Accelerated Algebra 2 Final Exam Flashcards

Questions and Answers

What is the mean?

Max - Min

Add up all numbers and divide by the number of numbers (correct)

Middle number

Number that occurs most often

What is the median?

Middle number

What is the mode?

Number that occurs most often

What is the range?

Max - Min Signup and view all the answers

What is variance?

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What is standard deviation?

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How do you sort a list on a calculator?

Stat, Sort A(, 2nd, one Signup and view all the answers

How do you enter data on a calculator?

Stat, edit Signup and view all the answers

What is the definition of a box and whisker plot?

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What is the interquartile range?

Median of upper quartile and maximum minus median of lower quartile and minimum Signup and view all the answers

What does the union in Venn diagrams represent?

All elements in A or B (AUB) Signup and view all the answers

What does the intersection in Venn diagrams represent?

All elements in A and B Signup and view all the answers

What is a frequency table?

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What is the Average Mean?

Find the mean of each interval, multiply it by the number of terms in that interval. Repeat for each interval and add all together then divide by the number of terms total. Signup and view all the answers

What is a skewed histogram?

Non symmetric histogram Signup and view all the answers

What is the sample space in probability?

All possible outcomes for an event Signup and view all the answers

How is probability defined?

(Possible outcomes for specific event)/(Possible outcomes for sample space) Signup and view all the answers

What does mutually exclusive mean?

No common outcomes. P(A or B) = P(A) + P(B) Signup and view all the answers

What defines independent events?

Outcomes that have no impact on each other. P(A and B) = P(A) * P(B) Signup and view all the answers

What are complements in probability?

1 - (possible outcomes for opposite events) Signup and view all the answers

What is conditional probability?

Sample space has been restricted. ex. Probability of choosing an iPhone 6 given that the phone is an iPhone. P(B|A) Signup and view all the answers

What percentage of data falls within one standard deviation from the mean in a normal distribution?

68% Signup and view all the answers

What is the domain for exponential functions?

(-infinity, infinity) Signup and view all the answers

What is the range for exponential functions?

(0, infinity) Signup and view all the answers

What is the y-intercept for exponential functions?

y = 1 Signup and view all the answers

What is the horizontal asymptote for exponential functions?

y = 0 Signup and view all the answers

What is 'e' in mathematics?

Natural irrational number and base of natural log Signup and view all the answers

How do you turn on the correlation coefficient on a calculator?

2nd, 0, diag on, enter, enter Signup and view all the answers

How do you find the correlation coefficient?

Stat, calc, 4, 5, 0 Signup and view all the answers

What is the log to exponential conversion?

(exponent) Base = Value ------ Log value = exponent base Signup and view all the answers

What are log properties 1-4?

Log base of 1 = 0, Log base of base = 1, Log base base^x = x, one to one property Signup and view all the answers

What are log properties 5-7?

Log base (uv) = log base U + log base V, log base (u/v) = log base u / log base V, log base U^m = m * log Base U Signup and view all the answers

What is the change of base formula?

Log x = Log X / Log B = ln X / ln B Signup and view all the answers

What is the domain of log graphs?

(0, infinity) Signup and view all the answers

What is the range of log graphs?

(-infinity, infinity) Signup and view all the answers

What is the x-intercept of logs?

(1, 0) Signup and view all the answers

What is the vertical asymptote of logs?

x = 0 Signup and view all the answers

What is the half-life formula?

A = a(1/2)^(t/h) Signup and view all the answers

What is the rule when solving logs?

Check for extraneous solutions Signup and view all the answers

How do you simplify rational expressions?

Cancel out common factors from top and bottom Signup and view all the answers

What are excluded values?

Factors canceled out when simplifying Signup and view all the answers

What is the sum of cubes?

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What is the difference of cubes?

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How do you divide rational expressions?

Multiply by the reciprocal Signup and view all the answers

How do you add and subtract rational expressions?

Find the lowest common denominator and simplify Signup and view all the answers

What is a complex fraction?

Simplify the numerator and denominator into one fraction each, then multiply by the reciprocal. Signup and view all the answers

What is the domain of rational fractions?

Zeros of original denominator Signup and view all the answers

What are the vertical asymptotes of rational fractions?

Zeros of simplified denominator Signup and view all the answers

What are the zeroes of rational fractions?

Zeroes of simplified numerator Signup and view all the answers

What are the horizontal asymptotes of rational fractions?

Leading coefficient: if nm, no horizontal asymptotes Signup and view all the answers

What are the holes of rational fractions?

Excluded values from simplified denominator Signup and view all the answers

What is completing the square?

x^2 + bx + (.5b)^2 = c + (.5b)^2 Signup and view all the answers

What are the key parts of a parabola?

Vertex, focus, directrix, axis of symmetry Signup and view all the answers

What are the key parts of a circle?

Center, radius Signup and view all the answers

How do you find the point of intersection of two circles?

Expand the equations, combine like terms, solve for X and Y Signup and view all the answers

What is a tangent?

Perpendicular to radius Signup and view all the answers

What are the key parts of an ellipse?

Center, vertices, covertices, foci Signup and view all the answers

What is the relationship among A, B, and C for an ellipse?

a^2 - b^2 = c^2 Signup and view all the answers

What are the key parts of a hyperbola?

Center, vertices, conjugate axis endpoints, foci, asymptotes Signup and view all the answers

What are the asymptotes of a hyperbola?

Y = ±(a/b)(x - h) + k vertical, Y = ±(b/a)(x - h) + k horizontal Signup and view all the answers

How to identify the features of a parabola?

Only one squared variable Signup and view all the answers

How to identify the features of a circle?

Two squared variables with the same coefficients Signup and view all the answers

How to identify the features of an ellipse?

Two squared variables with different coefficients Signup and view all the answers

How to identify the features of a hyperbola?

Two squared variables, subtraction sign Signup and view all the answers

What is a degenerate parabola?

Line Signup and view all the answers

What is a degenerate ellipse/circle?

Point (center) Signup and view all the answers

What is a degenerate hyperbola?

2 intersecting lines (asymptotes) Signup and view all the answers

When is a conic degenerate?

When standard form equals zero Signup and view all the answers

What is sequence notation?

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What is factorial notation?

n! = n(n-1)(n-2)(n-3)...1 Signup and view all the answers

What is sigma notation?

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What is the arithmetic sum?

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What is a common ratio?

r = a(k+1)/ak Signup and view all the answers

What is geometric notation?

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What is finite sum?

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What is infinite sum?

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What is geometric recursive?

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What is arithmetic recursive?

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How do you find the number of terms?

Plug in all information that is known and solve for n Signup and view all the answers

How do you write a repeating decimal as a fraction?

Expand and plug into an infinite equation and simplify Signup and view all the answers

Study Notes

Measures of Central Tendency

Mean: Average of a set of numbers; calculated by adding all values and dividing by the count of values.
Median: The middle value in a sorted list of numbers.
Mode: The value that appears most frequently in a data set.
Range: The difference between the maximum and minimum values in a data set.

Statistical Terms

Variance: A measure of the dispersion of a set of data points.
Standard Deviation: Indicates the amount of variation or dispersion in a set of values.

Calculator Functions

Sort List: Use the commands stat, sort A(, 2nd, one to organize a list.
Entering Data: Access data entry with stat and then edit.

Data Representation

Box and Whisker Plot: Visual representation of data dispersion using quartiles.
Interquartile Range: Difference between the median of the upper quartile and the lower quartile.

Set Theory

Union in Venn Diagrams: Represents all elements in sets A or B; denoted as ( A \cup B ).
Intersection in Venn Diagrams: Represents all elements common to both sets A and B.

Data Visualization

Stem and Leaf Plots: A method of displaying quantitative data that retains the original data values.
Frequency Table: A table that displays the number of occurrences of each value in a data set.

Probability Concepts

Sample Space: All possible outcomes for a random experiment.
Probability: Calculated as the number of favorable outcomes over the total number of outcomes.
Mutually Exclusive Events: Events that cannot happen simultaneously; ( P(A \cup B) = P(A) + P(B) ).
Independent Events: Events where the outcome of one does not affect the other; ( P(A \cap B) = P(A) \times P(B) ).
Complements: Finding probability of events not happening; calculated as ( 1 - P(\text{event}) ).

Distribution

Normal Distribution Curve Percentages: 68% of data falls within one standard deviation, 95% within two, and 99.7% within three.

Exponential Functions

Domain: The set of all real numbers, ( (-\infty, \infty) ).
Range: All positive real numbers, ( (0, \infty) ).
Y-Intercept: Always at ( (0, 1) ).
Horizontal Asymptote: The horizontal line where ( y = 0 ).

Logarithms

Conversion: Logs can be expressed as exponentials; ( \text{Base}^y = x ) translates to ( \log_{\text{Base}}(x) = y ).
Properties of Logs: Various properties include addition, subtraction, and transformations involving multiplication or division.
Domain of Logarithmic Functions: Defined for positive real numbers ( (0, \infty) ).
Vertical Asymptote: Occurs at ( x = 0 ).

Rational Expressions

Simplification: Involves canceling common factors from numerators and denominators.
Excluded Values: Values that make the denominator zero are not included in the domain.
Horizontal Asymptotes: Determined by comparing leading coefficients of the polynomial.

Conic Sections

Parabola: Key parts include vertex, focus, and axis of symmetry.
Circle: Defined by its center and radius.
Ellipse: Characterized by center, vertices, and foci; relationship between axes is described by ( a^2 - b^2 = c^2 ).
Hyperbola: Key features include center, vertices, and asymptotes.

Sequences and Series

Factorial Notation: Expressed as ( n! = n(n-1)(n-2)(\ldots) ).
Arithmetic and Geometric Sequences: Defined by a common difference or ratio; recursive and explicit formulas can represent both.

Additional Concepts

Degenerate Conics: When conic sections reduce to simpler forms such as points or lines.
Finding Terms in Sequences: Plugging known values into formulas to find unknowns.

General Tips

When solving logarithmic equations, always check for extraneous solutions.

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Test your knowledge of key terms in Algebra 2 with these flashcards. Each card includes definitions for important statistical concepts like mean, median, mode, range, variance, and standard deviation. Perfect for preparing for your final exam!