Mathematical Reasoning Study Guide for the GED Test

Algebra Concepts

Linear expressions and equations: These expressions form a straight line when put on a graph.

Rational expressions: A rational expression is written in fraction form, such as \(\frac{2x+5}{x+2}\). The denominator cannot be zero (0).

Linear inequalities, including constructing graphs of them. This type of expression is like an equation, but the sum of the two sides is not equal. The symbols < and > are used for “less than” and “greater than,” respectively.

Polynomials are sentences with numbers that have constants (numbers) and variables (letters or symbols). An example would be \(4x + 2y\). An expression that has a variable for a denominator or a variable with a negative exponent is not a polynomial. So \(3x^{-2}\) is not a polynomial, and \(\frac{6}{x}\) is also not a polynomial.

Factoring is determining what can be multiplied to get an expression in algebra. You do this by finding common factors of the numbers in the expression.

Example: \(2b + 4\)
\(2b = 2 \times b\) and \(4 = 2 \times 2\)
So, \(2b + 4\) factored is \(2(b + 2)\)

Operations in algebra: Be sure you know how to do all \(4\) of the basic operations with algebraic expressions.

Quadratic equations: In a quadratic equation, there can be no exponent higher than \(2\). This is one example:

\[2x^2 + 7x - 4 = 1\]

Graphs and functions:

Graphs are pictorial representations of numbers.

A function tells what is being done to any number inserted in that function. A function is usually written \(f(x)\). So if the function is \(f(x) = x + 4\), then any number that replaces \(x\) will have \(4\) added to it. If a question asks for \(f(2)\) in this case, it simply means substitute \(2\) for \(x\). If \(2\) is put in, then the answer would be \(6\), because \(2 + 4 = 6\).

Coordinates, lines, and equations: Coordinates are points on a graph. A line is made up of all of the points on that line. Equations can be shown on a graph.