Chapters

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

By studying Maths, you can first of all expect to **develop a range of key skills** that are sought after by employers and that will also help you throughout your day to day life. For example, Maths encourages **logical thinking, decision-making and problem-solving**, all of which are vital to survive in modern society.

To add to that, Maths is a **key area of study** for those seeking a career in the **Finance, Engineering and Information Technology industries**. Just some jobs that are directly related to a Maths qualification are Chartered Accountant, Investment Analyst, Systems Developer and Secondary School Teacher of Maths, all of which include **making use of Maths concepts** like those we will be looking at below.

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### Solving A Level Maths Problems: The Overarching Themes Of A Level Maths

The AQA A Level Mathematics (7357), which was **taught from September 2017**, with the first exams being sat in 2018 onwards, covers a broad range of Maths themes.

Some of this content includes **Trigonometry, Sequences and series, Exponentials and **logarithms**, Differentiation, Integration, Vectors, Statistical hypothesis testing, Kinematics as well as Algebra and functions**.

While all of the content covered is in the syllabus for a reason, there are some **overarching themes **that we will focus on below which are almost like **gateways to other areas of studies within Mathematics**, as well as tools that can be implemented in your **professional career**.

While many will not use all, if any, of the specific skills outlined in this article, they are nonetheless studies that are **relatable** and can be **referred to in many aspects of mathematical, technological and scientific roles**, and may even prove useful in other industries too.

### Maths Help For Students With Regards to Solving Maths Problems

Remember that **solving Maths problems **is reliant on completing a number of steps correctly to **reach a solution**. As such, it is important that you not only learn how to do the **correct working out processes**, but that you also practice putting them **on show.**

During exams, pupils will be given marks not only for getting a correct answer but also for **backing this up with a trail** of written sums, equations or the like. Consequently, even if you make a mistake down the line, you could still get awarded some **points for the method you used**.

This means that even if you get a wrong answer, you could still make up some points in comparison to someone who did get the right answer but didn’t note down their working out.

So, don’t let two years of **studying tools and methods **go to waste, make sure you brush up on the ways of solving problems and display this knowledge in your exams!

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### A Closer Look At The Maths Themes Featured On An A Level Course

## Calculus

Calculus, which takes its name from the Latin word for ‘small pebble’, is a Maths term that describes **the study of continuous change**. There are two principal branches of Calculus: Differential Calculus and Integral Calculus**.**

While the first is concerned with **rates of change and curves and slopes**, the latter is focused on the **accumulation of quantities and the spaces under and between curves**.

As such, they can be as somewhat opposites of one another yet the two are related by the **fundamental theorem of calculus**.

Modern Calculus was thought to have been developed by Isaac Newton and Gottfried Wilhelm Leibniz in the **17th century**. The mathematical theory has since been adopted by various subject fields, including the **Sciences, Engineering, and Economics**. Calculus itself acts as a gateway to other, more advanced areas of mathematics.

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

As defined by S-cool.co.uk, Differentiation is 'a tool of mathematics that is primarily used for calculating rates of change'. The tool thus allows us to find the **rate of change of velocity with respect to time** (i.e. acceleration) as well as the **rate of change of x with respect to 'y' on a graph** (i.e. the gradient of the curve).

As part of your A Level course, your teacher will no doubt 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.**

In addition to the above simple rule, you will almost certainly learn about **Differentiating x to the power of something**, bringing the power down to in front of the x and then reducing the power by one, along with studying **Notation**, the ways of writing the derivative.

Along with this power rule, other underlying themes within the Explicit Differential umbrella are the **constant rule, the constant multiple rule, the sum rule and the difference rule**.

Differentiation is, as stated above, concerned with **curves and gradients, **therefore, using all of the above knowledge, you will ultimately be able to **Differentiate the equation of a curve**, finding a formula for its gradient.

If all of this sounds a bit perplexing, rest assured that your Maths teacher will be able to explain the processes and functions so that they come to you easily.

## Mechanics

Finally, this **now-compulsory module **will make its appearance during your A Level Maths course, shedding light on **Acceleration, Newton's Laws, Vectors, Impulse and Momentum, Projectiles, Centre of Mass **and much, much more.

The module is absolutely vital for anyone with an interest in pursuing **a career in the engineering industry**, as it will teach you the fundamentals of Mechanics principles**.**

Fascinating content for fast car enthusiasts too, the **equations and functions** can be extremely useful to many, with a range of transferable skills on offer. For example, **the study of acceleration caused by gravity** is also linked to Physics courses and is relevant to scientists looking at gravitational acceleration at different points on Earth too.

The aim of this module is to ‘**up-skill’ students** within the mechanical field, enabling them to **solve real-world problems.** At the end of the module, you should have the confidence to apply how the maths and physics principles allow engineers to innovate and design.

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

While it is impossible to educate you on advanced Maths functions in a few short paragraphs, we hope that you now have **a better overview of some of the themes** covered, and can appreciate the level of detail you will be exposed to during your A Level Maths course.

Take comfort from the fact that **many people find Maths challenging** as a subject, and that it is perfectly normal for you to need a little time or extra tuition to help you along the way.

Remember also that the content you will be learning at A Level is no longer part of your **compulsory education**, so all the things you are learning are already **adding noteworthy skills to your resume**. Just think, even as a teenager you will have a higher level of knowledge and skill in this area than most adults who are much older and wiser than you!

As a matter of fact, adults who once passed their Maths qualifications back in the day would probably struggle to complete the content you are studying now, which shows that you can very feel **proud of your achievements** to date.

While this might be down to them not using the acquired skills enough and thus losing or forgetting them, it could also be because **the Maths syllabus has grown more advanced over the years**, producing **more talented and skilled mathematicians** than ever before.

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