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Differentiation of Polynomials

Polynomials, as the term implies, contain multiple terms, added or subtracted together. In order to differentiate the polynomial, each term must be differentiated separately. Here we will look at differentiating …

Overview of Sin, Cos, and Tan Functions

Introduction Trigonometry is the study of triangles. In this article, we’ll focus on sin, cos, and tan which are the three trigonometric functions that specifically concern right-angled triangles. They are …

The Factor Theorem and Algebraic Division

In science you will often use algebra to solve problems. This article describes two important tools in algebra which are the factor theorem and algebraic division. The Factor Theorem The …

What are logarithms?

In science there are many situations where we have a graph that is of the following form rather than linear. In this article, logarithms will be introduced as a tool …

Problem solving solutions

The solutions for the questions in the previous step are below. Use these to check your method and your answers. Question 1 A ball is thrown straight up, from 2 …

Sine and cosine rules

Watch this video to revise the sine and cosine rules. It should also help to make sure you know how to find the area of a triangle using the alternate …

Introduction to the trigonometric functions

In this video, Dr Ria Symmonds explains the concept of the unit circle and how understanding this helps us to recognise and sketch graphs of the sine and cosine functions. …

Law of indices

In this video, foundation year teacher Christina Brady shares an explanation of the law of indices. Share in the comments below: Do you have any strategies for remembering the laws …

Well done!

Thank you for joining the course on Introduction to Mathematical Methods for University-Level Science. Through this course, you have worked to: – Improve confidence in your mathematical skills in preparation …

Integration by parts

Watch this video to understand integration by parts – a process that finds the integral of a product of functions. Share in the comments below: Create your own question with …

Calculating components of a vector

In this video, Dr Lisa Mott explains how to go about calculating the components of a vector. In the comments below: Give advice – how do you ensure that the …

Introduction to integration

Watch the video for an explanation of integration, with a problem to practise solving yourself at the end. Discuss in the comments below: How coud you use the reverse chain …

Area between curves

In this video, Dr Lisa Mott explains the method for finding the area between curves. Share in the comments below: Can you find the area bounded by the x-axis and …

Differentiation of polynomials and more

Watch this video for an explanation of how to differentiate polynomials and more… Extension question Once you’ve watched the video, try the question which is presented at the end. Share …