Algebra 1 Keystone Study Guide – Vocabulary Flashcards (Video Notes)

Vocabulary flashcards covering key algebraic concepts from Units 1–15, including expressions, equations, functions, exponents, sequences, systems, polynomials, quadratics, data, and statistics.

Variables

Symbols that represent unknown values in expressions or equations.

Constants

Fixed values that do not change.

Coefficients

The numeric factor multiplying a variable.

Terms

Parts of an expression separated by + or − signs; can be constants, variables, or products.

Like Terms

Terms with the same variable factors raised to the same power.

Distributive Property

a(b + c) = ab + ac.

Combine Like Terms

Add or subtract coefficients of terms that have the same variable factors.

Evaluate Expressions by Substituting

Replace variables with given numbers to compute a value.

Linear Equations

Equations of one variable in the form ax + b = c.

Inequalities

Expressions with

Interval Notation

A way to express solution sets on a number line using brackets and parentheses.

Absolute Value

Distance from zero; |x| = x if x ≥ 0, otherwise −x.

Absolute Value Equations

Equations containing absolute value expressions.

Absolute Value Inequalities

Inequalities involving absolute value expressions.

Slope

m = (y2 − y1)/(x2 − x1), the rate of change of a line.

Slope-Intercept Form

y = mx + b, where m is slope and b is y-intercept.

Standard Form (of a Line)

Ax + By = C, with A, B, C as constants.

Function

A relation where each input has exactly one output.

Function Notation (f(x))

A way to denote the output of a function for input x.

Domain

All possible input values (x-values) for a function.

Range

All possible output values (y-values) of a function.

Exponents

Numbers or symbols representing repeated multiplication (power).

a^m × a^n = a^(m+n)

Product rule for same base exponents.

a^m / a^n = a^(m−n)

Quotient rule for same base exponents.

(a^m)^n = a^(mn)

Power of a power rule.

a^0 = 1

Zero exponent rule (for a ≠ 0).

Radicals

Roots, such as square roots, denoting the inverse operation of exponentiation.

nth Root

A number that, when raised to the nth power, gives the original number.

Rational Exponents

a^(m/n) equals the nth root of a^m.

Exponential Growth

Function f(x) = ab^x with b > 1; values increase rapidly.

Exponential Decay

Base 0 < b < 1; outputs decrease as x increases.

Base

The constant base b in an exponential expression b^x.

Arithmetic Sequence

Sequence with a constant difference d between consecutive terms.

Geometric Sequence

Sequence with a constant ratio r between consecutive terms.

Explicit Formula (Arithmetic)

an = a1 + (n−1)d.

Recursive Formula (Arithmetic)

an = a(n−1) + d.

Explicit Formula (Geometric)

an = a1 × r^(n−1).

Recursive Formula (Geometric)

an = r × a(n−1).

Common Ratio

r, the factor between consecutive terms in a geometric sequence.

Substitution Method

Solve one equation for a variable and substitute into the other.

Elimination Method

Add or subtract equations to eliminate a variable.

Graphing Systems

Solving by graphing the equations and finding the intersection point.

One Solution

A unique intersection point of two lines.

No Solution

Parallel lines with no intersection.

Infinite Solutions

Dependent system where lines coincide.

Polynomial

An expression with terms of nonnegative integer powers of variables.

Degree

The highest power of the variable in a polynomial.

FOIL

First, Outer, Inner, Last method for multiplying binomials.

Special Products

(a + b)^2 = a^2 + 2ab + b^2 and (a − b)^2 = a^2 − 2ab + b^2.

Difference of Squares

a^2 − b^2 = (a − b)(a + b).

Quadratic Equations

Equations of the form ax^2 + bx + c = 0.

Standard Form (Quadratic)

ax^2 + bx + c = 0.

Factored Form

(x − r)(x − s) = 0.

Vertex Form

a(x − h)^2 + k; vertex at (h, k).

Quadratic Formula

x = (-b ± √(b^2 − 4ac)) / (2a).

Completing the Square

A method to solve quadratics by transforming to a perfect square.

Factoring (Quadratics)

Expressing a quadratic as a product of binomials to find roots.

Roots

Solutions to the quadratic equation.

Univariate Data

Data with a single variable.

Mean

Average; sum of data divided by number of data points.

Median

Middle value when data are ordered.

Mode

Most frequent value in the data set.

Range

Difference between maximum and minimum values.

Interquartile Range (IQR)

Q3 − Q1; spread of the middle 50% of data.

Standard Deviation

A measure of how spread out data are from the mean.

Scatter Plot

Graph showing relationship between two variables.

Positive Correlation

As x increases, y tends to increase.

Negative Correlation

As x increases, y tends to decrease.

No Correlation

No linear relationship between x and y.

Line of Best Fit

Line that best represents the trend in a scatter plot.

Correlation Coefficient (r)

Number describing strength and direction of a linear relationship.

Batting Average

Hits divided by at-bats; a basic sports stat.

Averages (Statistics)

Mean or other central tendency measures used to summarize data.

Predictions

Forecasts based on data trends and models.

Variability

How data values spread around the center.

Trends

General direction of data over time or across categories.