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Beginning Algebra PDF

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Beginning Algebra PDF Details
Beginning Algebra
PDF Name Beginning Algebra PDF
No. of Pages 287
PDF Size 5.04 MB
Language English
CategoryEnglish
Source content.byui.edu
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Beginning Algebra

Dear readers, here we are providing a Beginning Algebra PDF to all of you. Algebra is one of the broad areas of mathematics. Often it takes a bit of practice to convert an English sentence into a mathematical sentence. This is what we will focus on here with some basic number problems, geometry problems, and parts problems.

This section and the next two introduce some group-theoretic notions that in principle apply to all groups but in practice are used with countable groups, often countably infinite groups that are nonabelian. But the formal development here will be completely algebraic, not making use of any definitions or theorems from topology.

Beginning Algebra PDF – Variables

Elementary algebra builds on and extends arithmetic by introducing letters called variables to represent general (non-specified) numbers. This is useful for several reasons.

  • Variables may represent numbers whose values are not yet known

For example, if the temperature of the current day, C, is 20 degrees higher than the temperature of the previous day, P, then the problem can be described algebraically as {\displaystyle C=P+20}.

  • Variables allow one to describe general problems, without specifying the values of the quantities that are involved.

For example, it can be stated specifically that 5 minutes is equivalent to {\displaystyle 60\times 5=300} seconds. A more general (algebraic) description may state that the number of seconds, {\displaystyle s=60\times m}, where m is the number of minutes.

  • Variables allow one to describe mathematical relationships between quantities that may vary

For example, the relationship between the circumference, c, and diameter, d, of a circle is described by {\displaystyle \pi =c/d}.

  • Variables allow one to describe some mathematical properties

For example, a basic property of addition is commutativity which states that the order of numbers being added together does not matter. Commutativity is stated algebraically as {\displaystyle (a+b)=(b+a)}.

Pre Algebra for Beginners PDF

1. Learn to graph x/y equations
Graphs can be valuable tools in algebra because they allow you to display ideas that you’d usually need numbers for in easy-to-understand pictures. Usually, in beginning algebra, graphing problems are restricted to equations with two variables (usually x and y) and are done on a simple 2-D graph with an x-axis and a y-axis. With these equations, all you need to do is plug in a value for x, then solve for y (or do the reverse) to get two numbers that correspond to a point on the graph.
  • For example, in the equation y = 3x, if we plug in 2 for x, we get y = 6. This means that the point (2,6) (two spaces to the right of the center and six spaces above the center) is part of this equation’s graph.
  • Equations with the form y = MX + b (where m and b are numbers) are especially common in basic algebra. These equations always have a slope of m and cross the y axis at y = b.

Learn to solve inequalities. What do you do when your equation doesn’t use an equals sign? Nothing much different than what you’d normally do, it turns out. For inequalities, which use signs like > (“greater than”) and < (“less than”), just solve as normal. You’ll be left with an answer that’s either less than or greater than your variable.

  • For instance, with the equation 3 > 5x – 2, we would solve just like we would for a normal equation:
    3 > 5x – 2
    5 > 5x
    1 > x, or x < 1.
  • This means that every number less than one works for x. In other words, x can be 0, -1, -2, and so on. If we plug these numbers into the equation for x, we’ll always get an answer less than 3.

2. Tackle quadratic equations.

One algebra topic that many beginners struggle with is solving quadratic equations. Quadratics are equations with the form ax2 + bx + c = 0, where a, b, and c are numbers (except that a can’t be 0.) These equations are solved with the formula x = [-b +/- √(b2 – 4ac)]/2a . Be careful — the +/- sign means you need to find the answers for adding and subtracting, so you can have two answers for these types of problems.

  • As an example, let’s solve the quadratic formula 3x2 + 2x -1 = 0.
    x = [-b +/- √(b2 – 4ac)]/2a
    x = [-2 +/- √(22 – 4(3)(-1))]/2(3)
    x = [-2 +/- √(4 – (-12))]/6
    x = [-2 +/- √(16)]/6
    x = [-2 +/- 4]/6
    x = -1 and 1/3

3. Experiment with systems of equations

Solving more than one equation at once may sound super-tricky, but when you’re working with simple algebra equations, it’s not actually that hard. Often, algebra teachers use a graphing approach to solving these problems. When you’re working with a system of two equations, the solutions are the points on a graph where the lines for both equations cross at.

  • For example, let’s say we’re working with a system that contains the equations y = 3x – 2 and y = -x – 6. If we draw these two lines on a graph, we get one line that goes up at a steep angle and one that goes down at a mild angle. Since these lines cross at the point (-1,-5), this is a solution to the system.
  • If we want to check our problem, we can do this by plugging our answer into the equations in the system — a right answer should “work” for both.
    y = 3x – 2
    -5 = 3(-1) – 2
    -5 = -3 – 2
    -5 = -5
    y = -x – 6
    -5 = -(-1) – 6
    -5 = 1 – 6
    -5 = -5
  • Both equations “check out,” so our answer is right!

You can download Beginning Algebra PDF by clicking on the following download button.


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