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Questions and Answers
What is the definition of absolute value?
What is the definition of absolute value?
- The sum of the exponents of all its variables
- The distance a number is from zero on a number line (correct)
- The longest side of a right triangle
- The opposite of a number
What does the additive identity property state?
What does the additive identity property state?
- Any number subtracted from itself is zero
- The sum of any number and one is that number plus one
- Any number or variable added to zero is that number or variable (correct)
- The sum of two positive numbers is positive
What is the additive inverse?
What is the additive inverse?
The opposite of a number
What is an algebraic expression?
What is an algebraic expression?
Define an arithmetic sequence.
Define an arithmetic sequence.
What does ascending order mean?
What does ascending order mean?
Which property states that changing the grouping does not change the sum or product?
Which property states that changing the grouping does not change the sum or product?
What are axes in a coordinate plane?
What are axes in a coordinate plane?
What is the axis of symmetry?
What is the axis of symmetry?
Define a binomial.
Define a binomial.
What is a boundary in math?
What is a boundary in math?
What does a box-and-whisker plot summarize?
What does a box-and-whisker plot summarize?
Define a circle graph.
Define a circle graph.
What is a coefficient in algebra?
What is a coefficient in algebra?
What is a common difference?
What is a common difference?
Define common ratio.
Define common ratio.
What does the commutative property state?
What does the commutative property state?
What is a composite number?
What is a composite number?
What is compound interest?
What is compound interest?
Define conjugates in algebra.
Define conjugates in algebra.
What are consecutive integers?
What are consecutive integers?
What does consistent mean in systems of equations?
What does consistent mean in systems of equations?
What is meant by a constant?
What is meant by a constant?
What is the coordinate plane?
What is the coordinate plane?
Define a coordinate system.
Define a coordinate system.
What is the cube root?
What is the cube root?
What does data refer to in statistics?
What does data refer to in statistics?
What is the degree of a monomial?
What is the degree of a monomial?
What is the degree of a polynomial?
What is the degree of a polynomial?
What is a dependent variable?
What is a dependent variable?
Define dependent in terms of systems of equations.
Define dependent in terms of systems of equations.
What does descending order mean?
What does descending order mean?
Define the difference of squares.
Define the difference of squares.
What is dilation in geometry?
What is dilation in geometry?
What is direct variation?
What is direct variation?
What does a discount refer to?
What does a discount refer to?
What is the distance formula?
What is the distance formula?
What is the distributive property?
What is the distributive property?
What does domain refer to in functions?
What does domain refer to in functions?
What is an element in set theory?
What is an element in set theory?
Define elimination in the context of solving equations.
Define elimination in the context of solving equations.
What is an equation?
What is an equation?
What does evaluate mean in mathematics?
What does evaluate mean in mathematics?
What are excluded values?
What are excluded values?
Define exponential decay.
Define exponential decay.
What is an exponential function?
What is an exponential function?
What does exponential growth refer to?
What does exponential growth refer to?
What is an extraneous solution?
What is an extraneous solution?
Define factored form.
Define factored form.
What is factoring by grouping?
What is factoring by grouping?
What does factoring mean in algebra?
What does factoring mean in algebra?
What is a family of graphs?
What is a family of graphs?
What does the FOIL method stand for?
What does the FOIL method stand for?
What is a formula in mathematics?
What is a formula in mathematics?
What does frequency mean in statistics?
What does frequency mean in statistics?
Define function notation.
Define function notation.
What is a function?
What is a function?
What are geometric means?
What are geometric means?
Define a geometric sequence.
Define a geometric sequence.
What is a graph in mathematics?
What is a graph in mathematics?
What is the greatest common factor (GCF)?
What is the greatest common factor (GCF)?
What is a half-plane in geometry?
What is a half-plane in geometry?
What is a hypotenuse?
What is a hypotenuse?
What is identity in mathematics?
What is identity in mathematics?
Define image in transformation.
Define image in transformation.
What does inconsistent mean in system solving?
What does inconsistent mean in system solving?
What is an independent variable?
What is an independent variable?
What is an independent system of equations?
What is an independent system of equations?
Define inductive reasoning.
Define inductive reasoning.
What is an inequality?
What is an inequality?
Define an integer.
Define an integer.
What is interest in finance?
What is interest in finance?
What is interquartile range?
What is interquartile range?
What is the inverse relation?
What is the inverse relation?
Define inverse variation.
Define inverse variation.
What is an irrational number?
What is an irrational number?
What are legs in a right triangle?
What are legs in a right triangle?
What are like terms in algebra?
What are like terms in algebra?
What is a line graph?
What is a line graph?
What is a line of best fit?
What is a line of best fit?
What is a linear equation?
What is a linear equation?
What is linear extrapolation?
What is linear extrapolation?
What is linear interpolation?
What is linear interpolation?
What is the lower quartile (LQ)?
What is the lower quartile (LQ)?
What is mapping in relation to functions?
What is mapping in relation to functions?
What is markup?
What is markup?
What is a matrix?
What is a matrix?
What is maximum in graphing?
What is maximum in graphing?
Define mean in mathematics.
Define mean in mathematics.
What are measures of central tendency?
What are measures of central tendency?
Define measures of variation.
Define measures of variation.
What is the median?
What is the median?
What is a midpoint?
What is a midpoint?
Define minimum in graphing.
Define minimum in graphing.
What are misleading graphs?
What are misleading graphs?
What is a mixture problem in mathematics?
What is a mixture problem in mathematics?
What does mode refer to in statistics?
What does mode refer to in statistics?
Define a monomial.
Define a monomial.
What is the multiplicative identity property?
What is the multiplicative identity property?
What is the multiplicative inverse property?
What is the multiplicative inverse property?
Study Notes
Absolute Value
- Measures the distance of a number from zero on a number line.
Additive Identity Property
- States that any number or variable added to zero remains unchanged.
Additive Inverse
- Refers to the opposite of a number, when added together they yield zero.
Algebraic Expression
- A mathematical phrase that includes numbers, variables, and operations.
Arithmetic Sequence
- A sequence where each term is generated by adding or subtracting a constant value.
Ascending Order
- Arrangement of numbers from least to greatest.
Associative Property
- Demonstrates that grouping does not affect the sum or product, expressed as (a+b) + c = a + (b+c).
Axes
- The two perpendicular lines (x-axis and y-axis) that create the coordinate plane.
Axis of Symmetry
- The vertical line that divides a parabola into two mirrored halves; determined by the formula x = -b/2a.
Binomial
- A sum or difference comprised of two monomials.
Boundary
- A line or curve that distinguishes different regions within the coordinate plane.
Box-and-Whisker Plot
- Visual representation summarizing data through median, quartiles, and extremes.
Circle Graph
- A circular diagram that illustrates data proportions relative to a whole.
Coefficient
- The numerical factor preceding a variable in a term.
Common Difference
- The consistent difference between consecutive terms in an arithmetic sequence.
Common Ratio
- The constant factor by which each term in a geometric sequence is multiplied.
Commutative Property
- Indicates that changing the order of addition or multiplication does not affect the outcome, such as a + b = b + a.
Composite Number
- A whole number greater than 1 with more than two factors.
Compound Interest
- Investment growth described by the formula A = P (1 + (r/n))^(nt), representing interest accrued on principal over time.
Conjugates
- Binomials structured as a√b + c√d and a√b - c√d, whose product yields a rational number.
Consecutive Integers
- A sequence of integers listed in counting order.
Consistent
- Refers to systems of equations with intersecting or coinciding graphs.
Constant
- A monomial representing a real number without any variable.
Coordinate Plane
- The two-dimensional space created by the intersection of the x-axis and y-axis.
Coordinate System
- A grid formed by two intersecting number lines.
Cube Root
- One of the three identical factors of a given number.
Data
- Quantitative information collected for analysis.
Degree of a Monomial
- Calculated as the total of all variable exponents in the term.
Degree of a Polynomial
- Defined by the highest degree of any individual term within the polynomial.
Dependent Variable
- A variable whose value is influenced by another variable.
Dependent
- Situations with infinitely many solutions in systems of equations.
Descending Order
- Arrangement of numbers from greatest to least.
Difference of Squares
- Formed by the subtraction of two perfect squares.
Dilation
- Transformation that enlarges or reduces a figure.
Direct Variation
- Expressed as y = kx, with a constant k not equal to zero.
Discount
- The reduction applied to the regular price of an item.
Distance Formula
- Formula to calculate distance between two points: d = √((x2 - x1)² + (y2 - y1)²).
Distributive Property
- States a(b + c) = ab + ac, allowing distribution of a term across terms within parentheses.
Domain
- The set of all possible first components in ordered pairs.
Element
- Each individual object or number within a set.
Elimination
- A method solving systems of equations by eliminating one variable through addition or subtraction.
Equation
- A mathematical statement asserting that two quantities are equal.
Evaluate
- The process of substituting variable values to determine an expression's outcome.
Excluded Values
- Values that create a denominator of zero must be excluded from the variable's domain.
Exponential Decay
- Describes situations where an initial quantity diminishes over time, represented by y = C (1 - r)^t.
Exponential Function
- Can be represented mathematically as y = a*b^x, where b > 0 and b ≠1.
Exponential Growth
- Depicts a situation in which an initial amount increases consistently over time: y = C (1 + r)^t.
Extraneous Solution
- An outcome derived from an equation that does not satisfy the original problem.
Factored Form
- Represents a monomial as a product of primes and variables with no variable exponent exceeding one.
Factoring by Grouping
- Utilizes the distributive property to factor polynomials with four or more terms.
Factoring
- The process of expressing a polynomial as a product of monomials or lower-degree polynomials.
Family of Graphs
- Graphs sharing at least one common characteristic.
FOIL Method
- A technique for multiplying two binomials through specific term pairing; stands for First, Outer, Inner, Last.
Formula
- An equation that describes the relationship between specific quantities.
Frequency
- The occurrences of specific data within a set.
Function Notation
- A method of naming functions represented by equations.
Function
- A relation where each input correlates to exactly one output.
Geometric Means
- Terms inserted between nonconsecutive terms in a geometric sequence to maintain proportionality.
Geometric Sequence
- A sequence where each term follows by multiplying by a constant factor post the first non-zero term.
Graph
- Visual depictions representing data relationships.
Greatest Common Factor (GCF)
- The product of shared prime factors among two or more monomials.
Half-Plane
- The section of a graph representing a half-region defined by an inequality.
Hypotenuse
- Longest side of a right triangle, opposite the right angle.
Identity
- An equation valid for all variable values.
Image
- The result of a transformation of a geometric figure.
Inconsistent
- Occurs when graphed equations do not intersect and are parallel.
Independent Variable
- A variable that influences or determines others' values.
Independent
- System of equations yielding exactly one solution.
Inductive Reasoning
- Forming conclusions based on observed patterns.
Inequality
- A comparison of two quantities using inequality symbols (<, >, ≤, ≥).
Integer
- Whole numbers that can be negative, positive, or zero, excluding fractions and decimals.
Interest
- Fees earned or paid for the utilization of capital.
Interquartile Range
- The difference between upper (UQ) and lower quartiles (LQ) of a data set.
Inverse Relation
- Ordered pairs created by switching original pair coordinates.
Inverse Variation
- Expressed as y = k/x, with k not equal to zero.
Irrational Number
- A number that cannot be precisely represented as a fraction.
Legs
- The sides that create the right angle in a right triangle.
Like Terms
- Terms sharing identical variables, with corresponding exponents remaining the same.
Line Graph
- A graph illustrating data variations over time.
Line of Best Fit
- A line on a scatter plot indicating correlation between two data sets, synonymous with a regression line.
Linear Equation
- An equation yielding a straight-line graph.
Linear Extrapolation
- Using a linear equation to predict values outside the data range.
Linear Interpolation
- Using a linear equation to estimate values within the data range.
Lower Quartile (LQ)
- Median of the lower segment of a dataset.
Mapping
- Illustration of domain elements paired with range counterparts.
Markup
- The increase in an item's price over its cost.
Matrix
- A structured arrangement of numbers presented in rows and columns.
Maximum
- The highest value on a parabola's graph.
Mean
- The average value calculated by the total of data divided by the data count.
Measures of Central Tendency
- Statistical values representing a dataset's overall characteristics.
Measures of Variation
- Figures showcasing the data's spread or distribution.
Median
- The central value of a dataset; average of the two center values if needed.
Midpoint
- The precise halfway point between two endpoints on a line segment.
Minimum
- The lowest point on a parabola’s graph.
Misleading Graphs
- Graphs with improper construction that lead to misunderstanding and incorrect interpretations.
Mixture Problem
- A scenario where multiple components are blended to form a complete entity.
Mode
- The value(s) that appear most frequently in a dataset.
Monomial
- Consists of a single number, variable, or a product comprising numbers and variables.
Multiplicative Identity Property
- Any number multiplied by one remains unchanged.
Multiplicative Inverse Property
- A relationship where the product of a number and its reciprocal equals one.
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