Precalculus

Precalculus, a critical precursor to calculus, merges elements of algebra and geometry to equip students for understanding more complex mathematical theories. It encompasses areas such as functions, equations, logarithms, limits, and trigonometry. Gaining proficiency in precalculus is vital for grasping the concepts of calculus and other advanced mathematical fields.

Algebra Concepts and Expressions

Solving for a Variable

Solving by Graphing

Polynomial Division

Finding the Remainder Using Long Polynomial Division

Synthetic Division

Factoring Using Any Method

Factoring a Difference of Squares

Factoring a Sum of Cubes

Factoring Out Greatest Common Factor (GCF)

Factoring by Grouping

Factoring Trinomials

Partial Fraction Decomposition

Finding the Perfect Square Trinomial

Finding a Perpendicular Line Containing a Given Point

Finding a Parallel Line Containing a Given Point

Reordering the Polynomial in Ascending Order

Finding the LCM of a List of Expressions

Finding the LCD of a List of Expressions

Determining if the Number is a Perfect Square

Evaluate

Combining

Finding the Domain

Dividing

Evaluate the Expression Using the Given Values

Evaluating the Difference Quotient

Evaluating Radicals

Determining if True

Finding the Holes in a Graph

Relations

Determining if the Relation is a Function

Finding the Domain and Range of the Relation

Finding the Inverse of the Relation

Finding the Inverse

Determining if One Relation is the Inverse of Another

Determining if Surjective (Onto)

Determining if Bijective (One-to-One)

Determining if Injective (One to One)

Functions

Determining if Linear

Rewriting as an Equation

Rewriting as y=mx+b

Find the Behavior (Leading Coefficient Test)

Finding Ordered Pair Solutions

Determining Odd and Even Functions

Describing the Transformation

Finding the Symmetry

Finding the Asymptotes

Difference Quotient

Finding Roots Using the Factor Theorem

Finding All Possible Roots/Zeros (RRT)

Finding Upper and Lower Bounds

Finding the Vertex

Rewriting as a Function

Determining if a Function is Rational

Determining if a Function is Proper or Improper

Maximum/Minimum of Quadratic Functions

Finding the Slope

Graphing

Operations on Functions

Evaluating Functions

Arithmetic of Functions

Domain of Composite Functions

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 Inverse

Finding Maximum Number of Real Roots

Function Composition

Finding the Domain and Range

Points, Lines, and Line Segments

Finding a Point's Quadrant

Finding the Midpoint of a Line Segment

Distance Formula

Finding Equations Using Slope-Intercept

Finding the Start Point Given the Mid and End Points

Finding the End Point Given the Start and Mid Points

Finding the Slope

Finding the y Intercept

Finding the Slope and y-Intercept

Finding the Equation of the Parabola

Finding the Average Rate of Change

Finding the Slope of the Perpendicular Line to the Line Through the Two Points

Absolute Value Expressions and Equations

Simplifying Absolute Value Expressions

Solving with Absolute Values

Finding the Vertex for the Absolute Value

Rewriting the Absolute Value as Piecewise

Radical Expressions and Equations

Calculating the Square Root

Simplifying Radical Expressions

Rationalizing Radical Expressions

Solving Radical Equations

Rewriting with Rational (Fractional) Exponents

Finding the Square Root End Point

Rational Expressions and Equations

Reducing

Cancelling the Common Factors

Rewriting in Standard Form

Operations on Rational Expressions

Determining if the Point is a Solution

Finding the Domain

Solving over the Interval

Finding the Range

Finding the Domain and Range

Solving Rational Equations

Adding Rational Expressions

Subtracting Rational Expressions

Multiplying Rational Expressions

Finding the Equation Given the Roots

Finding the Asymptotes

Finding the Constant of Variation

Finding the Equation of Variation

Polynomial and Rational Functions

Simplifying Absolute Value Expressions

Solving with Absolute Values

Rationalizing Radical Expressions

Simplifying Radical Expressions

Solving Radical Equations

Reducing

Cancelling the Common Factors

Operations on Rational Expressions

Solving Rational Equations

Quadratic Inequalities

Rational Inequalities

Determining if the Expression is a Polynomial

Determining if Polynomial is Prime

Determining if the Polynomial is a Perfect Square

Finding the Leading Term

Finding the Leading Coefficient

Finding the Degree, Leading Term, and Leading Coefficient

Factoring Polynomials

Finding the GCF of a Polynomial

Factoring Out Greatest Common Factor (GCF)

Identifying the Common Factors

Cancelling the Common Factors

Factoring Trinomials

Trinomial Squares

Factoring Using Any Method

Factoring a Difference of Squares

Factoring a Sum of Cubes

Factoring by Grouping

Factoring a Difference of Cubes

Determine if an Expression is a Factor

Determining if Factor Using Synthetic Division

Find the Factors Using the Factor Theorem

Determining if Polynomial is Prime

Determining if the Polynomial is a Perfect Square

Expand using the Binomial Theorem

Finding All Integers k Such That the Trinomial Can Be Factored

Conic Sections

Identifying Conic Sections

Identifying Circles

Finding a Circle Using the Center and Another Point

Finding a Circle by the Diameter End Points

Finding the Parabola Equation Using the Vertex and Another Point

Finding the Properties of the Parabola

Finding the Vertex

Finding the Vertex Form of the Parabola

Finding the Vertex Form of an Ellipse

Finding the Vertex Form of a Circle

Finding the Vertex Form of a Hyperbola

Finding the Standard Form of a Parabola

Finding the Expanded Form of an Ellipse

Finding the Expanded Form of a Circle

Finding the Expanded Form of a Hyperbola

Exponential and Logarithmic Functions

Simplifying Logarithmic Expressions

Expanding Logarithmic Expressions

Exponential Expressions

Exponential Equations

Evaluating Logarithms

Rewriting in Exponential Form

Converting to Logarithmic Form

Converting to Radical Form

Trigonometry

Converting Radians to Degrees

Converting Degrees to Radians

Right Triangle Trigonometry

Graphing Sine & Cosine Functions

Graphing Other Trigonometric Functions

Amplitude, Period, and Phase Shift

Converting RPM to Radians per Second

Finding a Reference Angle

Finding a Supplement

Finding a Complement

Finding the Quadrant of the Angle

Analytic Trigonometry

Using Fundamental Identities

Solving Standard Angle Equations

Expanding Using Double-Angle Formulas

Expanding Using Triple-Angle Formulas

Finding the Quadrant of the Angle

Inequalities

Solving for a Variable

Determining if the Point is a Solution

Quadratic Inequalities

Rational Inequalities

Converting from Interval to Inequality

Converting to Interval Notation

Rewriting as a Single Interval

Linear Equations

Determining if Linear

Solving Linear Equations

Calculating Slope and y-Intercept

Rewriting in Slope-Intercept Form

Rewriting in Standard Form

Finding x and y Intercepts

Finding Equations Using the Slope-Intercept Formula

Finding Equations Using the Point Slope Formula

Finding Equations Given Point and y-Intercept

Finding the Constant Using Slope

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 Slope of a Parallel Line

Finding a Parallel Line to the Given Line

Finding the Slope of a Perpendicular Line

Finding a Perpendicular Line to the Given Line

Finding Ordered Pair Solutions

Using a Table of Values to Graph an Equation

Finding the Equation Using Point-Slope Form

Systems of Equations

Substitution Method

Addition/Elimination Method

Determining Parallel Lines

Determining Perpendicular Lines

Graphing Method

Determining if the Point is a Solution

Finding the Constant of Variation

Dependent, Independent, and Inconsistent Systems

Finding the Intersection (and)

Finding the Union (or)

Finding the Equation with Real Coefficients

Solving in Terms of the Arbitrary Variable

Finding a Direct Variation Equation

Finding the Slope for Every Equation

Finding a Variable Using the Constant of Variation

Quadratic Equations

Quadratic Formula

Solving by Factoring

Solve by Completing the Square

Finding the Perfect Square Trinomial

Finding the Quadratic Equation Given the Solution Set

Finding a,b, and c in the Standard Form

Finding the Discriminant

Finding the Quadratic Constant of Variation

Matrices

Solving

Simplifying Matrices

Finding the Variables

Solving the System of Equations Using an Inverse Matrix

Finding the Dimensions

Multiplication by a Scalar

Multiplication

Subtraction

Finding the Determinant of the Resulting Matrix

Finding the Inverse of the Resulting Matrix

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

Null Space

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

Sequences and Series

Arithmetic Sequences/Progressions

Geometric Sequences/Progressions

Finding the Next Term of the Sequence

Finding the nth Term Given a List of Numbers

Finding the nth Term

Finding the Sum of First n Terms

Expanding Series Notation

Finding the Sum of the Series

Finding the Sum of the Infinite Geometric Series

Analytic Geometry in Rectangular Coordinates

Finding the Midpoint of a Line Segment

Distance Formula

Calculating Slope and y-Intercept

Identifying Conic Sections

Identifying Circles

Analytic Geometry in Polar Coordinates

Converting to Polar Coordinates

Converting to Rectangular Coordinates

Identifying and Graphing Circles

Identifying and Graphing Limacons

Identifying and Graphing Roses

Identifying and Graphing Cardioids

Limits and an Introduction to Calculus

Evaluating Limits Approaching a Value

Evaluating Limits Approaching Infinity

Vectors

Vector Addition

Vector Subtraction

Vector Multiplication by a Scalar

Finding the Variables

Finding the Length

Finding the Position Vector

Determining Column Spaces

Finding the Angle Between the Vectors

Number Sets

Finding the Intersection of Sets

Finding the Union of Number Sets

Determining if a Set is a Subset of Another Set

Determining if Two Sets are Mutually Exclusive

Finding the Set Complement of Two Sets

Finding the Power Set

Finding the Cardinality

Finding the Cartesian Product of Two Sets

Determining if a Set is a Proper Subset of Another Set

Popular Problems

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