Algebra 1 Final Study Guide Flashcards

Questions and Answers

What is an algebraic expression?

A mathematical sentence that includes at least one operation and a variable (correct)

A number without any operation

An equation with no variables

None of the above

What is a variable?

A letter used to represent one or more numbers

What is the y-intercept?

Where the line crosses the y-axis

What is the x-intercept?

The x-coordinate of a point where a graph crosses the x-axis Signup and view all the answers

What does the formula y=mx+b represent?

Slope-intercept formula Signup and view all the answers

What is the solution using substitution for 3x + 2y = 8, y = 4?

(0,4) Signup and view all the answers

What is the point-slope formula?

y - y1 = m(x - x1) Signup and view all the answers

What is the slope formula?

y2 - y1 / x2 - x1 Signup and view all the answers

What is the slope of the line formed by the points 16 and 8 over 6 and 2?

M = 2 Signup and view all the answers

What is a parabola?

A plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve Signup and view all the answers

What is a number line?

A line for representing and graphing numbers Signup and view all the answers

What is absolute value?

The distance a number is from zero on the number line Signup and view all the answers

What are equivalent equations?

Equations having the same solution Signup and view all the answers

What is the solution to the equation y - 4 = 6(x - 2)?

y = 6x - 8 Signup and view all the answers

What is a ratio?

A comparison of two numbers by division Signup and view all the answers

What are consecutive integers?

Integers in counting order Signup and view all the answers

What is the next number in the series 2, 4, 6...?

8 Signup and view all the answers

What is a proportion?

An equation stating that two ratios are equal Signup and view all the answers

What are perpendicular lines?

Lines that intersect at right angles Signup and view all the answers

What is a scatter plot?

A graph in which two sets of data are plotted as ordered pairs in a coordinate plane Signup and view all the answers

What is a positive correlation?

X and Y both increase Signup and view all the answers

What is a negative correlation?

X and Y both decrease Signup and view all the answers

What is no correlation?

Not related Signup and view all the answers

What is a system of equations?

A set of equations with the same variables Signup and view all the answers

What are exponents?

How many times the number is multiplied by itself Signup and view all the answers

What is the degree of a monomial?

The sum of the exponents of all its variables Signup and view all the answers

What is the degree of a polynomial?

The greatest degree of any term in the polynomial Signup and view all the answers

What is a prime number?

A number whose only factors are 1 and itself Signup and view all the answers

Which is a prime number?

5 Signup and view all the answers

Which is a composite number?

4 Signup and view all the answers

What is a prime polynomial?

A polynomial that cannot be written as a product of two polynomials with integral coefficients Signup and view all the answers

What is a quadratic equation?

F(x) = ax^2 + bx + c Signup and view all the answers

What is a vertex?

The maximum or minimum point of a parabola Signup and view all the answers

What is the compound interest equation?

A = P(1 + r/n)^(nt) Signup and view all the answers

What is a radical expression?

An expression that contains a square root Signup and view all the answers

What is a radicand?

The expression under the radical sign Signup and view all the answers

What is a simulation?

Allows you to use objects to act out an event that would be difficult to perform Signup and view all the answers

What is statistics?

The practice or science of collecting and analyzing numerical data in large quantities Signup and view all the answers

What is a point in geometry?

The most basic building block of geometry Signup and view all the answers

What is a line in geometry?

A straight, continuous arrangement of infinitely many points Signup and view all the answers

What is a plane in geometry?

Has length and width but no thickness Signup and view all the answers

What is collinear?

On the same line Signup and view all the answers

What is coplanar?

On the same plane Signup and view all the answers

What is a line segment?

A part of a line with two endpoints Signup and view all the answers

What are endpoints?

Points on the ends of line segments Signup and view all the answers

What are congruent segments?

Segments that have the same length Signup and view all the answers

What is the midpoint?

The point on the segment that is the same distance from both endpoints Signup and view all the answers

What does it mean to bisect?

To divide a segment into two congruent segments Signup and view all the answers

What is a ray in geometry?

A part of a line, with one endpoint, that continues without end in one direction Signup and view all the answers

Study Notes

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.

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Prepare for your Algebra 1 final with these comprehensive flashcards. Each card covers essential terms and concepts, from algebraic expressions to intercepts, helping you solidify your understanding. Perfect for revision and quick reference before the exam.