Absolute Value |x| (absolute value of x) is the magnitude (the non-negative value) of x, regardless of its original sign. The concept of an absolute value revolves around negative and positive numbers. A positive number doesn’t change when placed in an absolute value, but a negative value does change: it becomes a positive. Therefore, if a problem…

Special Right Triangles There are certain special triangles that students might be expected to know on the math section of the ACT. Like the formulas for the area of a circle or rectangle, these identities are normally presented to students at the beginning of the test, and so the challenge is knowing how to identify problems…

Midpoint Midpoint questions involve working with two ordered (x,y) pairs and finding their midpoint. Use the midpoint formula:(xM, yM) = (x1 + x2)/2, (y1 + y2)/2), where (xM, yM) is the midpoint and the x and y values on the right side of the equation are from the ordered pairs of that midpoint. Occasionally these questions might give…

Matrices A matrix is a series of rows and columns used to display numbers. ACT questions about matrices will generally be about performing fundamental math operations such as addition, subtraction, or multiplication between matrices. Is It Possible? A key note is that not all matrices can be added, subtracted, or multiplied. Adding and Subtracting Adding…

Composite function Composite functions are where one function is put inside of another. This can look intimidating at first, but these problems are quite simple once a student gets the hang of it. Inside Out It’s easiest to think of composite functions as a priority list or an order of operations. Work from the inside to…

Apply formula Applying formula problems will provide a student with a particular formula/equation, and will then ask a student to properly plug in numbers into that equation to calculate something. This will often be done in the context of a word problem that describes the real-world application of the equation. For these equations the main…

Pythagorean Theorem This is one of the most fundamental concepts in math, and as a result it is something that will be applicable on every single ACT. The pythagorean theorem applies to right triangles and states that the square of the hypotenuse is equal to the sum of the squares of the other sides. A…

Time Time Conversions Be able to convert between different units of time. The most common ones being between hours and minutes and between minutes and seconds. Time Variables Some equation questions might have variables that stand in for time, especially as an exponent. The question may then ask for how to maintain the same equation…

Angle How Many Degrees in ______ ? How Many Degrees in a Line There are 180 Degrees in a Line. This means that if there are two angles across a line, then the sum of those two angles will be 180 degrees. These are known as supplementary angles. How Many Degrees in Common Shapes There are…

System of Equations System of Equations involves taking a series (usually two) of equations and finding their “solution”, meaning variable values that make all equations in the series true. Another way to think of this is to imagine graphing those equations, and a system of equations problems asking students to find the intersection points between…