Mathematical Reasoning Study Guide for the GED Test

Geometry

You will have access to a page of formulas during the test. Be sure you know which formula to use for different questions and that you know the abbreviations in the formulas.

Triangles and rectangles: compute area, perimeter, and side lengths

Lengths of sides are usually given, or you can figure them out by using other information given.

Perimeter is the total length of all of the sides of a shape. Just add them together.

Area is the measurement of the space covered by a shape and is written in square units, such as square feet or \(ft^2\).

For a rectangle or square, multiply base \(\times\) height. [b \(\times\) h]
For a triangle, do the same and divide in half. [\(\frac{1}{2}\)(b \(\times\) h)]

Circles: Compute area, circumference, radius, and diameter.

When working with circles, you will need to use a number called Pi which is \(3.14\) and the symbol for Pi is \(\pi\). You will also need to work with these terms and formulas:

The radius (\(r\)) is the length of a line from the center point to any point on the circle.
The diameter (\(d\)) is the length of a line between any \(2\) points on the circle that goes through the center point. It is always \(2 \times\) radius (\(r\)).
The circumference is the distance around the circle. It is found using this formula: \(2 \times \pi \times r\) or \(2\pi r\)
The area of a circle is: \(\pi \times r^2\) or \(\pi r^2\)

Polygons: Compute area and side lengths. A polygon is a closed, flat shape, with three or more sides.

Composite figures: Compute perimeter and area. Composite shapes are figures made of two or more attached shapes. In order to find the perimeter and area, you would have to consider all of the outside sides or inside space of all of the shapes in the figure. These composite shapes may include circles.

Pythagorean theorem

This formula only works for a triangle with a \(90^\circ\) angle (right triangle). The hypotenuse is the side opposite the right angle. In this formula, \(c\) is the hypotenuse and \(a\) and \(b\) are the other sides, called the legs. The theorem is:

\(a^2\) + \(b^2\) = \(c^2\)

Volume, surface area, and other dimensions of 3-dimensional figures: rectangular prisms, cylinders, right prisms, right pyramids, spheres, and 3-D composite geometric figures. Surface area is the total area measurement of all of the outside surfaces of the 3-D shape.

Data

Interpret graphs including circle, bar, and number line plots.

Represent data using tables and plots including box plots, histograms, scatter plots, and graphs.

If you search for the above types of graphs, you will see lots of examples. Practice looking at them carefully to determine the meaning of the data presented. Read all captions for key words.

Use mean, mode, and weighted average

mean: same as average; computed by adding all of the values and dividing by how many values were given.

mode: the number(s) that occur(s) most often in a list of numbers

weighted average: This type of average is used often in computing grades. To find the weighted average, multiply the scores by the percentage of the grade (in decimal form) for which they count and then add those numbers.

Example:
Homework counts for 20% of the grade and Sam got an 80.
Classwork counts for 30% of the grade and Sam got a 90.
Tests count for 50% of the grade and Sam got an 85.

\(80 \times .20 + 90 \times .30 + 85 \times .50 = 85.5\) (weighted average grade)

Counting techniques used with combinations and permutations. These are ways of counting finding out how many ways things can be grouped. In a combination, the order of the objects does not matter, but in a permutation, it does.

Permutation is a technique for counting all possible arrangements of a set of objects where order is important. A common question involves permutation where repetition is allowed. The formula for this type of question is \(P = n^r\), where n is the number of objects to choose from and r is the number of objects we choose.

Example: A code for a lock has to be set. There are three digits for the code, and the numbers from \(0\) to \(9\) can be chosen with repetition of a number allowed. How many possible codes are there?

This is a permutation problem because the position of digits (objects) is important. The question also states that a number can be repeated for any of the digits.

Using the formula: \(P = n^r\)
\(P = 10^3 = 1,000\)

Probability When you assess probability, you are finding the likelihood of an event happening.

Example: If you flip a coin \(50\) times, the probability of it landing “heads” is \(25\) out of \(50\), which is always written as a number between \(0\) and \(1\), such as \(25/50\) (probability = \(1/2 = 0.5\)) for this problem.