Pre-Calculus
Pre-calculus bridges algebra and calculus, covering advanced functions, polynomial and rational expressions, exponential and logarithmic functions, sequences and series, conic sections, and an introduction to limits. It prepares students for the rigorous reasoning required in calculus.
Key Concepts
A deleted neighborhood of a point $a$ is the set of all points within a certain distance $\delta$ of $a$, but excludi...
Set-builder notation is a compact way to describe a set by stating a rule or condition that its elements must satisfy...
A limaçon is a family of polar curves defined by the equation r = b + a cos θ (or r = b + a sin θ), whose shape range...
A cardioid is a heart-shaped curve traced by a point on the circumference of a circle as it rolls around a fixed circ...
Focal radius is a term with two common meanings: (1) the distance from the center of an ellipse or hyperbola to a foc...
Average rate of change is the change in the output of a function divided by the change in the input over a given inte...
Average rate of change is the change in the output of a function divided by the change in the input over a given inte...
Degenerate conic sections are the special cases that arise when a plane intersects a double cone exactly at its apex,...
Dilation of a graph is a transformation that stretches or compresses a graph by multiplying all x-coordinates or all ...
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
All Pre-Calculus Terms (280)
- Absolute Maximum
- Absolute Minimum
- Absolute Value of a Complex Number
- Acceleration
- Additive Inverse of a Matrix
- Adjoint, Classical
- Adjugate
- Affine Transformation
- Algebra
- Algorithm
- Analytic Geometry
- Analytic Methods
- Angle of Inclination of a Line
- Antipodal Points
- ARC
- Area of a Convex Polygon
- Area of a Parabolic Segment
- Area of an Ellipse
- Argand Plane
- Argument of a Complex Number
- Argument of a Vector
- Augmented Matrix
- Axis of Rotation
- Back Substitution
- Binomial Coefficients
- Binomial Coefficients in Pascal's Triangle
- Binomial Theorem
- Bounded Function
- Bounded Sequence
- Brachistochrone
- Cardioid
- Cartesian Form
- Catenary
- Cavalieri’s Principle
- Ceiling Function
- Center of Rotation
- Centroid
- Centroid Formula
- Cis
- Closed Interval
- Coefficient Matrix
- Cofactor
- Cofactor Matrix
- Column of a Matrix
- Compatible Matrices
- Complex Conjugate
- Complex Number Formulas
- Complex Numbers
- Composite
- Compression
- Compression of a Graph
- Concave
- Concave Down
- Concave Up
- Conjugate Pair Theorem
- Continued Sum
- Continuous Function
- Contrapositive
- Converge
- Convergent Sequence
- Convergent Series
- Cramer’s Rule
- Cross Product
- Curve
- Cusp
- Cycloid
- De Moivre’s Theorem
- Decreasing Function
- Degenerate
- Degenerate Conic Sections
- Deleted Neighborhood
- Delta (Δ δ)
- Determinant
- Diagonal Matrix
- Difference Quotient
- Dihedral Angle
- Dilation
- Dilation of a Graph
- Dimensions
- Dimensions of a Matrix
- Directrices of a Hyperbola
- Directrices of an Ellipse
- Directrix of a Parabola
- Discontinuity
- Discontinuous Function
- Disk
- Distance Formula
- Distance from a Point to a Line
- Diverge
- Divergent Sequence
- Divergent Series
- Dot Product
- Double Cone
- e
- Eccentricity
- Element of a Matrix
- Ellipsoid
- End Behavior
- Euler's Formula
- Even Function
- Expansion by Cofactors
- Explicit Formula of a Sequence
- Explicit Function
- Extremum
- Factorial
- Falling Bodies
- Fibonacci Sequence
- Fixed
- Floor Function
- Focal Radius
- Foci of a Hyperbola
- Foci of an Ellipse
- Focus of a Parabola
- Frequency of a Periodic Function
- Frequency of Periodic Motion
- Function Operations
- Gaussian Elimination
- Graphic Methods
- Half-Closed Interval
- Harmonic Mean
- Harmonic Progression
- Harmonic Series
- Helix
- Hero’s Formula
- Hole
- Hole (in a Graph)
- Homogeneous System of Equations
- Horizontal Compression
- Horizontal Dilation
- Horizontal Line Test
- Horizontal Reflection
- Horizontal Shift
- Hyperbolic Trig
- Identity Function
- Identity Matrix
- Identity of an Operation
- Implicit Form
- Implicit Function or Relation
- Increasing Function
- Indeterminate Expression
- Infinite Geometric Series
- Inflection Point
- Inner Product
- Interval
- Interval Notation
- Invariant
- Inverse Function
- Inverse of a Matrix
- Invertible Matrix
- Isometry
- Iterative Process
- Jump Discontinuity
- Latus Rectum
- Lemniscate
- Limaçon
- Limit
- Linear
- Linear Combination
- Linear Equation
- Linear Factorization
- Linear Programming
- Linear Regression
- Linear System of Equations
- Local Behavior
- Local Maximum
- Local Minimum
- Locus
- Logistic Growth
- Magnitude
- Magnitude of a Vector
- Main Diagonal of a Matrix
- Mathematical Model
- Matrix
- Matrix Addition
- Matrix Multiplication
- Matrix Subtraction
- Maximize
- Maximum of a Function
- Minimize
- Minimum of a Function
- Mode
- Multivariable
- n Dimensions
- n-tuple
- Neighborhood
- Noninvertible Matrix
- Nontrivial
- Normal
- Normalizing a Vector
- nth Partial Sum
- Oblate Spheroid
- Oblique
- Oblique Asymptote
- Octants
- Odd Function
- One Dimension
- One-to-One Function
- Open Interval
- Parameter (algebra)
- Parametric Equations
- Parametrize
- Parent Functions
- Partial Fractions
- Partial Sum of a Series
- Period of a Periodic Function
- Period of Periodic Motion
- Periodic Function
- Periodic Motion
- Piecewise Continuous Function
- Piecewise Function
- Point of Division Formula
- Point of Symmetry
- Polar Axis
- Polar Conversion Formulas
- Polar Coordinates
- Polar Curves
- Polar Equation
- Polar Form of a Complex Number
- Prolate Spheroid
- Rational Inequality
- Real Part
- Recursive Formula of a Sequence
- Reduced Row-Echelon Form of a Matrix
- Regression Line
- Relation
- Restricted Domain
- Restricted Function
- RMS
- Rose Curve
- Rotation
- Row Operations
- Row Reduction
- RPM
- Scalar
- Scale Factor
- Secant Line
- Sequence
- Sequence of Partial Sums
- Series
- Set-Builder Notation
- Simple Closed Curve
- Simple Harmonic Motion (SHM)
- Skew Lines
- Solid
- Solve Analytically
- Solve Graphically
- Speed
- Sphere
- Spherical Trigonometry
- Spheroid
- Spiral
- Square Matrix
- Square System of Equations
- Step Function
- Surface
- Tangent Line
- Tautochrone
- Three Dimensional Coordinates
- Three Dimensions
- Transformations
- Transpose of a Matrix
- Triangle Inequality with Absolute Value
- Triple (Scalar) Product
- Two Dimensions
- Uniform
- Unit Vector
- Vector
- Velocity
- Vertical Compression
- Vertical Dilation
- Vertical Line Test
- Vertical Reflection
- Vertical Shift
- Volume
- x-y Plane
- x-z Plane
- y-z Plane
- z-intercept
- Zero Matrix
- Zero Vector