Algebra 2: EOC Review Flashcards

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Questions and Answers

What is an arithmetic sequence?

A sequence of prime numbers
A random sequence
A sequence in which each term after the first is found by adding a constant to the previous term (correct)
A sequence with multiple operations

What is the first term of a sequence?

What does 'an' refer to in a sequence?

nth term; output

What is the value of 'n' in the context of sequences?

input Signup and view all the answers

What does 'd' stand for in an arithmetic sequence?

common difference Signup and view all the answers

What is a sequence?

a list of numbers in a particular order Signup and view all the answers

What is a term in a sequence?

each number in a sequence or series Signup and view all the answers

What defines a finite sequence?

a sequence containing a limited number of terms Signup and view all the answers

What is an infinite sequence?

a sequence that continues without end Signup and view all the answers

What is an explicit formula?

a formula in which you can find any term by using substitution Signup and view all the answers

What is a recursive formula?

a formula that takes you to the next terms in a sequence Signup and view all the answers

What does iteration refer to in sequences?

using a previous term to find another Signup and view all the answers

What is the rate of change?

a ratio that compares how much one quantity changes, on average, relative to the change in another quantity Signup and view all the answers

What does slope represent?

the rate of change of a line Signup and view all the answers

What is the slope-intercept form of a line?

y = mx + b Signup and view all the answers

What is the standard form of a linear equation?

ax + by = c Signup and view all the answers

What is a system of equations?

two or more lines that relate to each other Signup and view all the answers

What are possible solutions of a system of equations?

one solution, infinite solutions, or no solution Signup and view all the answers

What defines one solution in terms of equations?

two lines that cross at one point (x,y) Signup and view all the answers

What are infinite solutions in a system of equations?

two lines exactly the same Signup and view all the answers

What does no solution mean in a system of equations?

two lines that don't intersect Signup and view all the answers

What is a consistent system?

a system with one or more solutions Signup and view all the answers

What is an inconsistent system?

a system with no solutions Signup and view all the answers

What defines an independent system?

the solutions of one line dictate the solutions of the other Signup and view all the answers

What is a dependent system?

the solutions of one line depend on the solutions of the other Signup and view all the answers

What is a parent function?

the simplest form of a function that doesn't have any transformations; the original Signup and view all the answers

What are transformations in the context of functions?

reflection, translation, and dilation Signup and view all the answers

What is the focus of a parabola?

a given point from which all points in the parabola are the same distance Signup and view all the answers

What is the directrix in a parabola?

a given line from which all the points in the parabola are the same distance Signup and view all the answers

What does 'p' represent in parabolas?

the distance from the vertex to the directrix, or from the focus to the vertex Signup and view all the answers

What is a parabola?

a set of points in a plane equidistant from a given point and a given line Signup and view all the answers

What is latus rectum?

the width of a parabola through the focus Signup and view all the answers

What does constant refer to in mathematics?

having a degree of 0 or no variable Signup and view all the answers

What is a monomial?

one term: 12 or 4x Signup and view all the answers

What is a binomial?

two terms: 2x - 1 or 3y + 9 Signup and view all the answers

What is a trinomial?

three terms: x + y - 7 Signup and view all the answers

What is the degree of a term?

the sum of the exponent of the variables Signup and view all the answers

What is the degree of a polynomial?

the highest degree of the terms Signup and view all the answers

What is the leading term in a polynomial?

the term with the highest degree in a polynomial Signup and view all the answers

What does the remainder theorem state?

P(k) is equal to the remainder of a division equation Signup and view all the answers

What is the factor theorem?

the binomial (x-k) is a factor of the polynomial iff P(k)=0 Signup and view all the answers

What does 'iff' mean?

if and only if Signup and view all the answers

What is a hole in graphing?

a point of discontinuity of a graph; factors cancel out in the numerator and the denominator Signup and view all the answers

What is a function?

a relationship between x and y such that each x corresponds to only one y Signup and view all the answers

What is a logarithm?

the exponent to which a base must be raised in order to obtain a given value Signup and view all the answers

What are special logs?

common logs and natural logs Signup and view all the answers

What is a natural log?

in the form of 'e' Signup and view all the answers

What is conditional probability?

subgroup of probability Signup and view all the answers

What is probability?

the number of ways an event can happen successfully divided by the total number of possible outcomes Signup and view all the answers

What is an outcome?

the result of an event Signup and view all the answers

What is a sample space?

the set of all possible outcomes of an event Signup and view all the answers

What is a set?

a well-defined collection of distinct objects or elements Signup and view all the answers

What does complement mean in set theory?

what is not in the set; ~a Signup and view all the answers

What is a union in set theory?

the set of all things or elements in set A or set B Signup and view all the answers

What is an intersection in set theory?

the set of all elements in both sets A and B Signup and view all the answers

What is theoretical probability?

probability determined using mathematical methods and assumptions about fairness Signup and view all the answers

What is experimental probability?

probability determined by conducting a trial Signup and view all the answers

What does mutually exclusive mean?

two events that cannot happen at the same time Signup and view all the answers

What does mutually inclusive mean?

two events that can happen at the same time Signup and view all the answers

What are independent events?

the outcome of one event does not affect the outcome of the other event Signup and view all the answers

What are dependent events?

the outcome of one event does affect the outcome of another event Signup and view all the answers

What does quantitative refer to?

numerical data Signup and view all the answers

What does qualitative refer to?

categorical data Signup and view all the answers

What is a parameter in statistics?

based on a census; a number that summarizes a characteristic of a population Signup and view all the answers

What is a statistic in statistics?

based on a sample; a number that summarizes a characteristic of a sample Signup and view all the answers

What is a census?

data collected from every member of a population Signup and view all the answers

What is a survey?

data collected from the responses given by members of a population regarding their characteristics, behaviors, or opinions Signup and view all the answers

What is an experiment in research?

a sample is divided into two groups, one that makes use of the subject of the study and one that does not Signup and view all the answers

What is an observational study?

members of a sample are measured or observed without being affected by the study Signup and view all the answers

What is bias in statistical research?

an error that results in misinterpretation of the members of a population Signup and view all the answers

What does random mean in sampling?

each individual in the population has an equal chance of being selected Signup and view all the answers

What is the mean in statistics?

the sum of all the data values divided by the number of total data values; the average Signup and view all the answers

What is the median in a data set?

the middle number of a data set arranged in numerical order Signup and view all the answers

What is the mode in statistics?

the value or values that occur most frequently in a set of data; the MOST Signup and view all the answers

What is a measure of dispersion?

a measure that indicates how the individual data values are scattered or spread out on either side of the mean Signup and view all the answers

What is range in statistics?

the difference between the highest and the lowest data values Signup and view all the answers

What is standard deviation?

the average distance of a data value from the mean of the data values Signup and view all the answers

What are quartiles in statistics?

separate the data into four equal parts Signup and view all the answers

What is a five number summary?

the three quartiles, the minimum, and the maximum of a data set Signup and view all the answers

What is the inner quartile range?

the difference between Q3 and Q1 Signup and view all the answers

What is an outlier?

an extremely high or low data value when compared to the rest of the values of the set Signup and view all the answers

What is a z score?

the deviation from the mean divided by the standard deviation Signup and view all the answers

What is a z score table used for?

converts z-scores into percentages or probability Signup and view all the answers

What does skew refer to in data distribution?

the distribution of a set of data Signup and view all the answers

What is normal distribution?

bell or mound shaped, symmetric, and unimodal data Signup and view all the answers

What is the empirical rule?

68-95-99.7% rule Signup and view all the answers

What does 'y' represent in functions?

range Signup and view all the answers

What does 'x' represent in functions?

domain Signup and view all the answers

What is an even function?

y-axis symmetry Signup and view all the answers

What is an odd function?

rotational symmetry Signup and view all the answers

What is standard position of an angle?

an angle with its vertex at the origin and its initial side is the nonnegative ray of the x-axis Signup and view all the answers

What is a quadrantal angle?

an angle that terminates on an axis Signup and view all the answers

What does coterminal angles mean?

two angles that terminate in the same place Signup and view all the answers

What is a radian?

the unit of measure of a central angle that intercepts an arc equal in length to the radius of the circle Signup and view all the answers

Study Notes

Sequences and Series

Arithmetic sequence involves terms formed by adding a constant (common difference) to the previous term.
a1 denotes the first term of a sequence, while an represents the nth term.
A sequence can be finite (limited terms) or infinite (continues indefinitely).
Explicit formulas allow direct calculation of any term utilizing substitution; recursive formulas derive subsequent terms based on preceding values.

Functions and Graphing

The slope indicates the rate of change in a line, expressed in slope-intercept form as y = mx + b, or standard form ax + by = c.
Systems of equations represent relationships between lines, leading to potential solutions: one solution (lines intersect), infinite solutions (identical lines), or no solution (parallel lines).
A consistent system has solutions, whereas an inconsistent system does not.

Polynomial and Rational Functions

Parent functions are the original forms lacking transformations.
The degree of a term is the total of the exponents of its variables; the leading term is the term with the highest degree in a polynomial.
The remainder theorem states P(k) equals the remainder in polynomial division; the factor theorem establishes a binomial as a factor iff P(k) equals zero.

Probability and Statistics

Probability assesses the likelihood of events occurring, calculated as successful outcomes divided by total possible outcomes.
A sample space encompasses all potential outcomes; complementary sets represent elements not in a defined set.
Experimental probability derives from conducting trials, while theoretical probability is based on assumptions.
Measures of central tendency include the mean (average), median (middle value), and mode (most frequent value).

Data Analysis

Measures of dispersion, like range (difference between max and min) and standard deviation (average distance from the mean), provide insight into data variability.
Quartiles divide data into four equal parts, with the interquartile range being the difference between the first (Q1) and third quartiles (Q3).
Outliers are extreme values that significantly differ from other data points.

Angles and Functions

Standard position defines an angle with its vertex at the origin; a quadrantal angle terminates on an axis.
Coterminal angles end in the same position, while a radian measures a central angle based on the radius of the circle.
Functions can exhibit symmetry: even functions possess y-axis symmetry, while odd functions show rotational symmetry.

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Prepare for your Algebra 2 EOC with these flashcards covering key terms and definitions. From arithmetic sequences to understanding nth terms, this quiz will help reinforce your knowledge. Test your understanding and improve your algebra skills effectively.