# SECTION 4: BASIC MATHEMATICAL APPLICATIONS

## A look at Statistics, Probability and Kinematics.

STATISTICS

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

• distinguish between types of data;
• outline the relative advantages and disadvantages of stem – and – leaf diagrams and box – and – whisker plots in data analyses;
• interpret stem – and – leaf diagrams and box – and – whiskers plots;
• determine quartiles and percentiles from raw data, grouped data, stem – and – leaf diagrams, box – and whiskers plots;
• calculate measures of central tendency and dispersion;
• explain how the standard deviation measures the spread of a set of data.

PROBABILITY

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

• distinguish among the terms experiment, outcome, sample space and event;
• calculate the probability of event $A, P(A),$ as the number of outcomes of $A$ divided by the total number of possible outcomes, when all outcomes are equally likely and the sample space is finite;
• use the laws of probability:
1. the sum of the probabilities of all the outcomes in a sample space is equal to one;
2. $0\leq P(A)\leq 1$ for any event;
3. $P(A')=1-P(A)$ where $P(A')$ is the probability that event $A$ does not occur
• use $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ to calculate probabilities;
• identify mutually exclusive events $A$ and $B$ such that $P(A\cap B)=0$;
• calculate the conditional probability $P(A|B)$ where $P(A|B)=\frac{P(A\cap B)}{P(B)}$;
• identify independent events;
• use the property $P(A\cap B)=P(A)\times P(B)$ or $P(A|B)=P(A)$ where $A$ and $B$ are independent events;
• construct and use possibility space diagrams, tree diagrams and Venn diagrams to solve problems involving probability.

KINEMATICS

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

• distinguish between distance and displacement and speed and velocity;
• draw and use displacement – time and velocity – time graphs;
• calculate and use displacement, velocity, acceleration and time in simple equations representing the motion of a particle in a straight line;
• apply where appropriate the following rates of change:

$v=\frac{dx}{dt}=\dot{x}$;

$a=\frac{d^2 x}{dt^2}=\frac{dv}{dt}=\ddot{x}$

where represent displacement, velocity and acceleration respectively.

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

STATISTICS
A look at Statistics for Additional Mathematics.
Sean Hunte
$10 KINEMATICS A look at Kinematics. Sean Hunte$10
A look at some of the more advanced aspects of Probability.
Sean Hunte