2. Develop or explain their understanding of mathematical concepts and principles.

$ Relations and Functions

$ Graphs of Functions

$ Slope

$ Equation of a Line

$ Graphing Linear Relations

$ Linear Modes

$ Parallel and Perpendicular Lines

$ Direct Variation

$ Graphing Inequalities

$ Graphing Linear Systems

$ The Substitution Method

$ The Linear Combination Method

$ Problem Solving: Money Problems / Mixture Problems

$ Problem Solving: Wind and Current Problems / Angle Problems

$ Systems of Three Linear Equations

$ Solving Systems of Linear Inequalities

$ Problem Solving : Using Quadratic Equations

$ The Zero-Product Property

$ Problem Solving: Using Quadratic Equations

$ Problem Solving: Area and Length

$ Inequalities Degree 2 and Degree 3

$ Synthetic Substitution and the Remainder Theorem

$ The Integral Zero Theorem

$ Rational Expressions and Functions

$ Products and Quotients of Rational Expressions

$ Dimensional Analysis

$ Sums and Differences of Rational Expressions

$ Complex Rational Expressions

$ Equations Containing Rational Expressions

$ Problem Solving: Rates of Work

$ Square Roots and Functions

$ Simplifying Square Roots

$ Sums, Differences and Products of Square Roots

$ Quotients of Square Roots

$ Simplifying Radicals with Indices Greater Than 2

$ Rational-Number Exponents

$ Complex Numbers: Addition and Absolute Value

$ Products, Quotients, Conjugates

$ Problem Solving: Maximum Values

$ The Quadratic Formula

$ Problem Solving: Irrational Answers

$ Vectors: Addition and Subtraction

$ Vectors and Complex Numbers

$ The Circle

$ The Ellipse

$ The Hyperbola

$ Translations of Ellipses and Hyperbolas

$ The Rectangular Hyperbola and Inverse Variation

$ Problem Solving: Joint and Combined Variation

$ The Parabola: Focus and Directrix

$ Identifying Conic Sections

$ Linear-Quadratic Systems

$ Quadratic-Quadratic Systems

$ Inverse Relations and Functions

$ Exponential Functions/Exponential Equations

$ Base-b Logarithms

$ Graphing Log Functions for Different Base Values

$ Common Logarithms and Antilogarithms

$ Measurement of Segments and Angles

$ Collinearity, Betweenness and Assumptions

$ Division of Segments and Angles

$ Paragraph Proofs

$ Deductive Structure

$ Statements of Logic

$ Probability

$ Perpendicularity

$ Complementary and Supplementary Angles

$ Congruent Supplements and Complements

$ Addition, Subtraction, Multiplication and Division Properties

$ Transitive and Substitution Properties

$ The Postulates to Prove Congruency of Triangles

$ Types and Properties of Triangles

$ Angle-Side Theorems

$ Midpoints and Distance Formula

$ The Equidistant Theorems

$ Introduction to Parallel Lines and Perpendicular Lines

$ Slope of Parallel Lines and Perpendicular Lines

$ Four-sided Polygons

$ Perimeters and Areas of Rectangles, Triangles and Parallelograms

$ Properties of Quadrilaterals

$ Formulas Involving Polygons

$ Similar Polygons and Theorems Involving Proportions

$ Methods of Proving Triangles Similar

$ Congruence and Proportions in Similar Triangles

$ Concepts Relating to Planes

$ Perpendicularity of a Line and a Plane

$ Coplanar Lines and Noncoplaner Lines

$ Methods to Determine a Plane

$ Parallel Planes

$ Review of Radicals and Quadratic Equations

$ Pythagorean Theorem and Converse

$ Families of Right Triangles

$ Special Right Triangles

$ Introduction to Trigonometry

$ Trigonometric Ratios

$ The Definition of a Circle

$ Chords, Arcs, Secants and Tangent Properties of a Circle

$ Angles Related to a Circle

$ Inscribed and Circumscribed Polygons

$ Areas of Circles, Sectors, and Segments

$ Surface Area of Prisms

$ Surface Area of Pyramid

$ Surface Area of Circular Solids

$ Volumes of Prisms and Cylinders

$ Volumes of Pyramids and Cones

$ Volumes of Spheres

$ Factoring

$ Solving Linear, Quadratic and Higher Degree Equations

$ Solving Linear and Compound Inequalities

$ Solving Absolute Value Equations and Inequalities

$ Simplify Radical Expressions

$ Simplify Expressions with Rational Exponents

$ Properties of Logarithms

$ Solving Exponential Equations

$ Inverse Relations and Functions

$ Introduction to Right Triangle Trigonometry

$ Solve Right Triangles Using Trigonometric Tables

$ Angles of Rotation

$ Find the Trigonometric Ratios of Angles of Any Measure Using the Reference Angle

$ Trigonometric Ratios of Special Angles

$ Find the Area of a Triangle Given Two Sides and the Included Angle

$ Use the Law of Sines and the Law of Cosines to Solve Triangles

$ Determine Whether One, Two, or No Triangles Can Be Constructed When Given the Measures of Two Sides and a Non-included Angle

$ Graph and Find Values of Trigonometric Functions

$ Convert between Degree and Radian Measure

$ Find Area and Arc Length of a Sector

$ Define Angles in Terms of Positive and Negative Rotation

$ Determine the Domain, Period and Range of Trigonometric Functions

$ Find the Inclination of a Line

$ Simplify Trigonometric Expressions

$ Prove Trigonometric Identities

$ Solve Trigonometric Equations

$ Graph, and Find Values of, the Inverse Trigonometric Functions

$ Use the Trigonometric Addition, Double Angle, and Half Angle Formulas

$ Simplify and Evaluate Expressions

$ Prove Identities and Solve Equations

$ Find the Angle between Two Intersecting Lines

$ Slope and Equations for Lines

$ Equation of Circles

$ Intersection of Lines and Circles

$ Proofs in Coordinate Geometry

$ The Complex Numbers

$ Find the Zeros of a Polynomial Function

$ Solve Second and Higher Degree Equations by Factoring

$ Sketch the Graphs of Polynomial Functions

$ Apply the Remainder Theorem and the Factor Theorem

$ Find the Maximum and Minimum Values of a Polynomial Function

$ General Theorems about Polynomial Equations

$ Solve and Graph Linear and Polynomial Inequalities in One and Two Variables

$ Graph the Solution Set of a System of Simultaneous Inequalities

$ Solve Linear Programming Problems in Two Dimensions

$ Use the Discriminant to Find an Equation of a Line Tangent to a Circle or Parabola

$ Relations Functions and Their Graphs

$ Distinguish Properties of Functions from Properties of Graphs

$ Determine the Domain, Range, and Zeros of a Function and Sketch the Graph of the Function

$ Write the Equation and Identify the Domain of the Composite of Two Functions

$ Define Functions from Verbal Descriptions

$ Find an Equation and Sketch the Graph of the Inverse of a Function

$ Use the Laws of Exponents and Logarithms to Simplify and Evaluate Expressions and Solve Equations

$ Define and Graph Exponential Functions and Their Inverse Logarithmic Functions

$ Find Logarithms of Numbers to Any Base by Changing to Base 10 or Base e

$ Solve Problems Involving Exponential Growth and Decay

$ Define the Number e and the Natural Logarithm

$ Determine whether a Function is Periodic and Find the Period and Amplitude of a Periodic Function

$ Geometric Transformations: Shifts, Reflections, Stretches and Shrinks of a Graph

$ Determine Whether a Graph a Symmetric with Respect to the Coordinate Axes, the Origin or the Line Y=X

$ Determine the Asymptotes of the Graph of a Function

$ Study Various Applications of the Sine and Cosine Functions

$ Approximate the Area Under a Curve

$ Identify the Type of Conic Section an Equation Represents and Locate Its Vertex/Vertices and Focus or Foci

$ Graph and Find the Equations of Parabolas, Ellipses and Hyperbolas

$ Find the Intersection Points of a System of Conic Equations

$ Solve Applied Problems Involving Conic Sections

$ Mathematical Studies SL - to enable the students to undertake investigations in mathematics individually and as a member of a team in order to apply mathematical skills and knowledge to everyday situations.

$ Mathematical Methods SL - to enable the students to develop a sound basis of mathematical skills and knowledge in order to facilitate the further study of mathematically related subjects.

$ Mathematical Studies SL - students will be expected to write a project in which mathematical techniques are used in defining a problem and searching for ways of solving the problem.

$ Mathematical Methods SL - students will be expected to demonstrate mathematical skills and knowledge and to apply various mathematical methods of reasoning and thought to problems in a wide variety of areas of mathematics.

$ Sums, Differences and Multiples of Vectors

$ Express a Vector in Polar or Component Form

$ Perform Vector Operations in Component Form

$ Given Two Points on a Line to Find a Direction Vector, A Vector Equation and a Pair of Parametric Equations of the Line

$ Find the Angle between Two Vectors or Determine that They Are Parallel or Perpendicular

$ Find the Equation of a Plane Using Vectors in Three Dimensions

$ Use Determinants to Solve Linear Equations in Two or More Variables

$ Matrix Multiplication

$ Matrices for Transformations

$ Matrices for Composites of Transformations

$ Storing Information

$ Addition of Matrices

$ Inverse of a Matrix

$ Determinants

$ Solving Simultaneous Equations Using Matrices

$ Further Applications of Matrices

$ Identify an Arithmetic or Geometric Sequence and Find a Formula for Its nth Term

$ Find the Sum of the First in Terms of an Arithmetic or Geometric Series

$ Find or Estimate the Limit of an Infinite Sequence or to Determine That the Limit Does Not Exist

$ Find the Sum of an Infinite Geometric Series

$ Represent Series Using Sigma Notation

$ Identify a Certain Power Series and Use These Series in Computation

$ Organize data into a frequency table and display it graphically using a histogram or Frequency polygon

$ Describe and analyze data using the Mean, Median, Mode, Variance and Standard Deviation

$ Use the standard normal distribution to study data known to have a normal distribution

$ Use Confidence Intervals and Sampling Theory to draw conclusions from samples that are representative of the entire population

$ Measure how closely two sets of data are related by finding their Correlation Coefficient

$ Use a Regression Line to predict trends

$ Use the Multiplication and Addition Principles to find the number of possible outcomes of two or more actions

$ Solve problems using Conditional Probability

$ Solve problems involving Permutations, Combinations and Probabilities

$ Expand Binomials and use the Binomial Theorem to solve probability problems

$ Definition of a set

$ Equality of sets

$ Subsets

$ Venn Diagrams

$ Union and intersection of sets

$ Complements and Universal Sets

$ Distributive Laws for Union and Intersection Odd Sets

$ DeMorgan=s Laws

$ Cartesian Products

$ Review functions and their graphs

$ Sketch the graphs of basic functions analytically and support using graphing technology

$ Review Geometric Transformations

$ Review Trigonometric Functions

$ Review Exponential and Logarithmic Functions

$ Continuous functions

$ One sided limits and continuity

$ The Sandwich Theorem

$ Limits involving Infinity

$ Horizontal Asymptotes and Vertical Asymptotes

$ Slopes, Tangent Lines, and Derivatives

$ Differentiation Rules

$ Derivatives of Trigonometric Functions

$ Implicit Differentiation and Fractional Powers

$ Linear Approximations and Differentials

$ Antiderivatives, Initial Value Problems and Mathematical Modeling

$ Maxima, Minima and Mean Value Theorem

$ Predicting the hidden behavior of graphs

$ Use of Newton - Raphson Process to Solve Equations

$ Applications involving Optimization

$ Related rates of change

$ Derivatives of Logarithmic Functions

$ Derivatives of Exponential Functions

$ Derivatives of Inverse Trigonometric Functions

$ Further Applications of Derivatives

$ Calculus and Area

$ Definite Integrals and Antiderivatives

$ The Fundamental Theorem of Calculus

$ Indefinite Integrals

$ Numerical Integration

$ Areas between Curves

$ Volumes of Solids of Revolution-Disks and Washers

$ Cylindrical Shells - An Alternate to Washers

$ Formulas for Elementary Integration

$ Integration by Parts

$ Integration by Substitution

$ Rational Functions and Partial Fractions