Pre-Calculus Examples

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Example Topics

• Pre-Calculus

  • Conic Sections+15 topics

    • Circles+1 topic

      • Determine the Equation of a Circle in Standard Form

    • Ellipses

    • Hyperbolas

    • Hyperbolas and Ellipses+1 topic

      • Understand features of hyperbolas and ellipses

    • Parabolas+3 topics

      • Determine the equation of a parabola and graph a parabola

      • Find the Vertex and the Axis of Symmetry of a Parabola

      • Graph a Parabola

    • Polar Equations of Conic Sections+2 topics

      • Find the Polar Equation of a Conic Section

      • Identify the Conic With a Given Polar Equation

    • Quadratic Systems+1 topic

      • Solve a System of Quadratic Equations

  • Exponential and Logarithmic Functions+12 topics

    • Application Problems

    • Exponential Equations and Inequalities+1 topic

      • Use Logarithms To Solve Exponential Equations and Inequalities

    • Exponential Functions+2 topics

      • Graph Exponential Functions

      • Solve Exponential Equations

    • Logarithmic Functions+1 topic

      • Graph Logarithms

    • Properties of Logarithms+1 topic

      • Solve Logarithmic Equations

    • Rational Exponents+1 topic

      • Simplify Expressions With Rational Exponents

  • Functions+21 topics

    • Algebra of Functions+2 topics

      • Add, Subtract, Multiply, and Divide Functions

      • Composition of Functions

    • Cartesian Coordinate System+2 topics

      • Graph Equations

      • Plot Points

    • Inverse Functions+2 topics

      • Find the Inverse of a Function

      • Find the Inverse of a Relation

    • Modeling+1 topic

      • Linear Modeling

    • Real Numbers+1 topic

      • Define a Field

    • Relations and Functions+3 topics

      • Determine if a Relation is a Function

      • Domain and Range

      • Evaluate Functions

    • Special Functions+3 topics

      • Absolute Value Functions

      • Greatest Integer Functions

      • Piecewise Functions

  • Graphing Functions+23 topics

    • Amplitude, Period, Phase Shift of a Trig Function

    • Distance+2 topics

      • Find the Distance Between a Point and a Line

      • Find the Distance Between Two Parallel Lines

    • Graphing Quadratic Functions+2 topics

      • Express a Quadratic Function in Vertex Form

      • Graph a Quadratic Function Using Intercepts, Vertex, and Axis of Symmetry

    • Graphs

    • Linear Functions+2 topics

      • Determine the Equation of a Linear Function

      • Graph a Linear Function

    • Solving Polynomial Equations+1 topic

      • Solve a Polynomial by Factoring

    • Solving Quadratic Equations+3 topics

      • Find roots of quadratic equation using discriminant

      • Solve a Quadratic Equation

      • Write a Quadratic Equation When Given Its Solutions

    • Symmetry+1 topic

      • Determine the Symmetry of an Equation

    • Transformations+2 topics

      • Reflections

      • Translations

    • Trigonometric Graphs (all six)

  • Graphs and Inverses of Trigonometric Functions+14 topics

    • Graphing Inverse Trig Functions

    • Graphing Tangent, Cosecant, Secant, and Cotangent Functions+1 topic

      • Find the Equations of Vertical Asymptotes of Tangent, Cosecant, Secant, and Cotangent Functions

    • Graphing the Sine and Cosine Functions+4 topics

      • Find the Amplitude of a Sine or Cosine Function

      • Find the Period of a Sine or Cosine Function

      • Find the Phase Shift of a Sine or Cosine Function

      • Graph the Sine or Cosine Function

    • Harmonic Motion+1 topic

      • Set Up an Equation That Models Harmonic Motion

    • Inverse Sine and Cosine Functions+1 topic

      • Evaluate Expressions That Include the Inverse Sine or Cosine Function

    • Inverse Trigonometric Functions+1 topic

      • Evaluate Expressions That Include the Inverse Tangent, Cosecant, Secant, or Cotangent Function

  • Inequalities and Linear Programming+11 topics

    • Linear Inequalities+2 topics

      • Solve Absolute Value Inequalities

      • Solve and Graph Linear Inequalities

    • Quadratic Inequalities+1 topic

      • Solve Quadratic Inequalities

    • Solving Polynomial and Rational Inequalities+2 topics

      • Solve and Graph Polynomial Inequalities

      • Solve and Graph Rational Inequalities

    • Systems of Equations+2 topics

      • Solve Nonlinear Systems of Equations

      • Solve Systems of Linear Equations

  • Introductory Calculus+16 topics

    • Area Under a Curve+2 topics

      • Approximate Area Using Rectangles

      • Find the Area Using Limits

    • Derivatives+6 topics

      • Determine Points of Inflection

      • Find the Critical Numbers of a Function

      • Find the First Derivative of a Function

      • Find the Second Derivative of a Function

      • Maximum and Minimum Problems

      • Rate of Change Problems

    • Limits+2 topics

      • Determine if a Function is Continuous Using Limits

      • Find the Limit of a Function

    • Tangents To a Curve+2 topics

      • Find the Equation of a Line Tangent to a Curve At a Given Point

      • Find the Slope of a Line Tangent to a Curve At a Given Point

  • Matrices and Vectors+21 topics

    • Algebraic Vectors and Parametric Equations+6 topics

      • Express a Vector in Component Form

      • Express a Vector in Polar Form

      • Find a Direction Vector When Given Two Points

      • Find a Vector Equation When Given Two Points

      • Find the Unit Vector in the Same Direction as a Given Vector

      • Parametric Equations

    • Augmented Matrices+1 topic

      • Solve a System of Equations in Three Variables Using Augmented Matrices

    • Geometric Vectors+1 topic

      • Evaluate geometric vectors

    • Inverses of Matrices+2 topics

      • Find the Multiplicative Inverse of a Matrix

      • Solve a System of Equations Using the Multiplicative Inverse

    • Multiplication of Matrices+2 topics

      • Find the Product of a Matrix and a Scalar

      • Find the Product of Two Matrices

    • Parallel and Perpendicular Vectors in Two Dimensions+1 topic

      • Determine if Two Vectors Are Parallel or Perpendicular

    • Sum or Difference of Two Matrices+1 topic

      • Find the Sum or Difference of Two Matrices

  • Polar Coordinates and Complex Numbers+15 topics

    • Graphs of Polar Equations+1 topic

      • Determine the Polar Equation of a Graph

    • Polar Coordinates+3 topics

      • Convert Polar Coordinates To Rectangular Coordinates

      • Convert Polar Equations To Rectangular Form and vice versa

      • Convert Rectangular Coordinates To Polar Coordinates and vice versa

    • Polar Form of Complex Numbers+2 topics

      • Express Complex Numbers In Polar Form

      • Express Complex Numbers In Rectangular Form

    • Powers and Roots of Complex Numbers+2 topics

      • Evaluate Powers of Complex Numbers Using DeMoivre's Theorem

      • Find the Roots of Complex Numbers

    • Products and Quotients of Complex Numbers in Polar Form+2 topics

      • Find the Product of Complex Numbers

      • Find the Quotient of Complex Numbers

  • Polynomial Functions+20 topics

    • Descartes' Rule, Intermediate Value Theorem, Sum and Product of Zeros+2 topics

      • Determine the Number of Positive and Negative Real Zeros of a Polynomial Using Descartes' Rule of Signs

      • Find the Sum and Product of the Zeros of a Polynomial

    • Fundamental Theorem of Algebra+2 topics

      • Express a Polynomial as a Product of Linear Factors

      • Find Complex Zeros of a Polynomial Using the Fundamental Theorem of Algebra

    • Graphs of Polynomial Functions+2 topics

      • Graph a Polynomial Function

      • Write the Equation of a Polynomial Function Based on Its Graph

    • Integral and Rational Zeros of Polynomial Functions+1 topic

      • Find the Zeros of a Function Using the Rational Zeros Theorem

    • Radical Functions+1 topic

      • Solve radical equations and inequalities

    • Rational Functions+3 topics

      • Find a Point of Discontinuity

      • Find Intercepts and Asymptotes

      • Rational Equations and Partial Fractions

    • Synthetic Division and the Remainder and Factor Theorems+2 topics

      • Divide Polynomials by Binomials Using Synthetic Division

      • Evaluate a Polynomial Using Synthetic Substitution

  • Sequences and Series+5 topics

    • Arithmetic and Geometric Series

    • Partial Sums of Series

    • Sigma Notation

    • Sums of Infinite Series

    • Terms in a Series

  • Trigonometric Applications+6 topics

    • Area of a Triangle+1 topic

      • Use trigonometric functions to calculate the area of a triangle

    • Law of Cosines and Sines+1 topic

      • Use the laws of cosines and sines

    • Solving Right Triangles+1 topic

      • Solve a Right Triangle

  • Trigonometric Functions+22 topics

    • Angle Measures in Degrees and Radians+3 topics

      • Convert Between Degrees and Radians

      • Find the Area of a Sector Using Radians

      • Find the Length of the Arc of a Circle Using Radians

    • Angles in the Coordinate Plane+2 topics

      • Find the Degree Measure of an Angle

      • Find the Measure of a Coterminal Angle

    • Angular and Linear Velocity+2 topics

      • Solve Angular Velocity Problems

      • Solve Linear Velocity Problems

    • Circular Functions+1 topic

      • Find the value of the sine or cosine functions of an angle given a point on its terminal side

    • Evaluating Trig Functions+2 topics

      • Find the decimal value of a trigonometric function

      • Find the degree measure of an angle for which the value of a trigonometric function is known

    • Fundamental Trigonometric Identities+1 topic

      • Simplify expressions using trigonometric identities

    • Proving Trig Identities+1 topic

      • Prove Trigonometric Identities

    • Trigonometric Functions+2 topics

      • Determine the domain of a trigonometric function

      • Find the value of any of the six trigonometric functions

  • Trigonometric Identities+8 topics

    • Solving Trigonometric Equations and Inequalities+2 topics

      • Solve Trigonometric Equations and Inequalities

      • Solve Trigonometric Equations and Inequalities in Quadratic Form

    • Sum and Difference Identities+4 topics

      • Solve Trigonometric Equations and Inequalities

      • Sum and Difference Identities For Cosine

      • Sum and Difference Identities For Sine

      • Sum and Difference Identities For Tangent