Please use **Google Chrome** or **Mozilla FireFox** to see the animations properly.

The specification of A-Level has changed dramatically: first of all, students who sit for A-Level as from 2017 onwards, are going to learn pure mathematics and combination of statistics and mechanics ; it used to be two core modules and statistics or mechanics.

Students have to sit for two three papers to earn their grades at the end of two years. There will be internal exams after the first year, at AS, mainly for assessment and checking the eligibility for the second year.

Edexcel, a major examination board in the UK, has updated its specification as follows:

According to the latest specification, the new topics in the **Statistics and Mechanics** are as follows for the first year:

- Statistical sampling - statistics
- Data presentation and interpretation - statistics
- Probability - statistics
- Statistical distributions - statistics
- Statistical hypothesis testing - statistics
- Quantities and units in mechanics - mechanics
- Kinematics - mechanics
- Forces and Newton's Laws - mechanics
- Moments

Among the new topics are probability distribution and hypothesis testing.

The binomial distribution, modelled in the following animation, has been added to this module.

According to the latest specification, the new topics in the **Pure Mathematics** are as follows:

- Proof
- Algebra and Functions
- Coordinate geometry in the (x, y) plane
- Sequences and series
- Trigonometry
- Exponentials and logarithms
- Differentiation
- Integration
- Numerical methods
- Vectors

In pure mathematics, a significant emphasis has been made on **mathematical modelling:** it's a step in the right direction, as it gives students an opportunity to see how maths is used in real life, apart from day-to-day mundane tasks.

For instance, modelling by quadratic equations has been introduced in chapter 2 in Pure Mathematics text book - how the motion of a ball under gravity can be modelled by a quadratic equation.

The following animation shows how it is done with the aid of a simple graphic programme - and, of course little imagination.

In this case, a ball is thrown upwards from a tower of height, 80m. The change in height is modelled and calculated automatically against time, until it hits the ground.

Mathematical modelling has been introduced in a few chapters - a clean, welcoming break with tradition, indeed.

Since the syllabus has changed completely, the old, existing text books have already become irrelevant. In statistics, a heavy emphasis has been placed on data handling with an extensive data set provided by Edexcel for analysing purposes, perhaps, in the light of explosive expansion of data science.

The following books and the graphical calculator are highly recommended for Pure Mathematics and the combination of Statistics and Mechanics for the first year - at AS Level; the graphics calculator will help the students, especially in newly-introduced mathematical modelling.

At the end of two-year course, you will be tested by three exams with 2-hour duration, each:

- Pure Mathematics 1 - earning 33.33% of the total mark
- Pure Mathematics 2 - earning 33.33% of the total mark
- Statistics and Mechanics - earning 33.33% of the total mark

Calculators are allowed for all three exams.

This is a **calculator** that can be recommended for this course:

It's sleek in design, easy to use and light. Above all, it has a relatively-large display panel for viewing - a must for graphical calculator.

**Ad:** The author of this site offers fully interactive tutorial on differentiation

Most of the contents of the new spec can be complemented by the extensive use of **Geogebra**, an open-source graphic app. This site offers a significant list of interactive animation for that. Here is a popular one:

**Additional Helpful Resources**

This is a **book** that can be recommended for this course, which will complement your understanding with additional high quality problems to broaden your understanding:

It deals with almost all major sections with proof and plenty of questions for practising.

Here is a good collection of tutorials, animations and worksheets on this site. Most of they are fully interactive, full of worked examples and offer plenty of questions for practice.

Tutorials for A-Level
Quadratic Equations - interactive
Quadratic Equations - Word Problems
Transformations of Graphs
Graph Creator - interactive
Venn Diagrams - interactive
The Binomial Expansion - interactive
Triangular Square Numbers - interactive
Even and Odd functions
Iteration
Basic Differentiation
Basic Integration
Parametric Equations and Integration
How to use Casio calculator for statistics
Integration by Observation
Volume of Revolution - Integration
Trapezium Rule - Integration
Differential Equations - Integration
Mathematical proof
Standard Deviation
Cumulative Frequency - Quartiles, Median, IQR and box plots
Histograms
Stem and Leaf diagrams
Probability
Linear Interpolation
Probability - tree diagrams
Binomial Distribution
Poisson Distribution
Mechanics (Kinematics)
Mechanics (Dynamics - pulleys)
Mechanics (Motion-time graphs)
Mechanics - Momentum
Decision Maths - Chinese Postman Problem
The Dot Product - scalar product
Exponential Functions and Logarithms
Complex Numbers - Further Maths
Projectile Motion
Polynomial Roots and coefficients
Modelling with Quadratics
Vector Animations
The Chain Rule
Edexcel Large Data Set Practice - fully interactive

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7^{th} edition in print.