MCCCD Official Course Competencies:

MAT187  2004 Spring – 2011 Summer II

Precalculus

1.

Solve and graph inequalities involving absolute value, rational expressions, and one or two variables. (I)

2.

Define function and give several examples. (II)

3.

Graph linear, quadratic, polynomial, rational, logarithmic, and trigonometric functions. (II)

4.

Use logarithms to solve exponential equations. (II)

5.

Find distance between points, midpoint of a line segment, and determine the equation of a line, given two points. (II)

6.

Solve any polynomial equation and graph any polynomial function. (II)

7.

Use right-triangle trigonometry, laws of sines and cosines to find missing parts of a triangle. (II)

8.

Find inverses of trigonometric functions and graph both the function and its inverse. (II)

9.

Solve trigonometric equations, write complex numbers in trigometric form, and graph using polar coordinates. (III)

10.

Solve systems of equations using matrices. (IV)

11.

Use symmetry, asymptotes, and other analytical aids to graph functions. (V)

12.

Graph equations of conic sections. (VI)

13.

Identify arithmetic or geometric sequences, find specific terms of a sequence or series, solve series problems, and use the binomial theorem to find a specific term of an expansion. (VII)

MCCCD Official Course Outline:

MAT187  2004 Spring – 2011 Summer II

Precalculus

I. Solving and graphing inequalities

A. Linear

B. Absolute value

C. Quadratic

D. Inequalities involving rational expressions

II. Functions

A. Concept of function

B. Graphs of functions

C. Special functions and properties

1. One-to-one

2. Composite functions

3. Inverse

D. Linear functions

1. Distance between points

2. Midpoint of a line segment

3. Parallel and perpendicular lines

4. Equation of a line

5. Graphs

E. Quadratic functions and graphs

F. Polynomials functions

1. Remainder and factor theorems

2. Synthetic division

3. Fundamental theorem of algebra

4. Rationbal and irrational roots

5. Graphs of polynomial functions

G. Rational functions and graphs

H. Exponential and logarithmic functions

1. Common logarithms

2. Natural logarithms

3. Properties of logarithms

4. Solving exponential equations

I. Trigonometric functions

1. Right-triangle trigonometry

2. Trigonometric functions of general angles

3. Law of sines

4. Law of cosines

5. Graphs

6. Inverses of trigonometric functions and graphs

III. Analytical trigonometry

A. Trigonometric functions of real numbers

B. Identities and proofs

C. Addition formulas for sine and cosine

D. Double-angle, half-angle, and reduction formulas

E. Trigonometric equations

F. Trigonometric form of complex numbers

G. Polar coordinates

IV. Systems of equations and inequalities

A. Linear systems

B. Matrices

1. Determinants

2. Cramer's rule

3. Algebra of matrices

4. Inverses of matrices

C. Nonlinear systems

D. Systems of inequalities

V. Graphing aids

A. Intercepts and symmetry

B. Asymptotes

C. Excluded regions

D. Curve sketching

VI. Conic sections and graphs

A. Parabola

B. Ellipse and circle

C. Hyperbola

VII. Sequences and series

A. Arithmetic and geometric sequences

B. Series

C. Infinite geometric series

D. Mathematical induction

E. Binomial theorem