Scientific notation Scientific Notation is a way to express very large or very small numbers by the number’s most significant digits combined with an exponential expression of base 10. This notation usually includes a whole number with one or two decimals after it: 2.38. This will then be followed by an exponential expression of: × 10a , where…
Least Common Multiple (LCM) The Least Common Multiple refers to the smallest possible number that is evenly divisible by a given pair or set of numbers. For example, the least common multiple of the numbers 2 and 3 is 6. The easiest trick for finding the least common multiple of any series of numbers is to find the…
Imaginary (Complex) numbers Imaginary numbers refer to irrational numbers that cannot exist in the real word, but which do exist in math. The most common imaginary number to see on the ACT is the imaginary number i, or the square root of -1. When in Doubt, Try to Square It The best piece of advice for problems…
Logarithms A logarithm is the inverse of taking something to an exponential power. When something is expressed as log5125, in a sense it’s asking what exponent would 5 need to be taken to to get 125. This is why log5125 = 3.That’s why the first core skill of logarithms is to be able to rewrite logs in exponential form.…
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…