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Questions and Answers

What is the definition of absolute value?

The numerical factor when a term has a variable

The distance that a number is from zero on the number line (correct)

Two numbers whose product is 1

A mathematical sentence with an equal sign

What is a coefficient?

The numerical factor when a term has a variable

What is a constant?

A quantity that does not vary

What is a counterexample?

An example that shows a conjecture is false Signup and view all the answers

What is an equation?

A mathematical sentence with an equal sign Signup and view all the answers

What is an expression?

A mathematical phrase that contains operations, numbers, and/or variables Signup and view all the answers

What does it mean to evaluate an expression?

Substituting a given number for each variable Signup and view all the answers

What is an inequality?

A statement that compares two quantities using <, ≤, ≥, or ≠ Signup and view all the answers

What are integers?

Whole numbers and their opposites Signup and view all the answers

What are irrational numbers?

Numbers that cannot be expressed in the form a/b, where a and b are integers and b ≠ 0 Signup and view all the answers

What are like terms?

Terms with exactly the same variable factors in a variable expression Signup and view all the answers

What are natural numbers?

The set of numbers 1, 2, 3, 4,... Also called counting numbers. Signup and view all the answers

What are opposites?

Two numbers that are the same distance from zero on a number line, but are in opposite directions. Signup and view all the answers

What are real numbers?

The set of numbers that includes rational and irrational numbers. Signup and view all the answers

What does it mean to simplify an expression?

To write an expression in a simpler form Signup and view all the answers

What is a term?

A number, a variable, or the product of a number and a variable Signup and view all the answers

What is a variable?

A symbol (like x or y) that is used in mathematical or logical expressions to represent a variable quantity Signup and view all the answers

What are whole numbers?

The set of numbers 0, 1, 2, 3, 4,... Signup and view all the answers

What does subtraction involve?

Adding the opposite Signup and view all the answers

What is a base?

The number or expression that is used as a factor in repeated multiplication Signup and view all the answers

What is an exponent?

A mathematical notation indicating the number of times a quantity is multiplied by itself Signup and view all the answers

What is a prime number?

A number that has no factor but itself and 1 Signup and view all the answers

What are reciprocals?

Two numbers whose product is 1 Signup and view all the answers

What is a coordinate plane?

A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis Signup and view all the answers

What are quadrants?

The four regions into which the x-axis and the y-axis separate the coordinate plane Signup and view all the answers

What is an identity?

An equation that is true for every value of the variable Signup and view all the answers

What is a solution?

A statement that solves a problem or explains how to solve the problem Signup and view all the answers

What are inverse operations?

Operations that undo each other Signup and view all the answers

What are consecutive integers?

Integers that increase or decrease incrementally by 1 Signup and view all the answers

What is the mean?

An average of n numbers computed by adding some function of the numbers and dividing by some function of n Signup and view all the answers

What is the median?

The middle number in a set of numbers that are listed in order Signup and view all the answers

What is the mode?

The number that occurs most often in a set of data Signup and view all the answers

What is the range?

The difference between the highest and lowest scores in a set of data Signup and view all the answers

What are composite numbers?

A whole number greater than 1 that has more than two factors Signup and view all the answers

What are factors?

Numbers that are multiplied together to get a product Signup and view all the answers

What is a linear equation?

An equation whose graph is a line Signup and view all the answers

What are vertical angles?

A pair of opposite angles formed when two lines meet at a point Signup and view all the answers

What is the solution of an inequality?

A number that produces a true statement when it is substituted for the variable in the inequality Signup and view all the answers

What is a compound inequality?

Two or more inequalities joined together by 'and' or 'or' Signup and view all the answers

What is an isosceles triangle?

A triangle that has at least 2 congruent sides Signup and view all the answers

What is a scalene triangle?

A triangle with no two sides of equal length Signup and view all the answers

What is an equilateral triangle?

A triangle with three congruent sides Signup and view all the answers

What is an absolute value equation?

A V-shaped graph that points upward or downward Signup and view all the answers

What is a ratio?

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

What is a rate?

A ratio that compares two quantities measured in different units Signup and view all the answers

What is a unit rate?

A rate that has a denominator of 1 Signup and view all the answers

What is a proportion?

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

What are similar figures?

Figures that have the same shape but not necessarily the same size Signup and view all the answers

What is theoretical probability?

The calculated chance that something will happen based on the number of ways possible Signup and view all the answers

What is experimental probability?

Probability based on data from repeating an event (doing an experiment) Signup and view all the answers

What is a relation?

A set of ordered pairs Signup and view all the answers

What is a function?

A relation where each number in the domain is paired with exactly one number in the range Signup and view all the answers

What is a domain?

The set of first coordinates of the ordered pairs of a relation Signup and view all the answers

What is the range in relation to functions?

The set of second coordinates of the ordered pairs of a relation Signup and view all the answers

What is function notation?

To write a rule in function notation, you use the symbol f(x) in place of y Signup and view all the answers

What is a conjecture?

A conclusion based on guesswork or insufficient evidence Signup and view all the answers

What is direct variation?

An equation of the form y=kx, where k does not equal 0 Signup and view all the answers

What is the constant of variation?

What the k is in the equation y = kx Signup and view all the answers

What is an independent variable?

The experimental factor that is manipulated; the variable whose effect is being studied Signup and view all the answers

What is a dependent variable?

The outcome factor; the variable that may change in response to manipulations of the independent variable Signup and view all the answers

What is inductive reasoning?

Making conclusions based on patterns you observe Signup and view all the answers

What is a sequence?

A number pattern Signup and view all the answers

What is a term in a sequence?

Each number in a sequence Signup and view all the answers

What is an arithmetic sequence?

Adding a fixed number to each previous term Signup and view all the answers

What is the common difference in a sequence?

The fixed number added to each previous term Signup and view all the answers

What is a rate of change?

The relationship between two quantities that are changing; this is also slope Signup and view all the answers

What is the y-intercept?

Where the line crosses the y-axis Signup and view all the answers

What is the slope-intercept form of a linear equation?

y=mx+b Signup and view all the answers

What is the standard form of a linear equation?

A linear equation of the form ax+by=c, where a, b, and c are real number constants and a and b do not equal 0 Signup and view all the answers

What is the x-intercept?

X coordinate of a point where a graph crosses the x-axis; y coordinate of this point is zero Signup and view all the answers

What is point-slope form?

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

What are parallel lines?

Lines in the same plane that never intersect Signup and view all the answers

What are perpendicular lines?

Two lines that intersect to form right angles Signup and view all the answers

What is the line of best fit?

Trend line that shows the relationship between two sets of data Signup and view all the answers

What is the correlation coefficient?

Tells you how closely the equation models the data Signup and view all the answers

What is a translation in graphing?

A shift of a graph horizontally, vertically, or both Signup and view all the answers

What is slope?

The steepness of a line Signup and view all the answers

Study Notes

Algebra 1 Vocabulary

Absolute Value: Measures the distance from zero on the number line, ignoring direction.
Coefficient: Numerical factor in a term that includes a variable.
Constant: A fixed quantity that does not change.
Counterexample: An example demonstrating that a conjecture is false.
Equation: A mathematical statement asserting equality, denoted by an equal sign.
Expression: A combination of numbers, variables, and operations without an equality sign.
Evaluate: The process of substituting variables with specific numbers to simplify expressions.
Inequality: A statement that compares two values, using symbols like <, ≤, ≥, or ≠.
Integers: Whole numbers that can be positive, negative, or zero.
Irrational Numbers: Numbers that cannot be written in fraction form (a/b), where both a and b are integers.
Like Terms: Terms in an expression that share the same variable factors.
Natural Numbers: Counting numbers, starting with 1 (i.e., 1, 2, 3...).
Opposites: Pairs of numbers that are equidistant from zero on the number line but in opposite directions (e.g., -2 and 2).
Real Numbers: The entire set of numbers, which includes rational and irrational numbers.
Simplify: To reduce an expression to its most basic form.
Term: A single component of an algebraic expression, which can be a number, variable, or a product of both.
Variable: A symbol that represents an unknown value, often denoted as x or y.
Whole Numbers: The set of non-negative integers including zero (0, 1, 2, 3...).
Subtraction: The operation of removing a quantity, it can be viewed as adding the opposite.
Base: The number being multiplied in repeated multiplication.
Exponent: Indicates how many times the base is multiplied by itself.
Prime Number: A natural number greater than 1 with no positive divisors other than itself and 1.
Reciprocals: Pairs of numbers whose product equals 1.
Coordinate Plane: Formed by the intersection of the x-axis (horizontal line) and the y-axis (vertical line).
Quadrants: Four sections of the coordinate plane separated by the axes.
Identity: An equation that holds true for all values of the variable.
Solution: A statement that solves a given problem or explains the solving process.
Inverse Operations: Operations that reverse each other's effects (e.g., addition and subtraction).
Consecutive Integers: Integers that follow one another in order, differing by 1.
Mean: The average value derived from the sum of values divided by their count.
Median: The middle value in an ordered set of numbers.
Mode: The most frequently occurring number in a data set.
Range: The difference between the maximum and minimum values in a dataset.
Composite Numbers: Whole numbers greater than 1 that have more than two factors.
Factors: Numbers that multiply together to yield a product.
Linear Equation: Represents a straight line when graphed, characterized by degree 1.
Vertical Angles: Opposite angles formed when two lines intersect, they are equal.
Solution of an Inequality: A value that makes the inequality a true statement when substituted.
Compound Inequality: Combination of two or more inequalities linked by "and" or "or."
Isosceles Triangle: A triangle with at least two sides of equal length.
Scalene Triangle: A triangle where all sides have different lengths.
Equilateral Triangle: A triangle with three equal sides.
Absolute Value Equation: Results in a V-shaped graph, can point upward or downward.
Ratio: A comparison of two quantities expressed as a division.
Rate: A ratio comparing two different units.
Unit Rate: A rate with a denominator of one.
Proportion: An equation stating that two ratios are equal.
Similar Figures: Figures that are similar in shape but may differ in size.
Theoretical Probability: Calculated chance based on the ratio of favorable outcomes to possible outcomes.
Experimental Probability: Probability determined through the performance of experiments.
Relation: A collection of ordered pairs.
Function: A specific type of relation where each input (domain) corresponds to exactly one output (range).
Domain: The set of all first elements (input) in a relation.
Range: The set of all second elements (output) in a relation.
Function Notation: Symbolic representation of a function, typically using f(x) instead of y.
Conjecture: A conclusion reached through inductive reasoning or observation.
Direct Variation: The relationship expressed in the form y = kx, where k is a non-zero constant.
Constant of Variation: The coefficient k in the direct variation equation.
Independent Variable: The variable manipulated in an experiment; it is presumed to affect the dependent variable.
Dependent Variable: The variable that responds to changes in the independent variable.
Inductive Reasoning: Drawing general conclusions from specific observations or patterns.
Sequence: An ordered list of numbers following a specific pattern or rule.
Arithmetic Sequence: Each term is produced by adding a fixed value to the preceding term.
Common Difference: The fixed number added each time in an arithmetic sequence.
Rate of Change: Describes how one quantity changes in relation to another, also interpreted as the slope.
Y-Intercept: The point where a line crosses the y-axis.
Slope: Measures the steepness or incline of a line.
Slope-Intercept Form: The form y = mx + b, where m is the slope and b is the y-intercept.
Standard Form of a Linear Equation: Written as Ax + By = C, where A, B, and C are constants and A and B are not zero.
X-Intercept: The x-coordinate at the point where the graph crosses the x-axis, where y = 0.
Point-Slope Form: Expressed as y - y₁ = m(x - x₁).
Parallel Lines: Lines in the same plane that do not intersect, always maintaining equal distance apart.
Perpendicular Lines: Lines that cross to form right angles.
Line of Best Fit: A trend line that visually represents the relationship between two datasets.
Correlation Coefficient: A numerical measure that indicates how well a line models the data.
Translation: Movement of a graph either horizontally, vertically, or both.

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