History records Math’s existence for centuries, with the first records dating back to Mesopotamia. Math is everywhere—everything from music and art to engineering and architecture. It’s used in science, business, and even politics.
Math can be divided into many different branches: geometry, algebra, statistics, logic/set theory, trigonometry, calculus, and pre-calculus, among others.
The main difference is that: while calculus is used to solve real-world problems, pre-calculus prepares students for the more complex mathematics they will encounter in future classes.
Let’s discuss these two branches of mathematics in detail.
What Is Calculus?
Calculus is a mathematical theory that studies the rate of change of functions. It can be used to find the slope of curves, find areas under curves, and determine volumes of solids.
Isaac Newton invented calculus in 1687. He was just 23 years old when he published his work on calculus. He used calculus to describe how gravity affects objects as they fall to Earth.
Calculus has many applications, including physics, engineering, economics, biology, and many more fields of study. For example, engineers can use calculus to analyze how much force a structure needs to support its weight while still being able to withstand the force of gravity pulling down on it from above.
What Is Pre-calculus?
Pre-calculus is a math class for students who have completed Algebra II or are about halfway through high school.
This class gives students an introduction to the algebraic and trigonometric functions they’ll use throughout the rest of their mathematical studies.
Pre-calculus is a prerequisite for calculus. Solving differential equations is easy if you know how to analyze functions and find roots of polynomials, you’ll need first to get a handle on pre-calculus.
It’s usually divided into two periods: one focused on algebra and another on trigonometry.
The algebra portion of pre-calculus involves solving equations and systems of equations and graphing linear functions. The trigonometry portion consists in working with trigonometric functions such as sine and cosine to solve for angles regarding the sides of triangles.
Know The Difference
Calculus and pre-calculus are two distinct areas of mathematics.
The main difference between calculus and pre-calculus is that calculus is a branch of mathematics that studies infinitesimals, derivatives, integrals, and infinite series. In contrast, pre-calculus is a branch of mathematics that deals with algebraic concepts like functions, equations, inequalities, and introductory trigonometry.
- Calculus is a higher-level course focusing on abstract concepts like limits, derivatives, and integrals.
- Pre-calculus is a lower-level course that teaches students how to apply basic mathematical concepts to real-world scenarios.
- Calculus is typically taken after high school, while pre-calculus is usually taken in high school before calculus.
- Calculus also covers topics such as limits and derivatives not covered in pre-calculus.
- Pre-calculus tends to focus more on algebraic operations like solving equations and graphing functions.
- Calculus is concerned with slopes of lines and curves, whereas pre-calculus is concerned with slopes of graphs and number lines.
Here are these differences in the form of a table.
| Calculus | Pre-calculus |
| It’s an advanced level maths course. | It’s a basic level maths course. |
| It is mostly taken after high school. | It is studied in high school as a base for STEM. |
| It helps you to find out the change in any form or shape. | It gives you basic information regarding different shapes. |
| You can study advanced derivatives and integrals in calculus. | You can study basic mathematical concepts in pre-calculus. |
Here is a video clip explaining the differences between calculus and pre-calculus.
Is Pre-Calculus Harder Than Calculus?
Pre-calculus is not harder than calculus but requires more time and effort. Pre-calculus can be viewed as a bridge between algebra and calculus.
It’s a necessary step in the progression of mathematical studies because, without it, you’d have trouble understanding other areas of math, such as trigonometry, geometry, or statistics. Like any other skill, you’ll need to put in some time and effort to master pre-calculus.
Can You Do Calculus Without Pre-calculus?
You can do calculus without pre-calculus but will have a more challenging time. Pre-calculus is the best way to prepare for calculus because it gives you a solid foundation in algebra and trigonometry, which are used extensively in calculus.
Is Trigonometry Part Of Calculus?
Trigonometry is a branch of mathematics that’s been around for thousands of years, but it’s more closely related to geometry than calculus.
Triangles are the subject matter of trigonometry and their relationships to each other. It is part of calculus, but it is not the same thing as calculus.
Calculus is a branch of mathematics that deals with limits and infinitesimals, functions, derivatives, integrals, and many other things. Calculus focuses on how fast or slow something changes, while trigonometry focuses on how much change there is over some time.
Both disciplines are important in understanding the world around us and how it works.
Is It Better To Take Pre-Calc Or Calculus?
The answer depends on what you want to do with your degree and how much time you want to spend in school.
If you’re planning on taking Calc 1 and Calc 2, then Pre-Calc is probably the way to go. Suppose you plan on taking just one semester of calculus (like many students majoring in a science or engineering field). In that case, it’s probably not worth taking two semesters of pre-calculus just so that you can take Calc 1 and 2.
But if you want to be a math major or an engineer, pre-calculus will give you a solid foundation for whatever other classes you take.
What Math Is Higher Than Pre-Calculus?
Higher math is just a classification of math classes with more difficult prerequisites and challenging content.
Several different math classes are higher than pre-calculus, depending on what you want to do with your degree.
The most common is calculus, a class that prepares you for many different math, science, and engineering careers. Other courses include linear algebra, abstract algebra, and discrete mathematics.
What Comes After Calculus?
It’s a common misconception that after calculus comes differential equations. The answer is much more complex; several different branches of mathematics could come after calculus, depending on your interests.
Some people choose to go into applied mathematics or mathematical physics, which involves studying real-world problems using math tools. Others may study pure mathematics, which studies abstract concepts without regard for how they might be applied in the real world.
Finally, some students pursue a second degree in an entirely different field.
Bottomline
- Calculus and pre-calculus are two math classes students often take during high school.
- Calculus focuses on more advanced topics, while pre-calculus focuses on the basics of algebra and trigonometry.
- Calculus studies a wide range of topics, such as limits, derivatives, integrals, infinite series, and applications to business and science.
- Pre-calculus focuses primarily on algebraic expressions, functions, graphs and their transformations, trigonometric identities, etc.
- Pre-calculus is usually taught in high school in preparation for calculus.
- Pre-calculus can be taken by students who have completed Algebra 1 or 2 and Geometry in high school before starting college; however, it’s not required for college admission.
- Calculus is typically taken after completing pre-calculus and trigonometry courses; however, it can be taken as early as freshman year if students meet specific prerequisites, such as a strong GPA.