# Algebra

## 18 videos in this playlist

Mathematical Language
This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
Powers or Indices
A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules…
Logarithms
Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by…
Substitution and Formulae
In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can…
Expanding and Removing Brackets
In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with…
Pascal's Triangle and the Binomial Theorem
A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a…
An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used…
Transposition of Formulae
It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
Linear Equations in One Variable
In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we…
Completing the Square
In this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number…
Completing the Square (max, min)
Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum…
This unit is about the solution of quadratic equations. These take the form ax^2+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square,…
Simultaneous Linear Equations
The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the…
Solving Inequalities
Inequalities are mathematical expressions involving the symbols >, <, >= and <= . To 'solve' an inequality means to find a range, or ranges, of values that an unknown x…
Cubic Equations
All cubic equations have either one real root, or three real roots. In this unit we explore why this is so.
Simplifying Fractions
The ability to simplify fractions and to write them in equivalent forms is an essential mathematical skill required of all engineers and physical scientists. This unit explains how these processes…
Polynomial Division
In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process.
Partial Fractions
After reading this text, and/or viewing the video tutorial on this topic, you should be able to: * explain the meaning of the terms 'proper fraction' and 'improper fraction' *…

## Related videos

An Introduction to the Course
Episode 1 of Algebra I
Professor Sellers introduces the general topics and themes for the course, describing his approach and recommending a strategy for making the best use of the lessons and supplementary workbook. Warm up with some simple problems that demonstrate signed numbers and operations.
Order of Operations
Episode 2 of Algebra I
The order in which you do simple operations of arithmetic can make a big difference. Learn how to solve problems that combine adding, subtracting, multiplying, and dividing, as well as raising numbers to various powers. These same concepts also apply when you need to simplify algebraic expressions, making it critical…
Percents, Decimals, and Fractions
Episode 3 of Algebra I
Continue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of presenting the same information in different forms.
Variables and Algebraic Expressions
Episode 4 of Algebra I
Advance to the next level of problem solving by using variables as the building blocks to create algebraic expressions, which are combinations of mathematical symbols that might include numbers, variables, and operation symbols. Also learn some tricks for translating the language of problems (phrases in English) into the language of…
Operations and Expressions
Episode 5 of Algebra I
Discover that by following basic rules on how to treat coefficients and exponents, you can reduce very complicated algebraic expressions to much simpler ones. You start by using the commutative property of multiplication to rearrange the terms of an expression, making combining them relatively easy.
Principles of Graphing in 2 Dimensions
Episode 6 of Algebra I
Using graph paper and pencil, begin your exploration of the coordinate plane, also known as the Cartesian plane. Learn how to plot points in the four quadrants of the plane, how to choose a scale for labeling the x and y axes, and how to graph a linear equation.
Solving Linear Equations, Part 1
Episode 7 of Algebra I
In this lesson, work through simple one- and two-step linear equations, learning how to isolate the variable by different operations. Professor Sellers also presents a word problem involving a two-step equation and gives tips for how to solve it.
Solving Linear Equations, Part 2
Episode 8 of Algebra I
Investigating more complicated examples of linear equations, learn that linear equations fall into three categories. First, the equation might have exactly one solution. Second, it might have no solutions at all. Third, it might be an identity, which means every number is a solution.
Slope of a Line
Episode 9 of Algebra I
Explore the concept of slope, which for a given straight line is its rate of change, defined as the rise over run. Learn the formula for calculating slope with coordinates only, and what it means to have a positive, negative, and undefined slope.
Graphing Linear Equations, Part 1
Episode 10 of Algebra I
Use what you've learned about slope to graph linear equations in the slope-intercept form, y = mx + b, where m is the slope, and b is the y intercept. Experiment with examples in which you calculate the equation from a graph and from a table of pairs of points.
Graphing Linear Equations, Part 2
Episode 11 of Algebra I
A more versatile approach to writing the equation of a line is the point-slope form, in which only two points are required, and neither needs to intercept the y axis. Work through several examples and become comfortable determining the equation using the line and the line using the equation.
Parallel and Perpendicular Lines
Episode 12 of Algebra I
Apply what you've discovered about equations of lines to two very special types of lines: parallel and perpendicular. Learn how to tell if lines are parallel or perpendicular from their equations alone, without having to see the lines themselves. Also try your hand at word problems that feature both types…