Finite Math

Finite Mathematics is a specialized sector of mathematics, focusing primarily on quantifiable, discrete quantities. It encompasses areas such as logic, set theory, probability, statistics, matrix theory, linear programming, and mathematical modeling. Finite Mathematics proves to be incredibly beneficial in disciplines where data is limited and necessitates meticulous analysis. Such disciplines include computer science, finance, and operations research.

Polynomials and Expressions

Simplifying
Synthetic Division
Polynomial Division
Finding the Remainder Using Long Polynomial Division
Reducing
Cancelling the Common Factors
Evaluate the Expression Using the Given Values
Identifying Degree
Multiplying Polynomials Using FOIL
Negative Exponents
Operations on Polynomials
Simplifying Expressions
Factoring Using Any Method
Factoring a Difference of Squares
Factoring a Sum of Cubes
Factoring Out Greatest Common Factor (GCF)
Trinomial Squares
Factoring by Grouping
Factoring a Difference of Cubes
Factoring Trinomials
Maximum Number of Real Roots/Zeros
Finding All Possible Roots/Zeros (RRT)
Finding All Roots with Rational Root Test (RRT)

Ratios, Proportions, and Percents

Converting Percents to Decimal
Converting Percents to Fractions
Converting the Percent Grade to Degree
Converting the Degree to Percent Grade

Equations and Inequalities

Solving for a Variable
Converting from Interval to Inequality
Solve by Completing the Square
Finding the Domain
Finding the Range
Finding the Domain and Range
Finding the Asymptotes
Solving by Factoring
Solving Rational Equations
Quadratic Formula
Quadratic Inequalities
Rational Inequalities
Finding the Discriminant
Finding the Quadratic Constant of Variation

Linear Functions and Points

Calculating Slope and y-Intercept
Solving Linear Equations
Solving Radical Equations
Finding the Midpoint of a Line Segment
Distance Formula
Finding a Point's Quadrant
Finding Equations Using the Slope-Intercept Formula
Finding Equations Using Slope-Intercept
Finding Equations Using Two Points
Finding a Perpendicular Line Containing a Given Point
Finding the Slope
Finding a Parallel Line Containing a Given Point
Finding the Equation Using Point-Slope Form

Functions

Find the Behavior (Leading Coefficient Test)
Determining Odd and Even Functions
Arithmetic of Functions
Finding Roots Using the Factor Theorem
Finding All Possible Roots/Zeros (RRT)
Determine if Injective (One to One)
Determine if Surjective (Onto)
Finding the Vertex
Finding the Sum
Finding the Difference
Finding the Product
Finding the Quotient
Finding the Domain of the Sum of the Functions
Finding the Domain of the Difference of the Functions
Finding the Domain of the Product of the Functions
Finding the Domain of the Quotient of the Functions
Finding Roots (Zeros)
Identifying Zeros and Their Multiplicities
Finding the Bounds of the Zeros
Proving a Root is on the Interval
Finding the Average Rate of Change
Finding the Inverse
Finding Maximum Number of Real Roots
Function Composition
Rewriting as a Function
Finding the Domain and Range
Determining if a Function is Rational
Determining if a Function is Proper or Improper
Maximum/Minimum of Quadratic Functions

Relations

Determining if the Relation is a Function
Finding the Domain and Range of the Relation
Finding the Inverse of the Relation
Determining if Surjective (Onto)
Determining if Bijective (One-to-One)

Matrices

Finding the Dimensions
Multiplication by a Scalar
Multiplication
Subtraction
Finding the Identity Matrix
Finding the Scalar multiplied by the Identity Matrix
Addition
Simplifying the Matrix Operation
Finding the Determinant of a 2x2 Matrix
Finding the Determinant of a 3x3 Matrix
Finding the Determinant of Large Matrices
Inverse of a 2x2 Matrix
Inverse of an nxn Matrix
Finding Reduced Row Echelon Form
Finding the Transpose
Finding the Adjoint
Finding the Cofactor Matrix
Finding the Basis and Dimension for the Column Space of the Matrix
Finding the Basis and Dimension for the Row Space of the Matrix
Finding the LU Decomposition of a Matrix

Systems of Linear Equations

Substitution Method
Determining Parallel Lines
Determining Perpendicular Lines
Cramer's Rule
Solving using Matrices by Elimination
Solving using Matrices by Row Operations
Solving using an Augmented Matrix

Mathematics of Finance

Finding the Simple Interest Received
Finding the Present Value with Compound Interest
Finding the Simple Interest Future Value
Finding the Future Value with Continuous Interest

Average Descriptive Statistics

Finding the Median
Finding the Mean (Arithmetic)
Finding the Mode
Finding the Geometric Mean
Finding the Quadratic Mean (RMS)
Finding the Minimum
Finding the Maximum
Finding the Mid-Range (Mid-Extreme)
Finding the Lower or First Quartile
Finding the Upper or Third Quartile
Finding the Interquartile Range (H-Spread)
Finding the Midhinge
Finding the Five Number Summary

Probability

Solving Combinations
Solving Permutations
Finding the Probability of Both Independent Events
Finding the Probability for Both Mutually Exclusive Events
Finding the Conditional Probability for Independent Events
Determining if Given Events are Mutually Exclusive Events
Finding the Probability of Both not Mutually Exclusive Events
Finding the Probability of the Complement

Dispersion Statistics

Finding the Median
Finding the Mean (Arithmetic)
Finding the Mode
Finding the Standard Deviation
Finding the Minimum
Finding the Maximum
Finding the Lower or First Quartile
Finding the Upper or Third Quartile
Finding the Five Number Summary

Statistical Distributions

Describing Distribution's Two Properties
Finding the Expectation
Finding the Standard Deviation
Finding the Variance
Finding a z-Score for a Normal Distribution
Approximating Using Normal Distribution
Finding the Probability of a Binomial Distribution
Finding the Probability of the Binomial Event
Finding the Mean

Frequency Distribution

Finding the Upper and Lower Class Limits of the Frequency Table
Finding the Class Boundaries of the Frequency Table
Finding the Class Width of the Frequency Table
Finding the Midpoints of the Frequency Table
Finding the Mean of the Frequency Table
Finding the Variance of the Frequency Table
Finding the Standard Deviation of the Frequency Table
Finding the Cumulative Frequency of the Frequency Table
Finding the Relative Frequency of the Frequency Table
Finding the Median Class Interval of the Frequency Table
Finding the Modal Class of the Frequency Table
Creating a Grouped Frequency Distribution Table
Finding the Data Range

Normal Distributions

Finding the Probability of the z-Score Range
Finding the Probability of a Range in a Nonstandard Normal Distribution
Finding the z-Score Using the Table
Finding a t-Value for a Confidence Level
Finding the Critical t-Value
Finding the z-Score

t-Distributions

Finding a t-Value for a Confidence Level
Finding the Critical t-Value

Hypothesis Testing

Setting the Alternative Hypothesis
Setting the Null Hypothesis
Determining if Left, Right, or Two Tailed Test Given the Null Hypothesis
Determining if Left, Right, or Two Tailed Test Given the Alternative Hypothesis

Estimation and Sample Size

Finding Standard Error

Correlation and Regression

Finding the Linear Correlation Coefficient
Determining if the Correlation is Significant
Finding a Regression Line

Vectors

Vector Addition
Vector Subtraction
Vector Multiplication by a Scalar
Finding the Position Vector

Popular Problems

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