Mindblown: a blog about philosophy.

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 refers to the distance from zero of a value. As such, it is always a positive value or zero The absolute value of 7 is 7 because its distance from zero is 7; the absolute value of -9 is 9 because its distance from zero is 9. The absolute value of an expression…

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…