While it’s easy to see that problem-solving skills are crucial for acing the ACT Math section, it’s just as easy to forget the importance of a strong foundation in math formulas and vocabulary before the problem-solving can happen. Formulas make sense, but vocab in the math section? Yep, that’s right. You might be surprised how many missed questions are the result of students just not knowing what “real value” or “irrational number” means. This may seem like basic terminology, but when these math vocab words are a focal point of the question, those are easy points lost! Let’s talk about formulas before diving into the rudimentary vocab we learned back in elementary school.
Formulas to Know
There are so many formulas in the world of math, and knowing when to use certain formulas is just as important as knowing them. The good news is some are more important than others for the ACT Math section. Geometry formulas are featured most on the SAT and ACT, but there are a few from other subject areas as well. The biggest difference between the two tests is the SAT Math sections have formula sheets to refer back to, whereas the ACT does not. It’s up to you to know the formulas for the ACT.
2-D Shapes
It’s important to know the area and perimeter formulas of quadrilaterals, triangles, and polygons. When memorizing formulas, I like to break down what’s happening in each one. For area formulas, you know you’re always multiplying; for perimeter formulas, you know you’re always adding. Circles are a little fancy because they don’t have distinct sides, so instead, you should know the formulas for area and circumference.
3-D Shapes
Surface area and volume formulas are the big ones to know here. In my experience, the ACT likes to focus on cubes, rectangular prisms, and cylinders.
Degrees to Radians
Converting radians to degrees and vice-versa sometimes confuses students because they don’t know if they’re using (π180) or (180π). This is a perfect example of the importance of knowing when to use a formula!
Right Triangles
So many fun formulas for right triangles! If you’re looking for side lengths, the Pythagorean Theorem is your best friend. With that being said, you should know the formulas for side lengths in Special Right Triangles with angles 45-45-90 and 30-60-90. When trigonometry questions pop up, you should know SOH CAH TOA. Also, recognize inverse trigonometric functions are necessary to find the non-right angles of a right triangle.
Arithmetic and Geometric Sequences
At the very least, keep in mind arithmetic sequences occur when the same number is being added to each term, and geometric sequences occur when each term is being multiplied by the same number. You should know formulas to find a certain term in each type of sequence as well as how to find the sum of a sequence
Coordinate Plane Formulas
You should know Distance, Midpoint, and Slope Formula. The slope-intercept form of a line is also crucial.
Math Vocabulary
The terminology you’ll find in the ACT Math section isn’t challenging, but it is important! Here’s a list of the vocab words I find most helpful:
Real number
Any value that is not imaginary; this category includes integers, natural, whole, rational, and irrational numbers.
Natural number
Any counting number from 1 to infinity (1, 2, 3, 4…). Reminder: counting number basically means positive integer.
Whole number
Any counting number from 0 to infinity (0, 1, 3, 4…).
Integers
Positive and negative numbers (excluding fractions) and 0.
Rational numbers
Any integers, fractions, terminating decimals, and repeating decimals.
Irrational numbers
Any non-terminating decimals and non-repeating decimals.
Imaginary numbers
The square root of a negative number.
Prime number
Any number that has 1 and itself as its only factors (ex: 17, factors are 1 and 17).
While there are certainly more rules, tips, and tricks, these few formulas and vocab words listed above will set you up for success on the ACT Math section!