Counting principle Counting principle questions are similar to probability questions, but instead of probabilities they are asking about possibilities. Often in ways such as: how many different possible combinations are there of several different groups of items or options, such as letters and numbers for a license plate or dice rolls from multiple pairs of dice…

Shaded area Shaded area questions will generally involve one of two things: a geometric shape (or possibly one inside of the other) or an inequality graph. Geometric Shading Problems Geometric shading problems will focus on calculating area. Students will be asked to calculate a shaded area from a larger whole area. This will often involve subtracting one…

Periodic function graph Sine and Cosine graphs appear fairly frequently on the ACT math section. It is less likely that you’ll be asked to calculate specific values on the graphs (though this does happen occasionally). Instead, it’s much more likely you’ll be asked to: Either of these types of questions can be quite easy, as…

Weird shape area Some ACT Math area questions will involve shapes that are irregular, meaning that they are not the standard triangle, circle, rectangle, or square. Instead, they might simply be polygons that combine portions of these shapes together. Sample Problem Here is an example problem from the July 2019 ACT: There are two different…

Remainders Remainder problems will generally either be: simple or pattern-based reminders. Simple Simple remainder questions will provide some kind of division problem, which will leave some remainder. The student will then generally have to find  whatever whole number is left over when the nearest factor of the denominator is taken away from our original number. For example: what is the remainder…

Multi Step conversion Multi-step conversions will involve a mixture of ratios and/or equations. Questions will either go from a proportional ratio to an overall total, or they will ask for a conversion of one ratio to another (usually in the form of a unit conversion). One of the most common versions of this question will…

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…