Calculus

Limits
Terms and Definitions
Algebraic Functions
Asymptote
Domain
Continuous at a point
Continuous on an open interval
Continuous everywhere
Discontinuity
Horizontal asymptotes
Indeterminate forms of a limit
Infinite limits
Limits
Limits at infinity
Non-removable discontinuity
One-sided limits
Range
Real-valued Function
Removable discontinuity
Transcendental Functions
Vertical Asymptotes
Topics and Theorems
Finding limits numerically (intuitively)
Finding limits by graphing
Finding limits algebraically
Finding limits at infinity
Finding one-sided limits
Asymptotic behavior
Unbounded behavior
Continuity and discontinuity
Theorems and Properties of Limits
Scalar multiple
Sum or difference
Product
Quotient
Power
Polynomial functions
Rational functions
Radical
Composite function
Trigonometric
Squeeze Theorem
General Theorems
Theorems and properties of continuity
Basic continuity properties
Scalar multiple
Sum and difference
Product
Quotient
Continuity of a Composite function
Intermediate Value Theorem
Theorems and properties of infinite limits
Sum or difference
Product
Quotient

The Derivative
Terms and Definitions
Average rate of change
Average velocity
Derivative
Difference Quotient
Differentiable and Differentiability
Differential
Differentiation
Explicit function
Implicit differentiation
Implicit function
Instantaneous rate of change
Instantaneous velocity
Notation for derivatives
Rate of change
Related rate
Secant line
Slope of a line
Tangent line
Topics and Theorems
Theorems or basic rules of differentiation
Graphic interpretation of the derivative
Higher order derivatives

Applications of the Derivative
Terms and definition
Absolute extrema
Absolute maximum
Absolute minimum
Acceleration function
Concavity
Critical number
Critical Point
Decreasing functions
Extrema or extreme values
Increasing functions
Inflection point
Maximum
Minimum
Point of inflection
Position function
Rectilinear motion
Relative Extrema
Relative Maximum
Relative Minimum
Velocity function
Topics and Theorems
Graphing and the first derivative
Graphing and the second derivative
Rolle's Theorem
The Mean Value Theorem
The Extended Mean Value Theorem
L'Hopital's Rule
Optimization problems (Max/Min)
Related rate problems
Marginal analysis
Rectilinear motion and the derivative

Antiderivatives/Integrals
Terms and definitions
Antidifferentiation
Antiderivative
Area under the graph
Definite integral
Differential equations
General or family of solutions for a differential equation
Improper Integrals
Indefinite integral
Integrable
Integrability
Integrals
Integrand
Integration
Initial condition
Midpoint rule
Particular solution
Riemann sums
Separable differential equation
Sigma notation
Simpson's rule
Summation notation
Trapezoidal rule
Topics and Theorems
Antiderivatives differ by a constant
Basic integral rules
Fundamental Theorem of Calculus
Graphic representation of integration
Indefinite integral form of the chain rule
Indefinite integrals of trigonometic functions
Summation properties and formulas
Numeric Approximation of Integrals
Midpoint rule and error bound
Trapezoidal Rule and error bound
Simpson's Rule and error bound
Integrating improper integrals
Properties of definite integrals

Application of Integrals
Terms and definitions
Arc length
Area
Area bounded by two graphs
Area of a surface of revolution
Average value of a function
Center of Mass
Disk method of finding volume
Force
Mass
Moments
Shell or washer method of finding volume
Solid of revolution
Surface of revolution
Volume by slicing
Work
Topics and Theorems
Finding area
Finding area between two graphs
Techniques for finding volume
Finding arc length or the length of a curve
Rectilinear motion and the integral
Mean value theorem for definite integrals
Using integrals to find work, force, centers of mass

Logarithmic, Exponential and Other Transcendental Functions
Terms and Definitions
Exponential functions
Hyperbolic functions
Inverse functions
Inverse hyperbolic functions
Inverse trigonometric functions
Logarithmic functions
One-to-one functions
The exponential function
The Natural logarithmic function
Transcendental number
Topics and Theorems
Properties of exponents
Properties of logarithms
Derivatives of logarithmic functions
Derivatives of exponential functions
Derivatives of other transcendental functions
Integrals of logarithmic, exponential and other transcendental functions
Theorems about inverse functions
Techniques of integration
Integration by substitution or "u" substitution
Integration by parts
Integration using partial fractions
Integration using trigonometric substitution
L'Hopital's rule
Differential equations

Sequences, Series and Polynomial Approximations
Terms and Definitions
Absolute convergence
Alternating series
Binomial series
Bounded sequence
Conditional convergence
Convergent sequence
Convergent series
Divergent sequences
Geometric series
Harmonic series
Infinite series
Interval of convergence
Maclaurin Series
Monotonic sequence
Power series
Radius of convergence
Sequence
Series
Taylor series
Topics and Theorems
Properties of sequences
Sequences of the form {1/n^r}
Sequences of the form {rⁿ}
Determining if a sequence converges
Sum of a geometric series
Theorems about convergent series
The n^th term test for divergence
Tests for convergence
Integral test
p-series
Comparison test
Limit comparison test
Ratio test
Root test
Alternating series test
Absolute convergence implies convergence
Differentiation of a power series
Integration of a power series
Using Taylor series to approximate transcendental functions
Maclaurin series to approximate transcendental functions
Sum of a binomial series

Parametric and Polar Equations, Vectors and Vector-Valued Functions
Terms and Definitions
Arc length parameter
Component form of a vector in the plane
Conics or conic sections
Continuity of a vector-valued function
Curvature
Degenerate conic or degenerate cases of conic sections cases
Derivative of a vector-valued function
Directrix
Dot product
Focus
Integration of a vector-valued function
Limit of a vector-valued function
Normal vector
Orthogonal vectors
Parametric equations
Plane curve
Polar axis
Polar coordinates
Polar coordinate system
Principal unit normal vector
Projection of u onto v
Smooth curve
Standard unit vectors
Unit tangent vector
Unit vector
Vector
Vector component of u orthogonal to v
Vector-valued functions
Work
Topics and Theorems
Equations for conics
Circle
Rectangular
Polar
Parabola
Rectangular
Polar
Ellipse
Rectangular
Polar
Hyperbola
Rectangular
Polar
Rotation of axes
Eliminating the parameter in a parametric equation
Slope of the tangent line to a smooth curve
Higher order derivatives for parametric equations
Arc length of a smooth curve
Conversion of polar coordinates to rectangular coordinates
Conversion of rectangular coordinates to polar coordinates
Slope of tangent line to the graph of a polar equation
Area in polar coordinates
ARc length of a polar equation curve
Vectors
Addition
Scalar multiplication
Equality
Length, magnitude or norm
Negastive
Zero vector
Subtraction
Properties of the dot product
Orthogonal vectors

Statistics
Introduction
Terms and Definitions
Bias
Bivariate
Categorical
Census
Cluster Sampling
Continuous
Convenience Sampling
Data
Discrete
Experiment
Experimental Design
Interval
Level of measurement
Multivariate
Nominal
Numerical
Ordinal
Parameter
Population
Qualitative data
Quantitative data
Random Sampling
Ratio
Sample
Sampling
Simple random sampling
Simulation
Statistic
Statistics
Stratified Sampling
Systematic Sampling

Descriptive Statistics
Terms and Definitions
Bimodal
Central tendency
Cumulative frequency
Cumulative frequency graph
Deviation
Dispersion
Distribution
First Quatrile
Five number summary
Frequency Distribution
Frequency Histogram
Interquartile range
Left skewed
Mean
Median
Mode
Multimodal
Negatively skewed
Ogive
Outlier
Percentile
Positively skewed
Proportion
Q-spread
Quartiles
Range
Relative Frequency
Right skewed
Second Quartile
Skewed
Standard Deviation
Standard score
Symmetric
Third Quartile
Unimodal
Variability
Weighted Mean
Z-score
Topics
Box-and-whiskey plot
Dot plot
Chebychev's Theorem
Empirical Rule
Ordered data values
Pareto chart
Pie chart
Sorted data
Stem-and-leaf display
Time Series Chart

Probability
Terms and Definitions
Binomial Experiment
Binomial probability distribution
Classical probability
Combination
Complement
Conditional probability
Continuous
Continuous probability distributions
Counting Techniques
Dependent events
Discrete
Discrete probability distribution
Disjoint events
Empirical probability
Equally likely
Event
Expected value
Experiment
Factorial
Geometric probability distribution
Independent events
Mean valyue of a probability distribution
Mutually exclusive
Normal Probability distribution
Outcome
Permutation
Poisson probability distribution
Posterior probability
Probability distributions
Probability Experiment
Sample space
Sampling distributions
Sampling distribution of the sample mean
Sampling distribution of the sample proportion
Standard normal curve
Standard normal distribution
Statistical probability
Subjective probability
Theoretical probability
Topics and Theorems
Addition Rule for the Probability of A or B
Area under the standard normal curve
Bayes's Theorem
Central Limit Theorem
Law of large numbers
Mean value for a discrete probability distribution
Multiplication rule
Multiplication rule for independent events
Standard deviation for a discrete probability distribution

Inferential Statistics
Terms and Definitions
Alternative hypothesis
Confidence interval
Confidence level
Critical region
Critical value
Degrees of freedom
Hypothesis testing
Interval estimate
Level of significance
Maximum error of estimate
Null hypothesis
P-value
Point estimate
Rejection region
Standardized test statistic
Student's t-distribution
t-distribution
Test statistic
Type I error
Type II error
Topics and Theorems
Calculating confidence intervals
Confidence interval for a population mean
Confidence interval for a population proportion
Hypothesis testing
Interpreting confidence interval"
Minimum sample size to estimate population mean
Minimum sample size to estimate a population proportion
Point estimate for a population mean
Point estimate for a population proportion
Rejection of the null hypothesis criteria using a P-value

Bivariate and Multivatiate Data
Adjusted R²
Coefficient of determination
Coefficient of multiple determination
Correlation
Correlation coefficient
Dependent variable
Explained variation
Explanatory variable
Independent Variable
Least squares line
Line of best fit
Multiple regression
Predicted y-value
Predition interval
R²
Regression equation
Regression line
Residual sum or squares
Residuals
Response variable
Scatter plot
Total sum of squares
Total variation
Standard error of estimate
Unexplained variation
Topics and Theorems
Causation and correlation
Confidence interval for the average value of population regression line for x = k
Confidence interval for the slope of the population regression line
Hypothesis Test for the population correlation coefficient
Hypothesis Test for the slope of the regression line
Predicting y-values using the regression line equation

Other Topics
Terms and Definitions
Cell
Chi -squared distribution
Chi-squared goodness of fit test
Chi-squared test for homogeneity
Chi-square independence test
Contingency table
F-distribution
Kruskal-Wallis test
Non-parametric tests
One-way analysis of variance (ANOVA)
Rank
Sign test
Spearman rank correlation coefficient
Wilcoxon rank sum test
Wilcoxon signed-rank test
Topics and Theorems
Confidence intervals for standard deviation
Hypothesis test for standard deviation
Hypothesis test using the sign test for a population median