What Formulas Do You Need to Know for the ACT Math Test Part 3

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Quadratic Formula

A quadratic function is an expression where the highest power of the function is two. Some of these can solved these by factorizing them but all can be solved by using the quadratic formula.

There is a standard form for writing a quadratic function:

The quadratic formula is:

To find the roots, put the values for a, b and c into the formula to find the values for x. The part of the formula is called the ‘discriminant’ . Depending on its value, there are different possibilities for the roots of the function:

  • If it is positive, there are two real roots.
  • If it is negative, the roots are imaginary.
  • If it is zero, there is one repeated root.

Exponent Laws

Exponent laws are rules that are used when solving problems with exponents.

When multiplying two exponential expressions with the same base, add the exponents.

When dividing two expressions, subtract the exponents.

When raising an exponential expression to a power, multiply the exponents.

When taking the root of an exponential expression, divide the exponent inside the square root by the one outside.

FOIL and Factoring

The FOIL method is used to expand polynomial expressions. FOIL stands for First, Outside, Inside, Last. For example:

To change the first side of the equation into the second side, the first terms in each set of parentheses multiplied the first terms in each set of parentheses to get . Then multiply the outside terms to get bx, then the inside to get ax and finally the last terms to get ab.

Another equation to know when you՚re factoring is a special factor called the difference of squares. This is what you get when you factor .

Try some FOIL practice problems and learn how to factorize quadratic equations to see how to use FOIL in reverse.

Log Laws

Logarithms are a special kind of notation that make it easier to solve for exponential functions. The expression in exponent form is written as in logarithm notation. There are a few rules to memorize in order to solve exponential functions with them.

Log laws:

Logarithms Are a Special Kind of Notation That Make It Easier to Solve for Exponential Functions


You can calculate the probability of an outcome by writing it as the number of desired outcomes over the total number of possible outcomes.

If you roll a die, the probability of getting a 5 is , because there are six possible outcomes (1, 2,3, 4,5 or 6) and only one of them is wanted (5) . To find the probability that two independent events will both happen, multiply the individual probabilities together. So, in rolling a die twice, the probability that it is a 5 both times is or .

Sequences and Series

A sequence is a set of things, usually numbers that make a pattern. There are two types of patterns to be aware of: ‘arithmetic’ and ‘geometric’ sequences.

An arithmetic sequence is one that is made through repeated addition and a geometric sequence is a pattern that is made through repeated multiplication.

There are a couple of useful formulas for working out the nth term of a sequence and the nth partial sum.

Sequences and Series
Arithmetic sequencesGeometric sequences

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