LESSON 17 - EXPONENTIAL FUNCTIONs
An exponential function is a function that contains a variable exponent. For example, f (x) = 2x and g(x) =
53x are exponential functions. We can graph exponential functions. Here is the graph of f (x) = 2x :
Figure %: f
LESSON 4 - Exponential and Logarithms
Functions of the form:
f(x) = ax
are known as exponential functions. The graphs of all such exponential functions pass
through (0, 1).
Logarithms are another way of writing indices.
LESSON 3 - INDICES AND SURDS
MAIN LECTURE:1. Indices
An index number is a number which is raised to a power. The power, also known as the
index, tells you how many times you have to multiply the number by itself. For example,
25 means that you have to mul
LESSON 2 - SIMULTANEOUS EQUATIONS
Main Lecture:In maths you must have already studied how to solve the simultaneous
equations. In add maths, its pretty much the same to be honest, however the
level of difficulty is taken a step further!
1. Simple simultan
LESSON 6 - QUADRATICS
Main Lecture:1. Maximum/Minimum Value of a Quadratic Expression
Ok people! So lets get started.
How is the graph of a quadratic equation suppose to be like? Before we
discuss that, you must familiarize yourself with the standard equa
LESSON 7 - MATRICES
MAIN VIDEO:1. Matrices and Matrix Addition
A matrix is just another way of representing data. An mn matrix has m rows and n columns, and each entry is given a
unique name, based on its row and column:
The matrix A is often denoted [
LESSON 11 - Coordinate Geometry
1. The Distance Between two Points
The length of the line joining the points (x1, y1) and (x2, y2) is:
Find the distance between the points (5, 3) and (1, 4).
(So in this case, x2 = 1, x1 = 5, y2 = 4 and y1 = 3).
LESSON 10 - FUNCTIONS
A relation is a set of inputs and outputs, often written as ordered pairs (input, output). We can also represent a relation as
a mapping diagram or a graph. For example, the relation can be represented as:
Mapping Diagram of
Lesson 9 - Binomial Theorem
What happens when you multiply a binomial by itself . many times?
Here is the answer:
Don't worry . I will explain it all!
And you will learn lots of cool math symbols along the way.
A binomial is a polynomial with two
Combinations and Permutations
What's the Difference?
In English we use the word "combination" loosely, without thinking if the order of things
is important. In other words:
"My fruit salad is a combination of apples, grapes and bananas" We don't c
LESSON 5 - Remainder Theorem and Factor
Or: how to avoid Polynomial Long Division when finding factors! :p
MAIN LECTURE: Do you remember doing division in Arithmetic?
"7 divided by 2 equals 3 with a remainder of 1"
Each part of the division has na
LESSON 12 - Circular Measure (Radians)
Introduction to Radian Measure
An angle with its
vertex at the center
of a circle that
intercepts an arc on
the circle equal in
length to the radius
of the circle has a
measure of 1
How to Convert Between Deg
LESSON 13 - TRIGNOMETRY(1)
1. Trigonometric Functions
The six trigonometric functions are called sine, cosine, tangent,
cosecant, secant, and cotangent. Their domain consists of real
numbers, but they only have practical purposes when these real
LESSON 14 - Trigonometry (2)
1. Trigonometric Identities
Now that we know the definitions of the trigonometric functions, and have a clear understanding how they behave as an
angle changes, we can explore the relationships that exist between th
LESSON 18 - LOGARITHIMIC FUNCTIONS
Like many types of functions, the exponential function has an inverse. This inverse is called the logarithmic
loga x = y means a y = x .
where a is called the base; a > 0 and a1 . For example, log232 = 5 becaus
LESSON 19 - DERIVATIVES
1. Intro to Calculus
There are two components to calculus. One is the measure the rate of change at
any given point on a curve. This rate of change is called the derivative. The
simplest example of a rate of change of a function is
LESSON 23 - Integration
1. Anti derivatives
An antiderivative of a function f is a function whose derivative is f . In other words, F is an antiderivative of f if
F' = f . To find an antiderivative for a function f , we can often reverse the process of di
LESSON 22: Calculus - Determining
Minimum & Maximum Values
One of the most important uses of calculus is determining minimum and
maximum values. This has its applications in manufacturing, finance,
engineering, and a host of other industries. Before we ex
LESSON 21- The Chain Rule
As a motivation for the chain rule, consider the function
f(x) = (1+x2)10.
Since f(x) is a polynomial function, we know from previous pages that f'(x) exists.
Naturally one may ask for an explicit formula for it. One tedious way
LESSON 20 - APPLICATION OF DERIVATIVES KINEMATICS
1. Average rates of Change
Suppose s(t) = 2t 3 represents the position of a race car along a straight track, measured in feet from the
starting line at time t seconds. What is the average rate of change of
LESSON 1 - SETS and VENN DIAGRAMS
Main Lecture:Hey everyone! Are you ready for some fun-filled maths? Well since you have actually
clicked on this video, it means that you really are ready! Anyway lets get started with our
first topic. Its about Sets. Thi