Secondary Catalogue

Mathematics


Vertex, Axis, Focus, Directrix of a Hyperbola

Analytic Geometry

Hyperbolas are conic sections that are like double parabolas. In this video we'll look at all the different geometric components of the graph of a hyperbola, including its vertex, axis, focus, and its directrix.

Confidence Interval for the Proportion

Sampling

In this video we'll look at how to build a confidence interval around the proportion of a population. The confidence level is something that we choose based on how confident we want to be in our conclusion. Of course, it's intuitive to think that...Show More

Building Histograms from Data Sets

Visualising Data

In this video we'll work on actually building a histogram from a data set. In order to build a histogram, we'll need to determine the class interval, which means we'll need to look at class width and class midpoint.

Normal Lines

Derivatives: Tangent and Normal Lines

Learn how to find the equation of the normal line at a given point. To find the equation of the normal line, you'll need to first calculate the derivative of the function, then plug the given point into the derivative to find the slope of the...Show More

Sampling Distribution of the Sample Mean

Sampling

The sampling distribution of the sample mean is created when we take every possible sample from our population, calculate the sample mean for each sample, and the plot all of those samples into a probability distribution. The SDSM is what allows...Show More

Confidence Interval for the Mean

Sampling

In this video we'll look at how to build a confidence interval around the mean of a population. The confidence level is something that we choose based on how confident we want to be in our conclusion. Of course, it's intuitive to think that we...Show More

Sampling Distribution of the Sample Proportion

Sampling

The sampling distribution of the sample proportion is created when we take every possible sample from our population, calculate the sample proportion for each sample, and the plot all of those samples into a probability distribution. The SDSP is...Show More

The Student’s T-Distribution

Sampling

The student's t-distribution is another probability distribution, very similar to the normal distribution. In fact, the values we find from the t-table are often almost identicial to the values we find from the z-table. But under certain...Show More

Conditions for Inference with the SDSP

Sampling

In order to make statistical inferences using the sampling distribution of the sample proportion, we have to meet three conditions with our sample. It must be normal, large enough, and independent. In this video we'll talk about the specific...Show More

Conditions for Inference with the SDSM

Sampling

In order to make statistical inferences using the sampling distribution of the sample mean, we have to meet three conditions with our sample. It must be normal, large enough, and independent. In this video we'll talk about the specific definition...Show More

Binomial Random Variables

Discrete Random Variables

Remember that “bi” means two, so a binomial variable is a variable that can take on exactly two values. A coin is the most obvious example of a binomial variable because flipping a coin can only result in two values: heads or tails.

Measures of Spread

Analysing Data

Range and interquartile range (IQR) are both measures of spread, also called measures of dispersion or scatter. They measure how much the data is spread out around the center point of the data set.

Horizontal Line Test

Manipulating Functions

Learn to use the horizontal line test to determine whether or not a function is 1-to-1.

Dividing Rational Functions

Rational Expressions

In this video we learn how to divide rational expressions, which are fractional expressions in which both the numerator and denominator are polynomials. We'll turn the division problem into a multiplication problem by taking the reciprocal of the...Show More
Converting to Polar Coordinates

Converting to Polar Coordinates

Polar & Parametric: Introduction to Polar Curves

In this video we'll learn to convert back and forth between rectangular (Cartesian) coordinates and polar coordinates. Rectangular coordinates are given as (x,y), where x is the horizontal distance from the origin and y is the vertical distance...Show More
Centroids of Plane Regions

Centroids of Plane Regions

Applications of Integrals: Geometry

In this video we'll look at how to find the centroid of a region. Think of the centroid as the center point of the region; it's the point at which you could perfectly balance the region on the tip of a pencil. Even when a region is irregularly...Show More
Moments of the System

Moments of the System

Applications of Integrals: Physics

Learn how to find the moments of a system given point masses and their coordinates.
Improper Integrals, Case 4

Improper Integrals, Case 4

Integrals: Improper Integrals

Learn how to integrate an improper integral with limits of integration [a,b], where an infinite discontinuity exists in the interval, and therefore the integral has to be split into to improper integrals.
Definite Integrals of Even and Odd Functions

Definite Integrals of Even and Odd Functions

Integrals: Definite Integrals

Even and odd functions take on special values when we evaluate them over symmetric intervals. Even functions are symmetric about the y-axis, so when we evaluate over an interval [-a,a], we'll get the same answer as if we evaluated over [0,a] and...Show More
Newton’s Law of Cooling

Newton’s Law of Cooling

Applications of Derivatives: Exponential Growth and Decay

Newton's Law of Cooling allows us to model the rate at which a hotter object gets gradually cooler as it sits in a colder environment. Therefore, it allows us to predict how long it will take something to cool to a certain temperature, or what...Show More
Precise Definition of the Limit

Precise Definition of the Limit

Limits & Continuity: Definition of the Limit

The precise definition of the limit, also called the epsilon-delta definition, is the proof of the concept of the limit. It proves the limit because it shows how, as you move closer and closer to a particular value of x, the value of the function...Show More
Sketching F(X) From F’(X)

Sketching F(X) From F’(X)

Applications of Derivatives: Optimization and Sketching Graphs

In this video, we'll learn to sketch the graph of f(x), using a sketch of the graph of f'(x). This requires us to draw relationships between the graph of a function and the graph of its derivative. For instance, if the graph of the derivative...Show More
Applied Optimization

Applied Optimization

Applications of Derivatives: Applied Optimization

In this video we'll look at several examples of applied optimization problems, which are problems that have us find some kind of real-world maximum or minimum. To set up these problems, we'll need to set up an optimization equation and a...Show More
Critical Points and the First Derivative Test

Critical Points and the First Derivative Test

Applications of Derivatives: Optimization and Sketching Graphs

Critical points are one of the best things we can do with derivatives, because critical points are the foundation of the optimization process. Optimization is all about finding the maxima and minima of a function, which are the points where the...Show More
Higher-Order Derivatives

Higher-Order Derivatives

Derivatives: Implicit Differentiation

Learn how to find second-order derivatives, third-order derivatives, etc. To find higher-order derivatives, we just need to continue differentiating. For instance, the second derivative is just the derivative of the first derivative, and the...Show More