Chapters

- 01. Calculus
- 02. Differentiation
- 03. Mechanics

Studying mathematics will help you develop a wide range of skills that will come in handy once you start searching for a job or in your day to day life. For example, logical thinking, decision-making, and problem-solving are only a few of the skills you’ll acquire in your math class.

If you are considering a career in engineering, technology, economy, or finance, math is a key subject that you’ll be required to take. And some of the jobs that are directly related to math are accounting, systems developer, math teacher, or investment analysis. For all of these, you’ll need to learn basic math concepts, which we will review below.

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**Solving AP Math Problems: AP Math** Themes

The AP Math syllabus covers a variety of topics that are important for your education, but in this article, we will cover those themes that are gateways to other important areas of studies within mathematics, and provide you with tools, resources, and strategies that can come in handy throughout your school years and professional career.

While many won't utilize all of the particular resources outlined in this article past June (aka past the end of the school year), some subjects are relatable and can be alluded to in numerous parts of mathematical, technological, and scientific jobs, and may even prove helpful in different industries as well.

**Help For Math Students Solving Math Problems**

Keep in mind that the process of solving math problems relies on your ability to complete a certain number of steps correctly to reach the solutions and correct answers. Therefore, it is key that you not only learn how to interpret the questions and problems correctly but to become a master at finding solutions to these questions and problems following each step you are taught in class.

The way to get a good grade is with dedicated time outside of school to practice, looking back into your textbooks, reading through all sorts of possible answers to different questions, and perhaps looking over a previous test to spot mistakes you’ve made. But, as already mentioned, practice is key and will ultimately help you get a good grade.

You must have noticed by now that students get points by showing the work and writing down all the equations and formulas needed to arrive at the correct answer to a question. Showing the work is key, even when you made a mistake and didn’t get the correct answer, you still get some points added to your final grade if you show each step you took. Showing the correct use of the methods to reach solutions to a question will always award you some points.

For instance, imagine student A and B both got an incorrect answer to a problem or question but student A marked some points and student B didn’t. This means that even though both students got the question wrong, student A wrote all of the problem-solving processes down, contrary to student B.

This is why you can’t drop the last two years of learned methods and processes at the moment of an exam or test, make sure you have a clear understanding of each step and that you display this knowledge while being tested, this is key. Half of the grade (sometimes even more) comes from the process, and a small percentage comes from correct answers.

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**A Closer Look At Math Themes On An AP Math Class **

## Calculus

The word *calculus *comes from Latin, originally meaning “small pebble” and it's the study of continuous change. This branch of math has two main subtopics: Differential Calculus and Integral Calculus.

Differential calculus studies the rates of change, curves, and slopes, and integral calculus focuses on the accumulation of quantities and the spaces under and between curves.

Therefore, these two branches can be considered as opposites but related by the fundamental theorem of calculus.

Isaac Newton and Gott-fried Wilhelm Leibniz are known as the fathers of modern calculus. The mathematical theories they each developed are key in the modern world and are now being used by different fields, some of which are Sciences, Geometry, Algebra, Economics, and Engineering, to name a few. This proves that this branch opens the way to other, highly advanced areas of mathematics.

Here are the individual principles of Calculus:

- Limits and Infinitesimals
- Differential Calculus
- Leibniz Notation
- Integral Calculus
- Fundamental Theorem.

As mentioned above, these principles are applied to many subjects aside from math. The perfect example of this is Physics, which makes particular use of this branch in maths, but also these principles are applied in Computer Science, Statistics, Geometry, Algebra Business, Economics, Engineering, and Medicine. This is why the concepts are so broad and applicable to many areas of study, they are universal!

## Differentiation

According to khana.org Differentiation is the process of finding the derivative, or rate of change, of a function. The objective is to find the rate of change of velocity concerning time (i.e. acceleration) or in other words, the rate of change of ‘x’ concerning ‘y’ on a graph (i.e. the gradient of the curve).

Ultimately, on an exam, you’re going to be faced with advanced problems, questions, and equations that are designed for you to show everything you’ve been learning throughout the school year, September through June.

Differentiation is part of the AP Math curriculum, which means that your teacher will dictate a few lessons about its basic rules. You’ll be learning how to solve mathematical equations, something that is hard to learn by just reading books, so appreciate your teacher and dedicate your time to understand everything they are teaching you.

For example, you’ll be taught that:

If y = a function of x (an expression containing x's and numbers), then the derivative of y concerning x is written dy/dx.

This rule is not the only thing you’ll be learning throughout this advanced course. You will also learn about Differentiating x to the power of something, bringing the power down to in front of the x, and afterward decreasing the power by one. If this is too wordy, don’t worry, you’ll have time to understand and practice how to properly solve a mathematical equation or problem.

Students are also going to learn about Notation, which is the method used to write a derivative. Plus, other basic themes under the Explicit Differential umbrella are the constant rule, the constant multiple rules, the sum rule, and the difference rule.

As it was explained previously, Differentiation studies curves and gradients, consequently, you are going to learn how to Differentiate the equation of a curve, finding a formula for its gradient.

If you feel a little intimidated by the things just mentioned, trust that your teacher is going to be able to explain the process in ways that are made easy to understand. Keep in mind that you will find some free time before the final exam in June, just be sure to use that free time wisely to understand all the strategies, prepare and practice how to solve an equation properly. It’s all about finding solutions.

Learn about the rules of logarithm here.

## Mechanics

Finally, Mechanics is a part of the AP Math syllabus. You’ll be learning about Acceleration, Newton's Laws, Vectors, Impulse and Momentum, Projectiles, Centre of Mass, and much, much more. An exam will most likely include questions or perhaps a problem on any of these topics, so be prepared.

The Mechanics module of the course is vital for you to get a good grade but also if you are interested in pursuing a career in the engineering industry, as you’ll learn the fundamentals of Mechanics principles. But don’t take our word for it, if you are curious a quick search will clear out your doubts.

If you are a little intimidated by it, reading about the subject during your free time is going to give you a head start.

Anyhow, if you are a car enthusiast, Mechanics will provide you with fascinating information, the equations and functions can be extremely useful to many, with a range of transferable skills on offer. For instance, the study of gravity causing acceleration is linked to Physics courses and is important to scientists looking at gravitational acceleration at different points on Earth.

The aim of this module is to ‘up-skill’ students within the mechanical field and allow them to solve or find solutions to real-world problems. When June comes around, you will have the knowledge and resources to apply how math and physics principles allow engineers to innovate and design. But don’t take our word for it, go ahead and talk to any engineer in your family, they will confirm!

**Sound Challenging? Don't Worry, You're Doing Great!**

It is practically impossible to learn about high-level math functions in a quick article like this, but our goal is for you to have a clear overview of some of the themes you’ll cover in class so that you are prepared for the level of complexity you’ll face in an AP Math class.

If maths is a course you are having trouble understanding, remember that you’re not alone, it is perfectly normal to be intimidated by a course’s syllabus and many people feel daunted by numbers. If you need a little extra effort you can always solve this problem by finding support in hiring a private tutor. They can provide you with several strategies and resources to ace the June test. You will just have to invest some of your free time into private lessons time.

AP Math is no longer part of your compulsory education (is this true for the US?), so all the things you are learning are already adding noteworthy skills to your resume. Keep in mind that even as a highschooler, the knowledge you’ll acquire in AP Math will provide you with skills that you will find useful throughout your college and professional career.

And remember that the syllabus for AP Math has changed and become more advanced throughout the years, and you are now part of the generation that educates more skilled mathematicians than before.

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