Mindblown: a blog about philosophy.

Things to Do With the Questions Simplify Sometimes an equation will be given in an unsimplified form. If a formula is given unsimplified, the first thing to do is to simplify it. The question is not written that way by accident, it’s done to make the problem seem more challenging or harder to solve. Once it’s…

A step function is a function that includes a series of horizontal lines, which jump from one to the other at regular intervals. Here is an example question from the 2017 ACT: For ABC cabs, the price of a taxi fare jumps $2 each time the fare reaches a new whole number value. This means…

The ACT sometimes likes to include questions that involve 3D objects that have a number of faces on the object. The faces on the object will be common geometric shapes such as triangles, squares, or occasionally more complex shapes such as hexagons. Key things to remember for faces on 3D figure questions are: Here is…

Factorials express a product of multiple consecutive integers starting at 1. Factorials look like an exclamation point, which is placed next to either a variable or a whole number. However, even when placed next to a variable it still indicates a whole number reached by multiplying that variable by all of the integers before that…

Angles within a triangle can be expressed one of two ways. This can either be in degrees or radians. Therefore to convert between the two:

Stem and Leaf Plots Stem and leaf plot questions are a way of displaying a set of data in a concise manner. The name refers to the fact that the leading digit (usually the tens digit) is removed from each data point, and instead is used as a label for a row that includes all…

Translations Translation questions will involve moving a shape or the graph of a function in one of three ways: translation, rotation, or reflection. Translation Rotation Reflection

Compare numbers Some questions on the ACT math section might require comparing the size of numbers expressed in different forms, or where the expressions contain only variables. For these questions, it’s important to remember simple things about different expressions: Radicals/Square Roots: The equivalent/value of a square root gets large as the number under the root/radical gets…

System of equations with three equations Most systems of equations problems only involve two equations, but occasionally they’ll include three equations, often in the form of a word problem. For these problems, students need to isolate two different variables in two of the equations. These then need to be substituted in for each other in…

Lowest Common Denominator The Lowest Common Denominator is the smallest number that can be a denominator for two separate fractions. Another way to think of it is that it’s the smallest number that both original denominators can factor into. This is why the most common way to find the LCD is simply to multiply the…