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Pre-Calculus - 1st year


Designed to prepare students for the calculus sequence. Begins with a review of algebraic concepts and skills: the real and complex number systems, polynomials, algebraic fractions, exponents and radicals, linear and quadratic equations, inequalities, rectangular coordinate systems, lines and circles. Study then turns to the elementary functions and their graphs: linear, quadratic, general polynomial, rational, exponential and logarithmic.



Objectives:

By the end of this course, students will be able to:

1. Evaluate and simplify algebraic expressions;

2. Solve various types of algebraic equations and inequalities;

3. Use the distance formula and the midpoint formula;

4. Graph lines and conic sections: circle, parabola, ellipse and hyperbola;

5. Demonstrate knowledge of concepts and skills relating to graphing techniques: intercepts, symmetry, asymptotes, shifts, stretches and reflections;

6. Demonstrate knowledge of concepts and skills relating to functions in general: domain, range, even/odd functions, operations on functions, one-to-one functions and inverse functions;

7. Draw graphs of the elementary functions: linear, quadratic, general polynomial, rational, exponential, logarithmic and trigonometric;

8. Solve these types of equations: exponential, logarithmic and trigonometric;

9. Solve practical problems involving the elementary functions.

Topics:

Course topics will include the following:

1. Algebraic concepts and skills

2. Rectangular coordinate systems

3. Lines and conic sections

4. Graphing techniques

5. Concepts and skills of functions in general

6. The elementary functions and their graphs

7. Equations: exponential, logarithmic and trigonometric

Method of Instruction:

1. Classroom lecture

2. Problem-solving activities


Types of Assignments:

1. Reading assignments

2. Problem solving


Sample Text:

1. PreCalculus: Functions and Graphs, 9th ed., Swokowski and Cole, 2002