Algebra 1 Final Study Guide Flashcards

Algebraic Expressions

• Mathematical sentence containing at least one operation and a variable.
• Variables are represented by letters, indicating one or more numbers.

Graphing Intercepts

• Y-intercept is the point where a line crosses the y-axis.
• X-intercept refers to the x-coordinate where the graph intersects the x-axis.

Key Formulas

• Slope-intercept formula: y = mx + b.
• Point-Slope Formula: y - y1 = m(x - x1).
• Slope can be calculated using: (y2 - y1) / (x2 - x1).

Solving Equations

• Example of substitution yields the solution (0, 4) for the equations 3x + 2y = 8 and y = 4.
• Linear equation solved: y - 4 = 6(x - 2) simplifies to y = 6x - 8.

Parabolas and Quadratics

• Parabolas form when a plane intersects a right circular cone parallel to its element.
• Quadratic Equation structure: F(x) = ax^2 + bx + c with a vertex as the max or min point.

Number Concepts

• Absolute value represents the distance from zero on a number line.
• A ratio is a comparison of two numbers through division.
• Consecutive integers are integers counted in sequential order.

Relationships and Correlations

• Positive correlation occurs when both x and y values increase.
• Negative correlation exists when both x and y values decrease.
• No correlation indicates no relationship between the two variables.

Systems and Equations

• A system of equations consists of multiple equations with shared variables.

Exponents and Polynomials

• Exponents denote how many times a number is multiplied by itself.
• Degree of a monomial is the sum of exponents of its variables; for polynomials, it is the highest degree present.

Prime and Composite Numbers

• Prime numbers have only two factors: 1 and itself.
• Composite numbers are defined as whole numbers greater than 1 with more than two factors.

Geometry Fundamentals

• Basic building blocks include points, lines, and planes.
• Collinear points lie on the same line, while coplanar points are within the same plane.
• Line segments have two endpoints; midpoint is equidistant from both.

Radicals and Statistics

• Radical expressions include square roots, with the radicand being the expression under the radical sign.
• Statistics involve collecting and analyzing numerical data, often to infer broader trends from sample data.

Compound Interest

• The compound interest formula is expressed as A = P(1 + r/n)^(nt), where variables represent principal, rate, and time.

Geometry Practice

• Geometric concepts include bisecting segments, determining congruent segments, and defining rays as parts of a line extending infinitely in one direction.