ADVANCED MATHEMATICS (PRE-CALCULUS)

This course is an extension of Algebra II with the emphasis in Trigonometry, Limits, and introductory calculus topics. All major areas covered in Algebra II are reinforced at a greater depth with additional applications aided by the use of calculators and computers. The course is designed to encompass all those topics necessary to be successful in a college calculus course.

In order to satisfy the state graduation requirements, Advanced Mathematics (Pre-calculus) should deal significantly with:

• Problem Solving
• The Complex Number System
• Equations and Inequalities
• Functions
• Sequences and Series
• Probability and Statistics
• Matrices, Determinants and Vectors
• Introductory Calculus
• Polar and Parametric Functions

I. Problem Solving

A. Goal:

Students will understand and show proficiency in problem solving.

Objectives:
Students will

1. Read and properly interpret problem statements.

2. Select appropriate problem solving strategies.

3. Apply strategies to solve "Real World" problems.

4. Use calculators and/or computers as problem solving tools.

5. Use estimation skills to check reasonableness of solutions.

B. Goal:

Students will apply an organized problem solving procedure.

Objectives:
Students will

1. Identify and analyze the problem.

2. Formulate a plan to solve the problem.

3. Solve the problem.

4. Check solution for accuracy.

5. look back for patterns that can be useful in solving other problems.

II. The Complex Number System

A. Goal:

The students will understand complex numbers as a mathematical system.

Objective:
Students will

1. Review and extend basic computational operations from the real to the complex number system and solve related problems.

III. Equations and Inequalities

A. Goal:

The students will understand the use of equations and inequalities.

Objectives:
Students will

1. Expand skills in solving and graphing equations and inequalities with applications.

2. Extend the use of absolute value functions.

3. Learn greatest integer function f(x) = [x].

IV. Functions

A. Goal:

Students will understand polynomial, trigonometric, exponential, and logarithmic functions.

Objectives:
Students will

1. Extend the use and methods involved in factoring, including synthetic division.

2. Expand binomials using the binomial theorem.

3. Solve exponential and logarithmic equations.

4. Solve trigonometric equations.

5. Define and use inverses as they relate to exponential, logarithmic, and trigonometric functions.

6. Solve triangles using trigonometric relationships, the law of sines, and the law of cosines.

7. Graph exponential, logarithmic, and trigonometric functions using translations and symmetry.

8. Prove trigonometric identities.

9. Graph conic sections.

10. Find equations of conic sections given pertinent data.

V. Sequences and Series

A. Goal:

Students will understand and use sequences and series.

Objectives:
Students will

1. Distinguish between arithmetic, geometric and other sequences and series.

2. Calculate various terms of all types of sequences.

3. Compute the sum of finite series.

4. Compute the n^th partial sum of a given infinite series and use limits to find the sum.

5. Use mathematical induction for appropriate proofs.

VI. Probability and Statistics

A.    Goal:

Students will understand the basic principles of probability and statistics.

Objectives:
Students will

1. Define and use permutations and combinations.

2. Apply the binomial theorem to probability.

3. Calculate the probability of an event.

4. Apply the binomial theorem to probability.

5. Solve for mean, median and mode.

6. Use frequency distributions and histograms.

VII. Matrices and Determinants

A. Goal:

Students will understand the use of matrices and determinants.

Objectives:
Students will

1. Evaluate determinants using minors.

2. Solve systems of equations using Cramer's Rule.

3. Perform arithmetic operations with matrices.

4. Use calculators when appropriate to solve matrices.

5. Solve Systems of equations using augmented matrices.

VIII. Introductory Calculus

A. Goal:

Students will understand the concept of limit, derivative, and integral and their applications.

Objectives:
Students will

1. Define limits at positive and negative infinity, and a point (in terms of epsilons and deltas).

2. Calculate limits of functions.

3. Define continuity.

4. Define and compute derivatives.

5. Find equations of tangent lines to curves.

6. Solve maximum-minimum problems.

7. Approximate a definite integral by computing and summing areas of rectangles.

8. Compute basic anti-derivatives.