Enhance your understanding of algebra with this set of flashcards focused on the Heart of Algebra section of the SAT. Each card defines key concepts, including solutions to systems of equations and the properties of absolute values. Perfect for quick review and memorization.