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…
Radicals Radicals (also known as “roots”) are the opposite of exponents. The most common radical that students are familiar with is the square root or root-2, which is why the default radical symbol is also the square root symbol: . A square root basically says: to get the number under the square root, what number would…
Median The median is the middle number of a data set when the data set is arranged in numerical order. Unlike the mean, it will always be one of the actual data points in the set itself. The set can be arranged as ascending or descending order: the median will still always be in the…
MPH Miles per hour is a way to express speed: distance covered over a time interval. Questions using MPH often involve some kind of unit conversion. This can be a conversion of distance units (miles to kilometers) or time units (hours to minutes). MPH also shows up in word problems very often, where a student…
Average sum trick The average sum trick simply refers to the idea that if a question gives the average of a data set and the number of data points in that data set, then that also allows a student to calculate the sum of all of the data points in the set. This is equal…