The Rules of Indices

\[ \begin{align*} a^m \times a^n & = a^{m+n} \\ \frac{a^m}{a^b} & = a^{m-n} \\ \left(a^m\right)^n & = a^{mn} \\ a^{\frac{1}{n}} & = \sqrt[n]{a} \\ a^{-n} & = \frac{1}{a^n} \end{align*} \]

Numbers

The study of numbers and their use in calculations is a foundation skill in Mathematics.

In GCSE, this involves topics such as the use of fractions, powers, approximation and standard form.

The demonstration shows the rules of indices.

Mathematics on this website is written in \( \LaTeX \) and rendered using MathJax.

Algebra

Algebra is the study of mathematical symbols and the rules for manipulating these symbols.

Proficiency in algebra is one of the most important skills for success in GCSE and A-level.

The Applet shows a graph of the function \( f(x) = ax^2+bx+c \).

An important GCSE result is that the solution to the general quadratic equation \( ax^2+bx+c=0 \) is

\[ x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a} \]

Geometry

Geography is the study of shapes and patterns.

The Applet shows tessellation (tiling) of quadrilaterals. Any quadrilateral can be tesselated. Try dragging the green circles to change the shape of the quadrilaterals.

This demonstration is produced by Geogebra a great free resource for illustrating Mathematical concepts

The Normal Density Function

Orange Orchid Picture
\[ f \left( x, \mu, \sigma \right) = \frac{1}{\sigma \sqrt{2\pi}} e ^ {-\frac{\left( x - \mu \right)^{2}}{2 \sigma^{2}}} \]

Statistics

Statistics is the science that deals with the collection, classification, analysis and interpretation of data.

The diagram shows the bell-shaped curve of the normal density function.

This function describes the probability distribution of the sum of a large sample of indepedent random variables.

Animate

Computing

Maths and Computing are heavily co-dependent. Mathematics underpins much of what can be done with Computing and Computing allows Mathematics to be implemented and displayed.

The animation illustrates a pictorial proof of the famous Pythagoras Formula for right-angled triangles:

\[ a^2 + b^2 = c^2 \]
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At Dalesworks tutoring, we believe that improvements in Mathematics come through practice, problem-solving and having fun, in a low pressure environment.

Tutoring sessions are tailored to meet the needs of each individual pupil and are designed to closely complement the Mathematics syllabus that the pupils are following at their school.

Tutoring Sessions

Mathematics tutoring sessions are available for North London pupils, aged 7 to 18. The sessions take place in a friendly home environment, which allows pupils to build their confidence and achieve top results in A-level, GCSE and 11+ entrance Exams.