Online High School Math Courses
There’s quite a lot of high school math courses available on High School of America’s online platform, including: algebra, geometry, trigonometry, pre-calculus, calculus and even statistics. The following sections will describe each of these courses in more detail and present multiple sources for study.
Algebra is the first course in most high school math programs. It teaches students about how to write and read mathematical equations, and how to solve for unknown variables using those equations.
Algebra can be considered a kind of elementary mathematics that serves as a foundation for higher level courses. This set of online resources are comprised of both textbook-like sources and interactive games designed to make algebra more engaging for students.
Here are some great options available:
The content in a geometry course covers shapes, measurements and spatial relationships. Geometry is generally considered an essential skill for science students as it lays out the foundation of math used to calculate results such as area, mass and volume in subjects like physics.
Here are some great resources available online that can help you learn geometry:
Trigonometry finds its roots in geometry. In trigonometry one not only takes on the study of triangles, but also how they relate to circles and other similar 3 dimensional figures. It’s quite simply the study of angles from a mathematical point of view. There are two main branches to trigonometry and each branch will cover different topics than the others.
The first Technical (or Analytic) branch, and the second is the Applied (or Synthetic) branch. The technical branch generally deals with functions like those found in simple electronics or physics settings. The applied branch deals research problems often related to astronomy or medical studies.
Calculus is a study of change that goes beyond what algebra teaches us about variables and constants. Calculus usually assume the learner already have an understanding of basic arithmetic, trigonometry, set theory as well as some mathematical maturity.
If you are interested in learning calculus then this set of online resources will be right up your alley:
While technically not covered by high school math courses, it is an essential part of many engineering programs and is considered advanced mathematics. Calculus studies the derivative including second order derivatives, and how they pertain to physics, chemistry and biology. There are three main branches of calculus:
- Differential Calculus – This study involves finding rates of change over time;
- Integral Calculus- This study involves approximations for definite solutions from indefinite integrals;
- Parametric Calculus- This study involves using parametric equations to produce motion or other results in a variety of settings. These include things like curve tracing where you follow a curve as it moves through space with time (e.g. Newton’s Laws, sound waves), or work done by a force applied continuously on an object such that the object travels along a curve.
This resource has more information:
The study of statistics is generally considered an advanced topic and often features in the last courses of many math programs. It involves collecting data (i.e., samples) from a population and using those samples to make decisions about the whole population, or conduct inferences on that population based on our sample data.
A good example would be gambling; if you had 100 winning tickets you could infer that the next ticket would be a winner too. Statistics is commonly used for business decision making as well as scientific studies, especially biology and medicine related fields where sampling is critical to their work.
Statistics is also very helpful when learning how to analyze large sets of data such as those found in computer science and engineering.
Here is a great resource on statistics:
This is one of the last courses many math students take before moving onto more advanced studies in their degree program. This course covers topics related to integrals, infinite series, parametric curves, polar coordinates and vectors. These are generally linked to algebra, geometry and calculus I so it’s important that you have a good grasp before moving onto this class.
Most people think of differential equations when they hear the phrase “advanced mathematics”. It’s actually used all around us from the heating element inside your oven or microwave to controlling vehicles for self-driving apps. The study of differential equations focuses on how a variable y depends on an unknown function f(x), such that y’ is also dependent upon x:
The solution to systems like this is called a “solution” because it describes the result over time of any system where y’ =f(x). Differential equations are used in many fields ranging from science (e.g. astronomy, biology) to economics and finance. There are several different types of differential equation including: linear, non-linear and partial derivatives, ordinary differential equations etc.
There is a lot of debate about whether Quantum Mechanics can actually be called “advanced mathematics” because it’s more based in Physics then Math. However there are many math concepts used in this field including Linear Algebra, Matrix Theory, Complex Numbers and Vector Calculus.
Most people think of mathematical physics as being an advanced subject but it’s actually one of the most applied areas of mathematics. This area focuses on how math can be used to solve problems in physics such as those set by Newton, Maxwell, Einstein and Schrödinger.
Group theory explores how objects are related through symmetry. You’ll notice that patterns like snowflakes or flowers have symmetries and each shape has either rotational or reflective symmetry (meaning that if you rotate it a certain number of times or flip it over then it’s back to what it was before).
The study of geometry and algebra has used symmetry for centuries but only recently have people started to explore those relationships. One thing that makes group theory particularly interesting is the fact that symmetries can transfer/transform into each other, which means there are underlying patterns in nature. Group theory also looks through things like permutations, states on finite groups and subgroups. Math related to these ideas is an important part of most math programs at universities and colleges.
Combinatorics focuses on counting the number of ways things can happen. One common application of this is referred to as Permutations and Combinations. Here’s an example:
The probability that a randomly chosen hexagon will have exactly three points in its interior is 1/75 (i.e., the probability that it has 0 points inside it is 36/50 multiplied by the probability that it has one point inside of it, which is 30/50 multiplied by the probability that two points are inside of it, which is 12/50). This happens because there are 75 different possible ways for a random hexagon to be formed so if any one of those possibilities cross out 3 “points” then we know there’s only 1 option remaining and hence only 1 probability of being correct.
This is a very simple example, in fact most problems are much more complex than this but the concept behind it remains the same whether you’re counting atoms, groups or library books.
Combinatorics & Graph Theory
This course focuses on graph theory which is another area used to solve math related problems where there are multiple variables. For example let’s say we have “X” number of people and “Y” number of activities to participate in over one day (e.g., 10 people doing 5 things). For every combination that can be formed between participants and activities what’s the probability that all participants complete each activity if they get to choose for themselves? The answer is 100% because if they don’t then there’s no option of them choosing to do the activity again.
This field focuses a lot on using graphs, which are formed by vertices and edges. For example in the above problem we could represent people as points (vertices) and activities as lines connecting that point with other points (edges). This way each person would have an edge going from them to all of their involved activities, while each activity would have multiple edges coming from it with different shapes depending on how many people chose that particular activity over all (e.g., some may be squares which connect 1 vertex to 4 others while some might be triangles which connect 3 vertices together). Using graphs allow us to study and represent problems within a visual context.
I want to stress that these are just general examples of applications of math, there’s a lot more out there which we haven’t even touched on yet (e.g., number theory). We hope this post has helped you think about how math can be applied to real life issues beyond the classroom!
5 Reasons to Take High School and College Prep Math Courses Online
Learning math can be a challenge for some students, especially for those who have trouble grasping the subject matter. Sometimes it’s just easier to learn in person with an experienced teacher.
However, many teachers are not available in rural communities or at schools that serve large numbers of minority and low-income kids. Fortunately, there is another alternative out there…online math classes! Here’s why you might consider taking your high school or college prep math course online.
1. It Can Be Less Expensive
Online math courses are usually less expensive than traditional courses offered by local schools. This is due to money saving features like short class times (usually between five and eight hours each week), a lack of expensive supplies, and less commuting and traveling time. Because the courses are completed online, there’s no need for textbooks. This saves money on book costs.
2. It Saves Time
You can consume all the math you need in one or two years instead of having to attend class four to six days each week for several months or whole semesters at a time. Once you’re done with your course, you’ll have earned your math credit in no time!
3. There Is No Summer School Required
Some students must take summer school if they fail to pass their traditional classes in the fall semester. If that is not an issue for you, consider taking your college prep math course during the summer break so that you can enjoy more time with your friends and family!
4. You Have A Lot of Control
Online math is all about self-study. You can work at your own pace, set study goals for yourself, and interact directly with the teacher during lessons to ask questions or clear up any confusion. With this freedom comes responsibility. If you decide to take an online math course, make sure it’s not just a quick way to get out of class—you’ll need to really buckle down and dedicate yourself in order to pass the classes on time, especially if you do not have much experience studying online courses before.
5. It May Be Easier Than a Physical Class
Some research suggests that math may be easier to learn online than in person. Students seem to do better with math concepts when they don’t have the stress of worrying about other people looking at them while they work.
In a traditional class, teachers can make mistakes or give students incorrect information without realizing it, which adds confusion and frustration for students who already find math tough. It’s easier to focus online since you’ll most likely not be distracted by others trying to call your attention away from an assignment!
Begin Your Path Toward Success Online Today!
High School of America’s online math courses are ideal for anyone who would like to expand their knowledge of mathematics and gain a better understanding of how it is used in the real world. Whether you’re looking to complete your high school diploma with advanced level math credits or you want to prepare yourself for college and career success, we have the course that will meet your needs.
Using fun, innovative, and engaging lessons, our instructors guide students through each topic using real-world examples that keep them engaged while allowing them to test their knowledge at regular intervals. Our intuitive learning management system makes it easy for students to track their progress throughout the course so they can move at a pace that’s right for them while still giving them the support they need when problems arise.
We know students often have a lot of questions about online learning, so we are here to help! With 24/7 support and extensive FAQs, you can learn all you need before you enroll.
Resources and References: