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Formulas to Memorize for the ACT Math

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  • 0:01 Act Formulas
  • 0:43 The Basics
  • 2:04 Exponents and Logs
  • 3:49 Geometry
  • 6:09 Other Formulas
  • 7:23 Lesson Summary
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Lesson Transcript
Instructor: Elizabeth Foster

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

Worried about what formulas you'll need to memorize for the ACT? Some good news: it's probably not as bad as you think! Here's a checklist to make sure you're on top of everything.

ACT Formulas

The list of topics covered on the ACT math test sounds pretty intimidating, so you might think you'll need to cram your head full of every formula in the book. On the ACT Math test, you won't need to memorize a huge number of special formulas. In fact, you probably already know most of what you need for the test! The ACT isn't really about cramming your head full of new equations; it's more about knowing how to apply the stuff you've already learned.

Just to make sure, though, here's a quick checklist of the formulas you'll want to brush up on for the test. If anything looks unfamiliar or you'd just like to review it, check out the math lessons for some more in-depth coverage.

The Basics

Let's start with some basic formulas, covering simple averages, statistics, probability and distances.

Distance and work:
Distance traveled or work done equals rate times time (d = r * t). If you have any two parts of this equation, you can just plug them in to solve for the third. For example, if you travel for four hours at 60 miles per hour, you would travel a total distance of 240 miles.

Averages:
To find the average, also called the arithmetic mean, take the sum of all the numbers and divide it by the number of numbers. For example, the average of 1, 2 and 9 is 4.

Probability:
The probability of a desired outcome equals the number of desired outcomes over the number of total possible outcomes. For example, if you flip a coin, the probability of getting tails is 1/2, since there are two possible outcomes (heads or tails) and only one of them is desired (tails). To find the probability that two independent events will both happen, multiply the individual probabilities together. For example, if you flip a coin twice, the probability that you'll get tails both times is 1/2 * 1/2 or 1/4.

Exponents and Logs

Now let's take a quick look at exponents. Exponents can be tricky if you're not comfortable with them, but having a solid grasp of the formulas should help.

General exponent rules:

  1. If you multiply two exponential expressions with the same base, add the exponents. x^a * x^b = x^(a + b)
  2. If you divide two expressions, subtract the exponents.x^a / x^b = x^(a - b)
  3. If you raise an exponential expression to a power, multiply the exponents. (x^a)^b = x^(ab)
  4. If you take the root of an exponential expression, divide the exponent inside the square root by the one outside. broot(x^a) = x^(a/b)

FOIL and Factoring:
FOIL stands for First, Outside, Inside, Last. This is the method for multiplying polynomials.

For example: (x + y)(a + b) = ax + bx + ay + by. You can see how first we multiplied the first terms in each set of parentheses to get ax. Then we multiplied the outside terms to get bx, then the inside to get ay and finally the last terms to get by.

One more equation to know when you're factoring is a special factor called the difference of squares. This is what you get when you factor x^2 - y^2.
x^2 - y^2 = (x + y)(x - y).

Log rules:
You won't need these unless you're going for a really elite score on the math, but in case you are, remember that if x equals log base a of b, then a to the x power equals b.

Geometry

Next up: shapes. Again, it's not really about memorizing everything in the world as it is about knowing the basics really well and being prepared to apply them whenever you need them. Here we'll break it all down by shape.

Triangles:
The area of a triangle equals one-half times the base times the height: A = 1/2(b * h).

The Pythagorean theorem states that in a triangle with side lengths a, b and c (where c is the longest side), a^2 + b^2 = c^2. Two triangles are worth memorizing so you don't have to do this every time: the 3-4-5 right triangle and the 5-12-13 right triangle.

You'll also want to know the special right triangles backwards and forwards. In a 45-45-90 triangle, the side lengths opposite each angle are x, x and x root 2, respectively. In a 30-60-90 triangle, the side lengths are x, x root 3 and 2x, respectively.

Circles:
The area of a circle is pi * r^2. The circumference is 2pi * r.

Rectangles and squares:
The area of a rectangle is l * w. The area of a square is just one side squared. To find the perimeter of either, just add all the sides together.

3D shapes: The volume of a cube, rectangular prism or cylinder is the area of the base times the height.

Lines and graphing:
To find the slope of a line, just pick two points on the line, and look at the distance between them vertically and horizontally. The vertical distance is called the rise, and the horizontal distance is called the run. Slope is just rise over run. The equation for a line in point-slope form is y = mx + b, where m is the slope and b is the y-intercept.

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