When it comes to mathematics, high school classes can be quite challenging. Just because you made it to high school and can do elementary-level math, doesn’t necessarily mean you’ll excel in all the advanced level classes. With different schools offering different levels of math classes, the most difficult courses shift from school to school.
In this article, we’ll cover the 4 main types of math found in American high schools: Algebra, Geometry, Trigonometry and Calculus — discussing the characteristics that make each one of these difficult, even for a particularly talented math student.
What Is Algebra?
Before considering which of the 4 major areas of math may be the hardest, let’s begin by explaining what each one is. Algebra is the study of mathematical equations. It is used in many different areas, from worksheet exercises found in grade school, to more advanced equations used in higher level math and sciences, including chemistry and physics.
Algebra is all about taking the familiar and making it abstract. You must be able to look at what you already know and apply it to a larger problem.
Algebra is one of the most important classes in high school and can be quite difficult to master. It requires you to use logical thinking and sometimes makes you think outside the box.
Growing accustomed to the rules and conventions of algebra requires time and a great deal of study. Taking the time to understand simpler concepts is important — they are the foundations needed to reach greater heights in the class.
What Is Geometry?
Geometry is the second biggest area of math in high school and deals mainly with shapes, angles and measurements. Geometry requires a good understanding and visualization of shapes as well as formulas used to express relationships between angles and sides.
Geometry also applies equations to figures and shapes and requires the student to interpret data in order to solve various problems. Geometry is considered by some to be the hardest of the math classes, due to its reliance on the visualization and manipulation of shapes. You can have all the formulas memorized, but if you don’t have the ability to understand and interpret this data to solve a certain problem, it can become a challenge.
Finding the relationships between different shapes and structures can be a daunting task that may require some true ingenuity on the part of the student.
What Is Trigonometry?
Trigonometry is the third biggest area of math available in high schools in the United States. Trigonometry uses the same core foundation of Algebra but extends it to include triangles and the measurement of angles within planes. This can be particularly difficult to master, because it requires measuring multiple sides of a triangle, which requires understanding the relationship between all three sides.
Understanding the basics of trigonometry is essential if you want to use more complex methods such as using sines, cosines and tangents to solve more complex equations. Trigonometry can be quite challenging, because it requires strong fundamental understanding of the properties of angles and the application of different formulas to solve for them.
You can have the strongest memory for formulas, but if you do not have an understanding of what the formulas prove, then you may end up floundering in the course. Trigonometry also requires a knack for problem solving, as many of the tasks will challenge your deductive reasoning abilities.
What Is Calculus?
Finally, when it comes to math in high school, the most challenging and difficult course is often thought to be Calculus. Calculus is the study of functions, limits and derivatives, and establishes the foundation for many real world and advanced engineering and sciences. It can be broken down into two basic branches – Differential Calculus and Integral Calculus.
Differential Calculus establishes the relationship between slopes of curves and functions, while Integral Calculus allows for solving for the area under a curve or a surface before it is divided into finite portions. Calculus is the foundation for many advanced math classes in college.
It requires strong fundamentals in Algebra and Trigonometry, as well as a good understanding of derivatives and integrals. You must have a very firm grasp of each of their principles and theorems and be able to apply them to solving complex equations.
Throughout the course, you will also encounter different proofs and derivations, that require strong reasoning and problem-solving skills.
Conclusion
When it comes to the hardest math class an American high school student may undertake, a general consensus suggests that Calculus is the most challenging, followed by Trigonometry, Geometry, and Algebra. Each of these four areas of mathematics is essentially an extension and elaboration of the one that came before it. That said, each of these expert problem-solving courses require strong fundamentals, an advanced level of learning, and problem solving abilities.
While they can be daunting and difficult, they are also an essential part of a student’s high school education — giving them the skills to understand complex mathematical principles and help prepare them for college.