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Math

Math Review of Binomial Distributions

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Overview A binomial experiment  has a fixed number of independent trials, and each trial has only two possible outcomes.  Each of the trials has the same probability of success.  The probability distribution is called a binomial distribution. What Types of Problems Are Binomial? All the characteristics of a binomial experiment are present, then the distribution…

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Properties of Probability

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Overview: Probability is the measure of the likelihood of an event.  The basic mathematics of probability theory started with games of chance, but it can be applied to many situations, from weather forecasting to politics.  Probabilities range from 0 (no likelihood) to 1 (certainty), and are expressed as rational numbers. What Is the Sample Space?…

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Math Review of Random Numbers

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Overview:  What Are Random Numbers? In a set of random numbers, the numbers do not follow any pattern.  Each number has an equal probability of occurring, and each number event is independent of any others .  Most of the time, numbers that are close to random are generated by computer programs or calculator programs designed…

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Measures of Central Tendency: Mean, Median, and Mode

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Overview:  What Are Measures of Central Tendency? Measures of central tendency represent the most typical score or value in a group of scores on some measure in either a population or a sample of that population.  Along with measures of variability, they convey much information about a distribution.  The three most common measurements are the…

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Review of Solid Geometry on the SAT and ACT

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Overview:  What Is Solid Geometry? Solid geometry was developed after plane geometry as a way to describe the three-dimensional world and the objects in it.  In the ideal three-dimensional world, objects exist with faces and angles, depth and volume.  Objects are regular, or consist of a combination of regular objects, just as two-dimensional figures can…

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Review of Math Functions on the SAT and ACT

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Overview:  What Are Functions? Functions in mathematics describe two different types of relationships between numbers.  The simplest definitions are that a function can be either the set of ordered pairs in which the first element is paired with a second element or the relationship between two sets of elements in which every element in Set…

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Math Review of Combinations and Permutations

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Overview Mathematical combinations occur in problems that involve the number of ways that sets can be combined, where order does not matter.  Permutations are similar arrangements, but order does matter.  They are related through principles of multiplication and arrangements involving factorials. How Many Choices Are There? If the problem is merely a combination of a…

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How to Read Math Questions on the SAT and ACT

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Overview: A Different Style of Reading Reading math questions on the SAT and ACT takes special attention to exact detail, following directions precisely, and watching for key words.  It is a different type of reading than students usually do in other sections of the test, such as reading comprehension or vocabulary sections.  The “plot” of…

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Using Math Proportions on the SAT and ACT

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Overview:  Why Proportions? Solving proportions is an important math skill, both on tests and in everyday life.  In addition, understanding proportions is critical in the sciences, as elements exist in varying quantities in compounds and mixtures.  Understanding proportions within populations and how they work can also be essential as part of statistical analysis in social…

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Do You Have Enough Information to Solve the Math Problem?

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Overview:  Common Strategies Some math problems on the SAT and ACT  present an equation or series, and then give a number of alternative solutions.  Like all problems of that type, only one answer is correct.  However, besides numerical solutions, there’s an additional choice: usually labeled (E)  Not enough information is available to solve this problem.…

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