MCCCD Official Course Competencies:

MAT150  20016-20045

College Algebra Concepts

1.

Solve single variable equations, including linear, absolute value, quadratic, quadratic type, rational, polynomial, radical, exponential, and logarithmic. (I,II,III)

2.

Use function notation. (I, II,III)

3.

State the domain and range of relations and functions. (I, II, III)

4.

Graph relations and functions. (I, II, III)

5.

Identify the equations of circles and parabolas. (I)

6.

Find the axis if symmetry, vertex, and intercepts of a quadratic relation. (I)

7.

Use quadratic functions to model and solve real world problems involving maxima and minima. (I)

8.

Find the center and radius of a circle. (I)

9.

Perform operations on and form compositions of functions and state the domain of the resulting function. (I)

10.

Determine graphically and algebraically whether a function is one-to-one, and find the equation for the inverse of a one-to-one function. (I, III)

11.

Use translations and reflections to graph relations. (I, III)

12.

Find real and complex zeros of polynomial functions. (II)

13.

Find the vertical and horizontal asymptotes of the graph of a rational function. (II)

14.

Use the properties of logarithms. (III)

15.

Solve linear and nonlinear systems of equations and inequalities. (IV, V)

16.

Perform operations on matrices. (V)

17.

Explain the difference between arithmetic and geometric sequences and series. (VI)

18.

Find a specified term of an arithmetic and a geometric sequence. (VI)

19.

Find the nth partial sum of an arithmetic and geometric series. (VI)

20.

Find the sum of an infinite geometric series. (VI)

21.

Explain the difference between combinations and permutations. (VI)

22.

Evaluate combinations and permutations. (VI)

23.

Use the binomial theorem. (VI)

24.

Model and solve real world problems. (I, II, III, IV, V, VI)

MCCCD Official Course Outline:

MAT150  20016-20045

College Algebra Concepts

I. Relations and Functions

A. Domain and Range

B. Graphs of relations and functions

C. Circles and Parabolas

D. Operations on functions

E. Applications

II. Polynomial Functions

A. Real and complex zeros

B. Graphs of polynomial functions C Rational functions

D. Applications

III. Exponential and Logarithmic Functions

A. Domain

B. Properties of logarithms

C. Graphs of exponential and logarithmic functions

D. Exponential and logarithmic equations

E. Applications

IV. Systems of Equations and Inequalities

A. Linear systems

B. Nonlinear systems

C. Systems of linear and nonlinear inequalities

D. Applications

V. Matrices

A. Operations on matrices

B. Matrix equations

C. Applications

VI. Sequence, and Series

A. Arithmetic sequences and series

B. Geometric sequences and series

C. Combinations and permutations

D. The binomial theorem

E. Applications