Is calculus harder than algebra? (solved and explained)
Calculus is harder than algebra, it is an advanced level of math that students study in high school and finish in college. While algebra is taught early from elementary school to college. So algebra is the base of calculus, without algebra calculus would not be existing.
algebra is the math that your dad or mam can use in the house, meaning simple arithmetic operations like subtraction, addition, and multiplication are algebra.
So the first foundation that students study is algebra then calculus came afterward. So if you don’t understand algebra you will suck in calculus without any doubt.
calculus has advanced and complex topics that a lot of students suffer on like:
- limits
- derivatives
- integrals
Most of the students suffer in these subjects because they have a weak foundation in algebra. As a result, force them to restudy the basics of algebra again.
what do students study in algebra?
we’re going to list the top interesting subjects that students study in algebra, we’re going to put them in order so you can follow and not lose the steps.
Study the basics of arithmetics
there are 4 mathematics operations that students base one staying algebra, which we use every day in our lives, including:
- addition
- multiplication
- subtraction
- division
Normally in algebra beginner classes students don’t face any problems with addition and subtractions. But, with multiplication and division, there is a challenge that everyone should break which is memorizing the multiplication tables. So finally to not sucking in these kinds of following operations like in the example below.
8×9
8×7
9/3
6/3
if you are stuck in table memorization you will surely suffer in the upcoming mathematics subjects or topics that were going to talk about and mention in the next paragraphs.
Factoring
The second thing that you should learn is factorization which is mean reducing and simplifying math numbers or equations. I will give one simple example in the line below.
The principal goal of factoring is to simplify mathematics complex equations, to operate on them easily without losing a lot of time and spending a lot of energy. For example
100 – 12 = 2 (50-6) = 88
Factoring is not also simple as you have seen in this example. but there is another example to see which is a little bit complicated.
X²-Y²+2(XY)²
X²(1- Y/X² + 2Y²)
ratios
Ratios or fractions are mathematical functions that have two parts nominator and denominators like in this example below:
5/4
5 is nomintor
4 is denominator
fractions or ratios are very interesting subjects in mathematics to learn about, in the image example below we will find the principal operations to make fractions.
In general, for fractions you have to be able to know how to:
- Add fractions
- Subtract fractions
- Multiply fractions
- Divide fractions
Learning these operations requires a lot of time and effort, but the most interesting thing is to have solid basics in the previous subjects that we mentioned before like factoring, multiplying, and dividing numbers.
First-degree equations
the first thing that you will be beginning with is learning first-degree equations. I’m going to solve one first degree equation to show you an example.
5x+4 = 10
5x = 10 – 4
5x = 6
x = 6/5
So as you can see first degree equations are simple to solve, you won’t stuck on them if you studied hard the arithmetics topics and all subjects we mentioned previously.
Second degree equaitons
Second-degree equations are written in this form below
ax² + bx +c =0
To solve second-degree equations you need to apply a different technic in this case, is a little bit completed compared to the first-degree equation. But if you followed well this video you will know how to do that.
Exponential functions
Exponential functions are functions that can be written in this form A², but I will let you this video to know more and in detail about exponential functions.
Logarithmic functions
System of linear equations
System of non-linear equations
Sequences
Functions and their graph
If you study this whole algebra program you will be normally good and able to study advanced math subjects like linear algebra that college students focus on, as well as calculus subjects that we will explain and talk about now in the next paragraph.
what do students study in calculus?
Normally what makes calculus harder than algebra, is firstly to be able to study calculus you need to have basics in algebra. So all the subjects that we mentioned above in the article.
But when we talk about calculus we talk about digesting and these 3 principal subjects that are:
- Limits
- Derivative
- Integrals
1 – limits
Limits are the first course that calculus students take and learn its basics, normally limits are functions that are written in this form below.
In this example of this function we say or read this function as the form below:
The limits of x square when X approaches 5,
It can be a little tricky to understand. But to keep things easier, in most cases limits functions where you will be applying replacement operations like in this case (replacing x² by 5² except in some cases where you should follow the specialized rule).
if you want to know more about limits you can watch this simplified video.
Normally limits are not hard or tough to understand, you just have to be good to differentiate between mathematics functions like polynomials, trigonometry exponential functions, and other functions.
2 – derivative
Derivatives are a little bit complicated subject in calculus that students should be working hard to understand. Derivatives require two important things:
Have solid Basics in algebra, especially factorization fractions
The second thing is memorization you would have a lot of rows you should memorize about derivatives.
We’re going to give a simple example of the derivative operations
This is was one of the most simple derivative questions that you would have, normally derivatives require memorizing rules like in this case as we have seen, But what makes them hard is sometimes you would have to the rebate some complex function which takes a lot of time and effort and even increase the ability to produce mistakes.
3 – Integral
But the hardest object that you will study and maybe face some problems on especially if you have weak basics in algebra is integrals. It needs to be good at this to previous calculus subjects including limits and derivatives and here is why.
Integral is the inverse operation of derivatives, meaning when you make a derivative of x² it will give you 2x. But when you make an integral of 2x you will go back and have x² in the result.
you will understand better the difference in this image below
So for sure if you are not good at derivatives you would suffer studying integrals. As a result, we recommend to take your time studying derivatives Before you take integral classes.
Conclusion
To be honest, calculus is harder than algebra is not a topic that you can digest easily it requires a double amount of work needed to put in algebra.
So as a student if you face some hardships in calculus this is noraml, you just have to push more and be more patient to learn the whole concept.
But if you still work hard and don’t get results, you will probably have a weak math foundation and should relearn math again.
you can read this article: 4 important steps to learn math from the ground up.
you can watch this pretty video talking about the difference between calculus and algebra.
