Individual Data Point Changes: Questions may also ask: how does increasing or decreasing one of the data points in the set change our mean? What data points would need to be added to get the mean to a particular value?.Data sets with more variation (or that are skewed in one direction or another) will have more distance between the mean and median. Mean-Median Comparison: Many ACT questions about the mean of a data set will ask students to compare the mean and the median: which is larger/smaller or are they the same? Data sets with numbers that are close to one another in value will have similar or identical means and medians.The mean is equal to the sum of all the data points divided by the number of data points in the set. The average of a data set is also known as the arithmetic mean. For example, to divide something by 12, that’s the same as doubling it, or multiplying by 2/1! Dividing by a fraction is the same as multiplying by its reciprocal (swap the numerator and the denominator: what was on top will now be on bottom, and vice versa). Divide: To divide fractions by each other, it’s easiest to turn division into multiplication. Add: Add the numerator and keep the denominator (bottom half of the fraction) the same.Once the fractions have the same denominator, they can be added or subtracted as follows: There are four different ways that fractions can interact: addition, subtraction, multiplication, and division.įor the first two (addition and subtraction), each fraction needs to have the same denominator, known as a common denominator. Since these are a mixture of two different things, these are referred to as mixed numbers. For example, 5/2 can also be written as 2 1/2. Improper fractions can also be written as a mixture of whole numbers and fractions.The latter case is known as an improper fraction, or a fraction where the numerator (top half of the fraction) is greater than the denominator (bottom half of the fraction). This is the form used when a fraction is equal to a value less than 1 or when when a fraction is larger than 1 but does not simplify to a whole number: 5/2. They make up the core material on the exam and students preparing for the test should know these topics first before approaching more Fractionsįractions can be expressed in two different ways: These concepts will appear on the ACT Math section. Translations, Reflections, and Rotations.System of Equations with Three Equations.If you see one on the list and you feel like you don’t understand it as well as you could, scroll down for an explanation! Must Know ACT Math Concepts We know this giant list of ACT math concepts seems scary - but don’t worry, we’ll go over each of them in this article. Below is a list of the most common ACT math concepts and how often they tend to appear! Which Topics are Most Important to Know for the ACT Math Section? Some terms and concepts appear on every test, and others appear on every other test or every fourth test. This is great news, because it means if you know you tend to struggle on the ACT math section, you can look over this comprehensive list of ACT topics to boost your ACT score. We can never know what exactly is going to be on the ACT Math section, but each test draws from a similar bank of concepts and terms. We are told that the ratio of circle A’s circumference to circle B’s circumference is 2:9.Just About Everything You Need to Know for the ACT Math Section Let the circumference of the larger circle be: $C = 2 \pi R$ Let the circumference of the smaller circle be: $c = 2 \pi r$ If the circumferences of A and B are in the ratio 2:9, the areas of A and B will be in the ratio: Circumference is a measurement of length (one-dimensional).
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