Hey, all. This is another something written by Leonard Williams on the GED forum, and I thought it’s pretty useful…explaining what the math formulas in the front of the GED test booklet mean…
Take a deep breath! Here’s a breakdown of the formulas. Remember, they’re in the GED test booklet to help you out….
|AREA of a:|
|square||Area = side2|
|rectangle||Area = length x width|
|parallelogram||Area = base x height|
|circle||Area = π x radius2; π is approximately equal to 3.14.|
So, what’s it mean? Area is just the amount of space on a surface. That’s all. For a square or rectangle, it’s just the length of two adjoining sides multiplied by each other. So, if you’ve got a 6×4 room, you need 6×4 square feet of carpet…24 square feet.
A parallelogram is just a four-sided figure where the opposite sides are parallel…slanting the same way. It’s like a rectangle, but instead of measuring the length of the sides, you measure 1 flat side, and then the height, straight up. Multiply them together to get area.
A triangle is easy…it’s half a parallelogram, so you get the area by multiplying 1/2 times the base (bottom) times the height (straight up).
A trapezoid is a 4-sided figure with 2 parallel sides. So, the sides that run parallel to each other are different lengths. Add them together and divide by two to get an average…then multiply by the height (straight up).
A circle is a little different… you need to use “pi.” That’s that funny-looking figure…just think of it as 3.14. To get the area (flat surface) of a circle, multiply 3.15 times the radius squared. The radius is the distance from the center of the circle to the edge, and squared just means multiply it by itself. So, if the circle is 4″ across, the radius is 2″, and the area is 3.14 x 2 x 2, or just over 12. (Approximating can be very helpful!)
Next up is perimeter and circumference…
|PERIMETER of a:|
|square||Perimeter = 4 x side|
|rectangle||Perimeter = 2 x length + 2 x width|
|triangle||Perimeter = side1 + side2 + side3|
|CIRCUMFERENCE of a:|
|circle||Circumference = π x diameter; π is approximately equal to 3.14.|
Perimeter is just how long the outside lines of a shape are…so, how much fence you’d need to put around a pasture, or how much framing you’d need to frame a picture. On the square, rectangle, or triangle, or any figure with straight sides, it’s just the length of all the sides added together. Easy.
On a circle, you’ve got to use pi again…so it’s 3.14 x diameter—that’s the length across the center of a circle. For a 5″ across circle, the circumference is just over 15.”
Next is volume…
|VOLUME of a:|
|cube||Volume = edge3|
|rectangular solid||Volume = length x width x height|
|cylinder||Volume = π x radius2 x height; π is approximately equal to 3.14.|
π is approximately equal to 3.14.
Volume is like area, except it’s three dimensional. It’s all the space inside something. For area, you multiplied one side times another, right? Well, for volume, you’re just adding a third side… so for a cube or a rectangular solid (like a box) you multiply length x width x height.
A cylinder is like a circle that’s got height. So, for the cylinder, you find the area of the circle at the bottom (pi times radius square, like we did for area), and then multiply it by the height of the cylinder.
Cones and pyramids have a circle or a square at the bottom, and then they come to a point instead of having a similar shape at the other side. So, they’re smaller in volume than a cylinder or rectangular solid. Turns out, they’re exactly 1/3 the volume. So, just find the volume of a cylinder or rectangular solid with the same size end, and divide that number by three. That’s all the formulas mean.
Now the next one…
|distance between points
(x1, y1) and (x2, y2) are two points in a plane.Slope of a line = ;
(x1, y1) and (x2, y2) are two points on the line.
Sounds confusing! But it’s not so bad, really. Points on a graph are shown by an x and y number, like this: (2, 3) The x number is the first number, and the y number is the second number. The numbers tell you where to find the points on the graph. Well, to find the distance between two points, you basically make a right triangle on the graph, by connecting the points. Then, you can use the Pythagorean formula to find the distance…
The Pythagorean idea is that, in a right triangle, the length of one (short) side squared + the length of the other (short) side squared = the length of the long side squared. That’s what you’re doing here. The distance between the x’s is the length of one short side, and the distance between the y’s is the length of the other short side.
Find the distances, square them, add them together. Then, find the square root…and you’ve got the distance between the two points.
The slope…that sounds confusing, too. But basically, it’s RISE over RUN….that is, how far it is up and down from one point on a line to another, over how far it is across between the same two points.
|a2 + b2 = c2; a and b are legs and c the hypotenuse of a right triangle.|
The next one is the Pythagorean relationship…exactly what I was just talking about. a and b are the two short sides of a right triangle (legs), and c is the long side (hypotenuse). You’ll use this formula whenever you know the lengths of two sides of a right triangle and want to know the third. This one’s a good one to know!
|MEASURES OF CENTRAL TENDENCY|
|mean = ;
where the x’s are the values for which a mean is desired, and n is the total
number of values for x.
|median = the middle value of an odd number of ordered scores, and halfway between the two middle values of an even number of ordered scores|
“Mean” is what we usually think of as an “average.” In plain English, add up all the numbers you’ve got, and divide by however many numbers you added together.
“Median” is just the middle number, if you put a group of numbers in order from smallest to largest (that’s what it means by ‘ordered scores’). If there are an even amount of numbers, there won’t be a middle number…so you use the number halfway between the two middle numbers.
|SIMPLE INTEREST DISTANCE TOTAL COST|
|interest = principal x rate x time|
|distance = rate x time|
|total cost = (number of units) x (price per unit)|
The last items are simple interest….so if the GED asks you about interest on a loan, you’ll calculate interest by multiplying the principal (amount borrowed) by the interest rate and multiplying that by the amount of time of the loan (usually in years).
Distance = rate x time is about how far you can go, how fast. So, if you’re traveling at 30 miles per hour for 6 hours, you’ll go 30 x 6 miles, or 180 miles.
Total cost = (number of units ) x (price per unit) is something you do every day…
if you’re buying 5 bananas, and bananas cost 20 cents each, how much is the total cost? It’s the number of bananas times the price per banana…or 5 x 20 cents, or 100 cents, or $1.
Don’t let the formulas confuse you! Most of it is pretty straightforward…
Good luck! And don’t panic!