# Videos

Choose from over 80 mathematical videos.

Our team of top teacher mathematicians have put together all the important topics and explain them with the types of examples that you would find in a normal textbook or exam.
• #### a cos x + b sin x = R cos(x - a)

a cos x + b sin x = R cos(x - a) . In this unit we explore how the sum of two trigonometric functions e.g. 3 cos x + 4 sin x, can be expressed as a single trigonometric function. Having the ability to do this enables us to solve trigonometric equations and find maximum and minimum values.
Length: 29 minutes
• #### Arithmetic and geometric progressions

Arithmetic and geometric progression. This unit introduces sequences and series, and gives some simple examples of each. It also explores particular types of sequence known as arithmetic progressions and geometric progressions, together with the corresponding series.
Length: 65 minutes
• #### Cartesian components of vectors

Cartesian components of vectors. Any vector may be expressed in Cartesian components by using unit vectors in the directions of the coordinate axes. These unit vectors in two dimensions and in three dimensions are described.
Length: 20 minutes
• #### Completing the Square - By Inspection

Quadratic expressions can be written in an equivalent form using the technique known as completing the square. This video explains the basic ideas behind completing the square and how to use the method to solve quadratic equations.
Length: 18 minutes
• #### Completing the Square - Maxima & Maxima

This video shows how to find the maximum or minimum values of quadratic functions by using the 'completing the square' technique.
Length: 19 minutes
• #### Composition of functions

Composition of functions. Complicated functions can be built up from simple functions by using the process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to decompose a function into two simpler functions.
Length: 11 minutes
• #### Conic Sections

Conic sections. Conic sections are the curves obtained when a cone is cut by a plane. The equation of one of these curves, the parabola, is found by using an alternative description in terms of points whose distances from a fixed point and a fixed line are equal.
Length: 36 minutes
• #### Decimals

This video looks at decimals, and how they are related to fractions. It covers multiplying and dividing by 10, rounding to given numbers of decimal places or significant figures and finally looks at irrational numbers.
Length: 44 minutes
• #### Differentiating logs and exponents

Differentiating logs and exponentials. This unit gives details of how logarithmic functions (ln x) and exponential functions (e^x) are differentiated.
Length: 26 minutes
• #### Differentiating Powers of x

Differentiating powers of x. If y=x^n then dy/dx = nx^n-1. This result is derived in this video and illustrated with several examples, including cases where n is negative, or is a fraction.
Length: 14 minutes