Algebra
Algebra is math that represents numbers with symbols, enabling equations to be more easily solved.
For example, if you want to buy four new tires for your car, with each one costing $75, you could calculate
the price by simple addition: $75 + $75 + $75 + $75 = $300. But you could also represent the price as 4P,
where "P" represents the price of a single tire. This would be easier to write down, for one thing. It is also
more flexible: say you decide to buy tires that cost $100 each instead. You can still use 4P as the equation
for the total, which now would be 4 x ($100 each) = $400.
The above example is extremely simple. In reality, most algebraic expressions have at least two variables
(hotspot link?). In the above example, you would have:
TOTAL = 4 x (Price per tire)
Which might be represented as:
T = 4P
Often, equations are expressed using y and x. You must seek an answer for y, depending on changes in x.
There are some priority rules for operations in algebra:
1. Perform all operations in parentheses first. You must follow the parentheses OUTWARDS: do
operations in the innermost parentheses first.
2. Raising a number to a power or taking the root of a number comes first.
3. Multiplication and division come next.
4. Addition and subtraction take lowest priority.
Look at these examples for more:
a) 5x + 4y = 7
Solve for y:
4y = 7 5x > y = (7 5x)/4
b) x^2 = y^(1/2)
Solve for y:
[y^(1/2)]^2 = (x^2)^2 > y = x^4
Circles
Some terms to know:
Radius: The distance from the center of a circle to any point on its perimeter.
Diameter: Twice the radius. The distance straight from one point on the perimeter, passing through the
center, meeting the perimeter on the other side.
Circumference: The perimeter of a circle. Calculated as 2 x pi x radius.
Area: The twodimensional area enclosed by a circle. Calculated as pi x (radius)^2.
Exponents
Exponents just represent the number of times to multiply something by. For example:...