## 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:

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

1.1 Exponents

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

3.4 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

6.3 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

Assignments 25%

Mid-term 25%

Final Exam 50%

100%

## Required Text and Materials

New Comprehensive Mathematics for “O” Level – A. Greer