Weighted average Weighted averages are a way to combine the averages of two data sets of different sizes. This is similar to calculating sum totals on a histogram. For example, two classes are described. Class A has 10 students who had an average test score of 75. Class B has 15 students with an average…
Exponential Growth/Decay The Exponential Growth/Decay formula is one of the most common equation forms to see on the ACT. It can be used to express a multitude of different situations, which means it can show up theoretically as a variable function or practically within a word problem. The formula looks like this: Final = Initial (1±growth/decay rate)time Key Takeaways…
Conjugates Conjugates are binomial pairs that have the same numbers/variables within them, but opposite signs. So for example (x-1) and (x+1) are conjugates. Conjugates have special properties that can be useful to know when they appear in questions or answers on the ACT. Simplifying and Rationalizing Denominators This particularly true when the original denominator contains either a radical…
Domain and Range Domain and Range are two common terms used in reference to functions and data sets, respectively.
Trapezoid Trapezoid questions on the ACT usually relate to the area of the shape or the internal angles of the shape. As a result, it’s worth knowing that the area formula for a trapezoid is: And that a trapezoid has 360 degrees of internal angles inside of it. Key points to remember for ACT trapezoid…
Factors Factors refer to numbers that can be multiplied together to reach a specific product. For example, 2 and 3 are factors of 6 because their product is 6. Quadratic factors were discussed above, while this section will focus on whole number/constant factors. These types of factors usually come up on the ACT in the following…
Probability with “not” Probability questions with not are similar to normal probability questions. The main difference is that the odds that need to be calculated are the odds of failure rather than success. In the earlier examples on probability, the focus was on drawing a specific color of starburst out of a bag. The odds there were…
Similar triangles Similar triangles are triangles that have the same angles, but different side lengths. The easiest way to think of this is to imagine a triangle being scaled up or scaled down. If specific numbers aren’t given for a similar triangles problem, then it’s best to look at the shape of the triangle. If the original…
Change the base – If 9x = 275, what is x? Some questions will require changing the base of a number with an exponent. For example, 16x = 2564, then what is x? 256 = 162 , meaning that the original equation can be rewritten as 16x = (162)4 = 168 This will usually involve numbers whose square or cube roots are simple integers. So it’s useful…
Triangle opposite side rule The sides of triangles and the angles opposite them are related and this relationship may be useful on certain triangle questions. The most important thing to remember is that the length of the side of a triangle is proportional to the angle opposite that angle. So the largest side will also have…