A: Probability

A.1: To define the principle of inclusion and exclusion when working with two or more sets and/or events.

Geometric Probability
Independent and Dependent Events
Theoretical and Experimental Probability

A.3: To determine the probability of two or more independent events.

Binomial Probabilities
Independent and Dependent Events

A.4: To determine the probability of dependent events (conditional probabilities).

Independent and Dependent Events

A.5: To set up, analyze, estimate, and solve word problems based on objectives 1-4.

Independent and Dependent Events

A.6: To determine the coefficients of terms in a binomial expansion using the Binomial Theorem. (Pascal's Triangle or combinations could be used to introduce this topic.)

Binomial Probabilities

A.8: To solve word problems associated with Objectives 6 and 7.

Permutations and Combinations

B: Data Analysis

B.1: To describe and illustrate normal and skewed distributions using real-world examples.

Mean, Median, and Mode
Polling: City
Real-Time Histogram

B.2: To calculate the standard deviation of a set of data.

Polling: City
Real-Time Histogram
Sight vs. Sound Reactions

B.3: To utilize the standard deviation to interpret data represented by a normal distribution.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

C: Matrices

C.3: To add and subtract matrices.

Translations

C.6: To determine the properties of matrices with respect to addition, scalar multiplication, and multiplication.

Translations

C.10: To graph systems of inequalities.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

C.11: To determine the points of intersection of lines drawn in objective C.10.

Linear Programming

D: Complex Numbers

D.1: To define and illustrate complex numbers.

Points in the Complex Plane
Roots of a Quadratic

D.2: To express complex numbers in the form a+bi.

Points in the Complex Plane

D.3: To add and subtract complex numbers.

Points in the Complex Plane

D.4: To multiply and divide complex numbers.

Points in the Complex Plane

D.5: To divide complex numbers using conjugates.

Points in the Complex Plane

E: Quadratic Equations

E.1: To solve quadratic equations using the quadratic formula.

Roots of a Quadratic

E.2: To solve quadratic equations having complex roots.

Roots of a Quadratic

E.3: To solve word problems involving real-world applications of quadratic equations.

Addition and Subtraction of Functions

E.4: To determine the nature of the roots of a quadratic equation using the discriminant.

Roots of a Quadratic

E.5: To determine that the sum of the roots of a quadratic equation ax² + bx + c = 0 equals (-b/a), and the product of the roots equals (c/a).

Roots of a Quadratic

E.6: To write a quadratic equation, given the roots.

Quadratics in Polynomial Form

E.8: To solve quadratic inequalities.

Quadratic Inequalities

F: Polynomial and Rational Functions

F.1: To define and illustrate polynomial and rational functions.

Polynomials and Linear Factors

F.3: To analyze the characteristics of the graphs of polynomial and rational functions and to identify the 'zeros' of these graphs.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form

F.4: To define, determine, and sketch the inverse of a function, where it exists.

Logarithmic Functions

G: Exponential and Logarithmic Functions

G.1: To define exponential functions and logarithmic functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

G.2: To use correctly the laws of exponents for integral and rational exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

G.4: To construct graphs of exponential functions and logarithmic functions, to identify the properties of these graphs, and to recognize they are inverses of each other.

Logarithmic Functions

G.5: To sketch graphs of exponential and logarithmic functions by selecting an appropriate point for the new origin.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

G.6: To solve exponential and logarithmic equations.

Exponential Functions

G.8: To identify a geometric sequence.

Arithmetic and Geometric Sequences
Geometric Sequences

G.9: To determine the nth term of a geometric sequence.

Geometric Sequences

G.10: To calculate the required number of geometric means between given terms.

Arithmetic and Geometric Sequences
Geometric Sequences

G.12: To define and illustrate the following terms: geometric sequence, compound interest, present value, annuity, geometric means.

Arithmetic and Geometric Sequences
Geometric Sequences

G.15: To solve word problems containing arithmetic or geometric series.

Arithmetic and Geometric Sequences