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…
Function shifts Vertical Shifts Vertical function shifts are highly intuitive. They occur from either a coefficient placed in front of the variable(s) in the function or because of a constant term added to the function equation. Sample Function: y = 2(x+1)2 − 5 Here the function is shifted down by 5 units, and is multiplied by a factor of 2.…
SOHCAHTOA SOHCAHTOA is a pneumonic device used to remind students of the three trigonometric functions and their equivalents on a right triangle. Problems utilizing SOHCAHTOA will often have students solve for a missing side length on a triangle, or occasionally find a formula to express a side length (where there may only be variables or a mixture…
Negatives The easiest simple mistake to make on an ACT math section is to make a sign error. Whether it’s addition, subtraction, division, or multiplication, negatives make it easy to switch a sign (or to forget to switch a sign) and lose points on a question that a student would otherwise have gotten right.It’s important…
Area/Perimeter of basic shapes On the ACT, students may be asked to calculate the areas of certain common shapes, including triangles, rectangles, and circles. The test will provide students with these formulas, but it’s good to be comfortable with using them before the test, so that questions involving these concepts are just about automatic! The…
Quadratic skills There are four crucial skills a student needs to have when it comes to quadratic equations: to factor, foil, zero parentheses, and graph parabolas. To start, it’s worth remembering what a typical quadratic equation looks like: ax2 + bx + c There are three terms: a quadratic (squared) term, a linear term, and a constant. Quadratics are often expressed…
Ratio Ratios tell the proportional quantity of one thing to another. Ratios are often expressed either with a colon – the ratio of kids to adults is 6:1 (read six to one, meaning there are six kids for each 1 adult) – or like a fraction – the ratio of kids to adults is 61. It’s…