Solving Systems Of Equations By Substitution MethodIn this method, we first find the value of one   variable (y) in terms of another variable (x) from one equation. Substitute this value of y in the second equation. Second equation becomes a linear equa…

Probability and PermutationsThings to remember: • When dealing with probability and permutations, it is important to know if the problem deals with replacement, or without replacement. For example, “with replacement” would be drawing an ace from a deck o…

Angle Sum and Difference, Double Angle and Half Angle FormulasHipparchus, considered to be the most eminent of Greek astronomers (born 160 B.C.), derived the formulas for The following formulas (or formulae, in Latin) are trigonometric identities.Sum an…

Scatter Plots and ModelsBefore attempting a regression analysis of data, it is often helpful to examine a scatter plot of the data to see which regression model is most likely going to be a good fit. Keep in mind that when working with real world data, i…

Logarithmic Functions Most logarithmic graphs resemble this same shape. This graph is very, very close to the y-axis but does not cross it. The graph increases as it progresses to the right (as seen in the graph at the right). In a straight line, the “r…

Permutations with RepetitionNumber of permutations with repetition(1) The number of permutations (arrangements) of n different objects, taken r at a time, when each object may occur once, twice, thrice,……..upto r times in any arrangement = The number of …

Regression AnalysisDEFINITION: Statistical Regression -the relation between selected values of x and observed values of y, from which the most probable value of y can be predicted for any value of x.The term “regression” is attributed to Sir Francis Galt…

Binomial Probability “At Least / At Most”When computing “at least” and “at most” probabilities, it is necessary to consider, in addition to the given probability, • all probabilities larger than the given probability (“at least”) • all probabilities sma…

Theoretical and Empirical ProbabilitiesYou are already familiar with a plethora (a bunch) of information about working with probability. Let’s quickly refresh our memories: Here are some warm-up examples:1. At a school fair, the spinner represented in th…

Measures of Central TendencyYou are already familiar with measures of central tendency used with single data sets: mean, median and mode.Let’s quickly refresh our memories on these methods of indicating the center of a data set: Median (middle): (n is t…