/ CTYOnline / Courses / Mathematics

**Prerequisites:** Qualifying math score and completion of Algebra I or the equivalent

**Course Format:** Individually Paced

**Course Length:** Typically 6 months

**Recommended School Credit:** One academic year

**Course Code:** AL2

Description

This course, drawing on software provided by Thinkwell, prepares students for success in Honors Precalculus with Trigonometry. In addition to a full year’s Algebra II honors curriculum, this course includes some precalculus.

This course, along with Honors Geometry, helps prepare students for the math portion of the College Board SAT.

- review of advanced algebra concepts
- functions and graphing
- exponential and logarithmic functions
- non-linear equations and inequalities
- conic sections
- matrices and determinants
- induction
- sequences and series

Graphing calculator recommended, such as TI-83 PLUS or TI-84 PLUS.

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

- The Top Ten List of Mistakes
- Concepts of Inequality
- Inequalities and Interval Notation
- Properties of Absolute Value
- Evaluating Absolute Value Expressions
- An Introduction to Exponents
- Evaluating Exponential Expressions
- Applying the Rules of Exponents
- Evaluating Expressions with Negative Exponents
- Converting between Decimal and Scientific Notation
- Converting Rational Exponents and Radicals
- Simplifying Radical Expressions
- Simplifying Radical Expressions with Variables
- Rationalizing Denominators
- Determining Components and Degree
- Adding, Subtracting, and Multiplying Polynomials
- Multiplying Big Products
- Using Special Products
- Factoring Using the Greatest Common Factor
- Factoring by Grouping
- Factoring Trinomials
- Factoring Perfect Square Trinomials
- Factoring the Difference of Two Squares
- Factoring Sums and Differences of Cubes
- Factoring by Any Method
- Rational Expressions and Domain
- Working with Fractions
- Writing Rational Expressions in Lowest Terms
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Rewriting Complex Fractions
- Introducing and Writing Complex Numbers
- Rewriting powers of i
- Adding and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Dividing Complex Numbers

- An Introduction to Solving Equations
- Solving a Linear Equation
- Solving a Linear Equation with Rationals
- Solving a Linear Equation That Has Restrictions
- An Introduction to Solving Word Problems
- Solving for Perimeter
- Solving a Linear Geometry Problem
- Solving for Consecutive Numbers
- Solving to Find the Average
- Solving for Constant Velocity
- Solving a Problem about Work
- Solving a Mixture Problem
- Solving an Investment Problem
- Solving Business Problems
- Solving Quadratics by Factoring
- Solving Quadratics by Completing the Square
- Completing the Square: Another Example
- Proving the Quadratic Formula
- Using the Quadratic Formula
- Predicting the Type of Solutions Using the Discriminant
- Solving for a Squared Variable
- Finding Real Number Restrictions
- Solving Fancy Quadratics
- An Introduction to Word Problems with Quadratics
- Solving a Quadratic Geometry Problem
- Solving with the Pythagorean Theorem
- Solving a Motion Problem
- Solving a Projectile Problem
- Solving Other Problems
- Determining Extraneous Roots
- Solving an Equation Containing a Radical
- Solving an Equation with Two Radicals
- Solving an Equation with Rational Exponents
- An Introduction to Variation
- Direct Proportion
- Inverse Proportion
- An Introduction to Solving Inequalities
- Solving Compound Inequalities
- More on Compound Inequalities
- Solving Word Problems Involving Inequalities
- Solving Quadratic Inequalities
- Solving Quadratic Inequalities: Another Example
- Solving Rational Inequalities
- Solving Rational Inequalities: Another Example
- Determining the Domains of Expressions with Radicals
- Matching Number Lines with Absolute Values
- Solving Absolute Value Equations
- Solving Equations with Two Absolute Value Expressions
- Solving Absolute Value Inequalities
- Solving Absolute Value Inequalities: More Examples

- Functions and the Vertical Line Test
- Identifying Functions
- Function Notation and Finding Function Values
- Determining Intervals Over Which a Function Is Increasing
- Evaluating Piecewise-Defined Functions for Given Values
- Solving Word Problems Involving Functions
- Finding the Domain and Range of a Function
- Domain and Range: One Explicit Example
- Satisfying the Domain of a Function
- An Introduction to Slope
- Finding the Slope of a Line Given Two Points
- Interpreting Slope from a Graph
- Graphing a Line Using Point and Slope
- Finding the Distance between Two Points
- Finding the Second Endpoint of a Segment
- Collinearity and Distance
- Triangles
- Finding the Center-Radius Form of the Equation of a Circle
- Finding the Center and Radius of a Circle
- Decoding the Circle Formula
- Solving Word Problems Involving Circles
- Graphing Equations by Locating Points
- Finding the x- and y-Intercepts of an Equation
- Writing an Equation in Slope-Intercept Form
- Writing an Equation Given Two Points
- Writing an Equation in Point-Slope Form
- Matching a Slope-Intercept Equation with Its Graph
- Slope with Parallel and Perpendicular Lines
- Constructing Linear Function Models of a Set of Data
- Linear Cost and Revenue Functions
- Graphing Some Important Functions
- Graphing Piecewise-Defined Functions
- Matching Equations with Their Graphs
- The Greatest Integer Function
- Graphing the Greatest Integer Function
- Using Operations on Functions
- Composite Functions
- Components of Composite Functions
- Finding Functions That Form a Given Composite
- Finding the Difference Quotient of a Function
- Deconstructing the Graph of a Quadratic Function
- Nice-Looking Parabolas
- Using Discriminants to Graph Parabolas
- Maximum Height in the Real World
- Finding the Vertex by Completing the Square
- Using the Vertex to Write the Quadratic Equation
- Finding the Maximum or Minimum of a Quadratic
- Graphing Parabolas
- Shifting Curves along Axes
- Shifting or Translating Curves along Axes
- Stretching a Graph
- Graphing Quadratics Using Patterns
- Determining Symmetry
- Reflections
- Reflecting Specific Functions

- Using Long Division with Polynomials
- Long Division: Another Example
- Using Synthetic Division with Polynomials
- More Synthetic Division
- The Remainder Theorem
- More on the Remainder Theorem
- The Factor Theorem and Its Uses
- Factoring a Polynomial Given a Zero
- Presenting the Rational Zero Theorem
- Considering Possible Solutions
- Finding Polynomials Given Zeros, Degree, and One Point
- Finding all Zeros and Multiplicities of a Polynomial
- Finding the Real Zeros for a Polynomial
- Using Descartes' Rule of Signs
- Finding the Zeros of a Polynomial from Start to Finish
- Matching Graphs to Polynomial Functions
- Sketching the Graphs of Basic Polynomial Functions
- Understanding Rational Functions
- Basic Rational Functions
- Vertical Asymptotes
- Horizontal Asymptotes
- Graphing Rational Functions
- Graphing Rational Functions: More Examples

- Understanding Inverse Functions
- The Horizontal Line Test
- Are Two Functions Inverses of Each Other?
- Graphing the Inverse
- Finding the Inverse of a Function
- Finding the Inverse of a Function with Higher Powers
- An Introduction to Exponential Functions
- Graphing Exponential Functions: Useful Patterns
- Graphing Exponential Functions: More Examples
- Using Properties of Exponents to Solve Exponential Equations
- Finding Present Value and Future Value
- Finding an Interest Rate to Match Given Goals
- e
- Applying Exponential Functions
- An Introduction to Logarithmic Functions
- Converting between Exponential and Logarithmic Functions
- Finding the Value of a Logarithmic Function
- Solving for x in Logarithmic Equations
- Graphing Logarithmic Functions
- Matching Logarithmic Functions with Their Graphs
- Properties of Logarithms
- Expanding a Logarithmic Expression Using Properties
- Combining Logarithmic Expressions
- Evaluating Logarithmic Functions Using a Calculator
- Using the Change of Base Formula
- The Richter Scale
- The Distance Modulus Formula
- Solving Exponential Equations
- Solving Logarithmic Equations
- Solving Equations with Logarithmic Exponents
- Compound Interest
- Predicting Change
- An Introduction to Exponential Growth and Decay
- Half-Life
- Newton 's Law of Cooling
- Continuously Compounded Interest
- Systems of Equations
- An Introduction to Linear Systems
- Solving Systems with Substitution
- Solving Systems by Elimination
- An Introduction to Linear Systems in Three Variables
- Solving Linear Systems in Three Variables
- Solving Inconsistent Systems
- Solving Dependent Systems
- Solving Systems with Two Equations
- Investments
- Solving with Partial Fractions
- Solving Nonlinear Systems Using Elimination
- Solving Nonlinear Systems with Substitution
- An Introduction to Systems of Inequalities
- Graphing Systems of Inequalities
- Graphing the Solution Set of a System of Inequalities
- Solving for Maxima-Minima
- Applying Linear Programming

- An Introduction to Matrices
- The Arithmetic of Matrices
- Multiplying Matrices by a Scalar
- Multiplying Matrices
- Multiplying Matrices: Can They Multiply?
- Using the Gauss-Jordan Method
- Using Gauss-Jordan: Another Example
- Evaluating 2x2 Determinants
- Evaluating 3x3 Determinants
- Applying Determinants
- Using Cramer's Rule
- Using Cramer's Rule in a 3x3 Matrix
- An Introduction to Inverses
- Inverses: 2x2 Matrices
- Another Look at 2x2 Inverses
- Inverses: 3x3 Matrices
- Solving a System of Equations with Inverses

- An Introduction to Conic Sections
- An Introduction to Parabolas
- Determining Information about a Parabola from Its Equation
- Writing an Equation for a Parabola
- An Introduction to Ellipses
- Finding the Equation for an Ellipse
- Applying Ellipses: Satellites
- An Introduction to Hyperbolas
- Finding the Equation for a Hyperbola
- Applying Hyperbolas: Navigation
- Identifying a Conic
- Name That Conic

- Using the Binomial Theorem
- Binomial Coefficients
- Understanding Sequence Problems
- Solving Problems Involving Arithmetic Sequences
- Solving Problems Involving Geometric Sequences
- Proving Formulas Using Mathematical Induction
- Examples of Induction
- Solving Problems Involving Permutations
- Solving Problems Involving Combinations
- Solving for Probability and Odds: Dice Rolls
- Solving for Probability and Odds: Decks of Cards

CTY*Online* courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course requires high-speed Internet access (such as Cable or DSL) for online lesson videos. Your browser will need to allow javascript, login cookies, and popup windows from ctyjhu.org and other CTY course web sites.

You may also need the Java Runtime Environment.

This course uses an online classroom for individual or group discussions with the instructor. The classroom works on standard computers with the Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile app.

Sample Video

This demo requires the Flash plugin.