# SECTION 1: ALGEBRA AND FUNCTIONS

## A look at Functions, Polynomials, Surds, Indices and Logarithms ...

**POLYNOMIALS**

At the end of this section, students should be able to:

- factorise polynomial expressions of degree less than or equal to 4, leading to real linear factors;
- apply the Remainder Theorem;
- use the Factor Theorem to find factors and to evaluate unknown coefficients;

**INEQUALITIES**

At the end of this lesson students should be able to

- solve quadratic inequalities
- solve rational inequalties

**THE DISCRIMINANT**

At the end of this section, students should be able to:

- determine the nature of roots of a quadratic equation

**FUNCTIONS**

At the end of this section, students should be able to:

- use terms to functions;
- determine the range of a function given its domain;
- determine whether a given function is many – to – one or one – to – one;
- determine the inverse of a given function, (if it exists);
- plot and sketch functions and their inverse, (if they exist);
- state the geometrical relationship between and its inverse ;
- find the composition of two functions;
- recognise that, if is the inverse of , then , for all , in the domain of .

**SURDS**

At the end of this course students should be able to:

- simplify surds
- rationalize fractions involving surds

**INDICES and DISGUISED QUADRATICS**

At the end of this course students should be able to:

- solve equations reducible to quadratic form

**LOGARITHMS**

At the end of this section, students should be able to;

- use the fact that where is any positive whole number;
- simplify expressions by using the laws:

- solve logarithmic equations;
- use logarithms to solve equations of the form ;
- apply logarithms to problems involving the transformation of a given relationship to linear form.

**SEQUENCES and SERIES**

At the end of this section, students should be able to:

- define a sequence of terms, , where is a positive integer;
- write a specific term from the formula for the term of a sequence;
- use the summation () notation;
- define a series, as the sum of the terms of a sequence;
- identify arithmetic and geometric series;
- obtain expressions for the general terms and sums of finite and infinite geometric series;
- show that all arithmetic series (except for zero common difference) are divergent, and that geometric series are convergent only if , where is the common ratio;
- calculate the sum of arithmetic series to a given number of terms;
- calculate the sum of geometric series to a given number of terms;
- find the sum of a convergent geometric series.

## Your Instructor

Sean Hunte, Your Passionate Mathematics Teacher

I was once a student just like you. I struggled with Mathematics for the first two (2) years of my secondary school life. In third form my teacher, Dr Sargeant, taught Mathematics in a unique way which allowed me to successfully learn the subject which I was passionate about. Her teaching enabled me to thrive in an area which I would eventually pursue as a career.

Therefore, I have successfully completed CXC's CSEC General Mathematics and CAPE Pure Mathematics Units 1 and 2 before obtaining a degree in Economics and Mathematics.

I have ten (10) years of experience teaching Mathematics at the secondary level in Barbados. During this time I have taught hundreds of students who have successfully completed the following courses:

- CSEC GENERAL MATHEMATICS
- CSEC ADDITIONAL MATHEMATICS
- CAPE PURE MATHEMATICS UNIT 1
- CAPE PURE MATHEMATICS UNIT 2
- SAT MATHEMATICS

Your story will be different from mine but both of us desire the same result. SUCCESS!

I know that for many students Mathematics can be a struggle. I am therefore here to offer assistance in making the learning of Mathematics easier.