### Outline: Math 138

## Course Title: College Algebra

## Course Code: Math 138

## Hours per week: 3 hours

## Duration: 45 hours

### Course Description

This course provides students with a solid foundation of algebraic concepts. It focuses on the application of algebra and arithmetic to the solution of linear and polynomial equations as well as inequalities.

### Course Objectives

Upon completion of this course, students should be able to:

- Solve algebraic equations.
- Understand and plot linear and quadratic graphs.
- Apply linear inequalities to simple linear programming problems.
- Identify functions and functional notation and apply these to the sketching of graphs.
- Identify and perform mathematical operations on matrices including the use of simultaneous linear equations.
- Apply differentiation to polynomial functions.

### Course Content

### 1. Types of Functions

1.1 Exponents

1.2 Radicals

1.3 Exponentials

1.4 Logarithms

### 2. Equations

2.1 Solution of simple linear equations involving brackets and fractions

2.2 Solution of quadratic equations by formula

2.3 Worded problems solved by linear and quadratic equations

### 3. Graphs

3.1 Linear graphs

3.2 Gradients of Linear graphs

3.3 Quadratic graphs

3.4 Intersecting graphs

3.5 Graphical solutions of equations

### 4. Inequalities and Linear Programming

4.1 Inequality symbols

4.2 Graphic representation of inequalities involving one or two variables

4.3 Sets of inequalities defining a region of the plane

4.4 Solving inequalities

4.5 Introduction to the fundamental theorem of linear programming

4.6 Using a search line ax+by=k

### 5. Functions and Relations

5.1 Relations

5.2 Functions

5.3 Graphical representations of functions

5.4 The inverse of a function

5.5 Composite functions

### 6. Matrices

6.1 Introduction- matrix notation, the order of a matrix

6.2 Matrix addition and subtraction

6.3 Multiplication by a scalar

6.4 Matrix multiplication

6.5 Determinat of a matrix

6.6 The inverse of a matrix

6.7 Matrix solutions of simultaneous equations

### 7. Series

7.1 Sequences

7.2 Arithmetical Progressions

7.3 Geometrical Progressions

7.4 Sums of A.P.’s and G.P.’s

### 8. Permutations and Combinations

8.1 Arrangements

8.2 Factorial Notation

8.3 Permutations

8.4 Combinations

### 9. Differentiation

9.1 The gradient of a line

9.2 The gradient of a curve

9.3 Equation of a tangent to a curve at a point

9.4 The differentiation of a polynomial

#### Pre-requisites: MA 011, BGCSE or equivalent

## Evaluation

Assignments 25%

Mid-term 25%

Final Exam __50%__

100%

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