Math Knowledge: Algebra
Expressions
Classifications
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms. Linear expressions have no exponents. A quadratic expression contains variables that are squared (raised to the exponent of 2).
Operations Involving Monomials
You can only add or subtract monomials that have the same variable and the same exponent. However, you can multiply and divide monomials with unlike terms.
Multiplying Binomials
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.
How to Factor
Factoring Quadratics
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
Solving Equations
One Variable
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
Two Variables
When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
Two Equations
When presented with two equations with two variables, evaluate the first equation in terms of the variable you're not solving for then insert that value into the second equation. For example, if you have x and y as variables and you're solving for x, evaluate one equation in terms of y and insert that value into the second equation then solve it for x.
Quadratic Equations
When solving quadratic equations, if the equation is not set equal to zero, first manipulate the equation so that it is set equal to zero: ax2 + bx + c = 0. Then, factor the quadratic and, because it's set to zero, you know that one of the factors must equal zero for the equation to equal zero. Finding the value that will make each factor, i.e. (x + ?), equal to zero will give you the possible value(s) of x.
Inequalities
Solving equations with an inequality (<, >) uses the same process as solving equations with an equal sign. Isolate the variable that you're solving for on one wide of the equation and put everything else on the other side. The only difference is that your answer will be expressed as an inequality (x > 5) and not as an equality (x = 5).
Previous Section: 4. Paragraph Comprehension (PC)
Jump To: What You Need to Know to do Well on the Mathematics Knowledge Section, Math Knowledge: Algebra, Math Knowledge: Geometry
Next Section: 6. Electronics Information (EI)