With any hypothesis test, we need to state the null and alternative hypotheses, then determine the level of significance. We’ve already covered these first two steps, and now we want to learn how to calculate the test statistic, which will depend on whether we’re running a two-tail test or a one-tail test.

Read MoreLaws of logarithms (or laws of logs) include product, quotient, and power rules for logarithms, as well as the general rule for logs (and the change of base formula we’ll cover in the next lesson), can all be used together, in any combination, in order to solve log problems.

Read MoreU-substitution in definite integrals is just like substitution in indefinite integrals except that, since the variable is changed, the limits of integration must be changed as well. If you don’t change the limits of integration, then you’ll need to back-substitute for the original variable at the end.

Read MoreExponents are a tool we can use to write numbers in a simpler way. An exponent is a little number that you write above and to the right of another number, and it tells you how many times to multiply the base number by itself.

Read MoreThe comparison test for convergence lets us determine the convergence or divergence of the given series by *comparing* it to a similar, but simpler comparison series. We’re usually trying to find a comparison series that’s a geometric or p-series, since it’s very easy to determine the convergence of a geometric or p-series.

When we talk about unit price, what we’re really talking about is the “price per unit” of a product (the price per pound of tomatoes or the price per quart of milk). This is the math that helps us compare the prices of things.

Read MoreWhen two three-dimensional surfaces intersect each other, the intersection is a curve. We can find the vector equation of that intersection curve using three steps.

Read MoreIn order to model sales decline with the exponential decay equation, the decline must have a constantly and exponentially rate of decline. If it does, we can use our standard exponential change equation.

Read MoreThere are three signs associated with every fraction, one with the numerator, one with the denominator, and one with the fraction in general. But this can be hard to remember, because not all of the signs are always visible.

Read MoreAny point in the coordinate plane can be expressed in both rectangular coordinates and polar coordinates. Instead of moving out from the origin using horizontal and vertical lines, like we would with rectangular coordinates, in polar coordinates we instead pick the angle, which is the direction, and then move out from the origin a certain distance.

Read MoreVertical angles are angles in opposite corners of intersecting lines. So vertical angles always share the same vertex, or corner point of the angle. They’re a special angle pair because their measures are always equal to one another, which means that vertical angles are congruent angles.

Read MoreTwo-step problems are problems in which you need to not only solve an equation for the value of a variable, but then also use the solution to evaluate some other expression that depends on that same variable.

Read MoreThe domain is all x-values or inputs of a function and the range is all y-values or outputs of a function. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.

Read MoreThe Theorem of Pappus tells us that the volume of a three-dimensional solid object that’s created by rotating a two-dimensional shape around an axis is given by V=Ad. V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the two-dimensional figure.

Read MoreThe absolute value operation turns any value inside it into its distance from the origin, essentially turning both positive and negative numbers into only positive numbers. Always calculate the value inside the absolute value first, then apply the absolute value last.

Read MoreThe vast majority of the numbers you’ll use in most math classes are called **real numbers**, and the whole universe of real numbers is what makes up the **Real Number System**. Let’s start with a diagram.

The alternating series estimation theorem gives us a way to approximate the sum of an alternating series with a remainder or error that we can calculate. To use the theorem, the alternating series must follow two rules.

Read MoreProbability density refers to the probability that a continuous random variable X will exist within a set of conditions. It follows that using the probability density equations will tell us the likelihood of an X existing in the interval [a,b].

Read MoreRemember that a solution to a system of equations is the set of numbers that makes all of the equations true. If a three variable system has a solution, it’ll have a solution for each of the three variables.

Read MoreThere’s a special relationship between two secants that intersect outside of a circle. The length outside the circle, multiplied by the length of the whole secant is equal to the outside length of the other secant multiplied by the whole length of the other secant.

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