# 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 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 $y=f(x)$ and its inverse $f^{-1} (x)$;
• find the composition of two functions;
• recognise that, if $g$ is the inverse of $f$, then $f[g(x)]=x$, for all $x$, in the domain of $g$.

SURDS

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

• simplify surds
• rationalize fractions involving surds

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 $\log_a{b}=c\Leftrightarrow a^c=b$ where is any positive whole number;
• simplify expressions by using the laws:
1. $\log_a{PQ}=\log_a{P}+\log_a{Q}$
2. $\log_a\left ( {\frac{P}{Q}} \right )=\log_a{P}-\log_a{Q}$
3. $\log_a{P^b}=b\log_a{P}$
4. $\log_a{a}=1$
5. $\log_a{1}=0$
• solve logarithmic equations;
• use logarithms to solve equations of the form $a^x=b$;
• 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, $a_n$, where $n$ is a positive integer;
• write a specific term from the formula for the $n^{th}$ term of a sequence;
• use the summation ($\sum$) 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 $-1, where $r$ 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.

Sean Hunte

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
• 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.

## Courses Included with Purchase

Learn how to determine the solution set of quadratic and rational inequalities.
Sean Hunte
$5 SURDS Learn how to simplify and rationalise expressions with surds. Sean Hunte$5
Learn how to solve problems involving Disguised Quadratic Equations.
Sean Hunte
$5 ADVANCED FUNCTIONS An advanced look at Functions. Sean Hunte$7
POLYNOMIALS and SUM AND PRODUCT OF ROOTS
An in - depth look at Polynomials and the Sum and Product of Roots of a Quadratic.
Sean Hunte
$7 LOGARITHMS FOR ADDITIONAL MATHEMATICS An in - depth look at Logarithms. Sean Hunte$7
SEQUENCES, SERIES AND PROGRESSIONS
Learn about Sigma Notation, Arithmetic and Geometric Progressions.
Sean Hunte