When you study math, you learn more than just math, you also develop key transferable skills that can be used in your everyday life and during your career. Math teaches us logic, decision-making, and problem-solving, skills that we need and use every day.
If you're interested in a career in finance, engineering, or information technology (IT), math is one of the main areas you should be studying. Studying math is essential for anybody looking to become an accountant, investment analyst, systems developer, math teacher, and a broad range of other jobs that we'll see throughout this article.
Here, we're going to look at some of the key areas of mathematics studied in high school math classes, the importance of showing your work, and looking at some of the key areas of calculus that you may encounter.
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High School Math Areas
Generally, high schoolers will take a standard set of math courses. Naturally, different students can opt for different math classes, but it's common for them to study algebra, geometry, trigonometry, pre-calculus, calculus, and even take advanced placement or AP classes.
Through studying these classes, students should gain a good understanding of trigonometry, sequences and series, exponentials and logarithms, differentiation, integration, vectors, statistical hypothesis testing, kinematics as well as algebra and functions.
There are a few reasons why these are the topics covered in high school, but the two main reasons are that they will give students the mathematical understanding and reasoning they can use in their everyday lives while also providing them with the necessary foundations in math to study it at college if they so wish.
Beyond math, the skills we'll see here are certainly useful for career paths involving math, technology, and science as well as lots of other fields.
Math Help For Students With Regards to Solving Math Problems
When you solve math problems, you need to follow all the necessary steps to arrive at a solution. This means that you need to both understand how you reach a solution and also show your work.
In tests, students are graded both on getting the correct answer and also on showing how they got there (to show that it wasn't by chance). It's even possible for students to still get points in a test or exam just for their working and mathematical reasoning even if they didn't arrive at the correct answer.
It's a good idea in exams and tests to attempt every question. Even if you get the answer wrong, you can still salvage some points just by using the right mathematical approaches and reasoning. In some cases, a student who gets every answer right without showing their work will only slightly outperform a student who showed their work but got a lot of answers wrong.
Don't let all the time you spent studying math go to waste by not showing off what you know in your tests. Always show your work!
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A Closer Look At The Math Themes Covered In High School
Calculus
Did you know that calculus comes from the Latin for "small pebble"? This is because early mathematicians would use pebbles to count. You can fin a whole guide on the instruction of Calculus. Now, the term refers to a mathematical means of computation involving the study of continuous change. There are two principal branches of calculus: Differential Calculus and Integral Calculus.
Differential calculus involves rates of change and curves and slopes whereas integral calculus looks at the accumulation of quantities and the spaces under and between curves. They are two sides of the same coin, with that coin being the fundamental theorem of calculus.
The calculus we see today, modern calculus, arose during the 17th century thanks to the work in mathematics by pioneering mathematicians such as Isaac Newton and Gottfried Wilhelm Leibniz. It's an important area of mathematics as it can lead to other more advanced areas of math.
The individual principles of calculus include limits and infinitesimals, differential calculus, Leibniz notation, integral calculus, and fundamental theorem.
As previously mentioned, Physics makes particular use of calculus and its principles, however, it is also applied to Computer Science, Statistics, Business, Economics, Engineering and Medicine. This shows just how broad the concepts and theories reach.
Differentiation
Differentiation is a mathematical method that computes a rate of change. This means you can use differentiation to calculate the rate of change of velocity with respect to time (also known as acceleration) or the rate of change of x with respect to y on a graph (the gradient of a curve).
As differentiation is part of calculus, your calculus teacher will likely teach you the basic rules of differentiation.
For instance, you will learn that:
If y = a function of x (an expression containing x's and numbers), then the derivative of y with respect to x is written dy/dx.
You'll also probably learn how to differentiate x to a given power where you bring the power down to in front of the x and then reduce the power by one. In addition to this, you'll likely study notation, which is how we write the derivative. Other areas you'll likely cover include the constant rule, the multiple rule, the sum rule, and the difference rule.
As we've already mentioned, differentiation looks at curves and gradients so you'll learn how to differentiate the equation of a curve and find the formula for its gradient.
Don't worry if this all sounds foreign to you, you can find out more about calculus online or ask your math teacher about them in calculus class.
Mechanics
Depending on their class choices, students will also learn about math in the physical world including acceleration, Newton's laws, vectors, impulse and momentum, projectiles, the center of mass, and others.
Some of these will be taught in high school physics classes whereas others will be dealt with more mathematically in calculus or pre-calculus classes.
These areas of math are essential for those interested in a career in the engineering industry as are a lot of the fundamentals of mechanics principles.
If you like cars, you'll likely find the equations and functions from this area of math to be very useful. When you combine the study of acceleration caused by gravity with what you learn in mathematical mechanics, you'll start to overlap with some of your physics classes.
For many, mathematical mechanics is one of the more interesting areas to study as they get to see and solve real-world problems.
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Sound Challenging? Don't Worry, You're Doing Great!
We can't teach you high school math in just a single article, but you'll hopefully have a better idea of some of the areas that you'll study and what you'll be expected to know by the time you graduate high school.
Math classes can be difficult and there's no harm in needing some extra help during your studies. Math will teach you a lot of useful transferable skills so it's worth putting the time and effort into it. If you take some of the more advanced math classes available to you, you'll likely end up with a better understanding of mathematics than the average person.
Even if you don't take your math studies any further beyond high school, you can be proud of the level you achieve in high school as you'll know enough mathematics for use in everyday life and will always have the option to further your understanding of math through further study.
Of course, over time, your understanding of math may diminish if you're not using these skills in your everyday life. You can always look to private math tutors (such as the many talented ones on our platform) to help you refresh the math you learned in high school or even advance your understanding of math.
If you're still interested in finding out more about math, you should check out some of our other articles on our blog or start your search for a math tutor.
Every tutor is different so find the one that's right for you, your level, and your budget and take your math to the next level!
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