# Mathematics at Outwood Academy Hemsworth

## Course description

Mathematics involves the evolution of the theory to devise techniques to solve numerical problems. the subject is correctly seen as challenging and rewarding. At A Level the subject is split into pure and applied mathematics modules.

## Course content

** Pure Core 1**

Basic Algebra - surds, solving quadratic equations, inequalities and simultaneous equations.

Polynomials - the factor theorem, the remainder theorem, algebraic division, translation of curves.

Co-ordinate Geometry - equations of straight lines and circles including mid-points, gradients and tangents.

Differentiation - differentiating polynomials, tangents and normals to curves and stationary points.

Integration - definite integrals, area under a curve.

** Pure Core 2**

Transformation of Functions - translations, reflections and stretch transformations.

Sequences and Series - sigma notation, arithmetic and geometric progressions, infinite geometric progressions and the binomial expansion.

Trigonometry - sine and cosine rules, areas of a triangle, radian measure and trigonometric equations.

Indices and Logs - negative and fractional indices, solving equations involving logs and the graph of y = a x.

Further Differentiation - sum and difference of two functions, second derivative, stationary points and increasing and decreasing functions.

Further Integration - the trapezium rule, further area under a curve.

**Pure Core 3 **

Functions - many-one and one-one functions, the range of a function, inverse functions.

Transforming Graphs - effect of translation, stretch, reflection on an equation and combined transformations.

Trigonometry - inverse circular functions, sec, cosec and cot, solving trigonometric equations and transforming graphs.

Natural logs and e x - 1n notation, manipulating logs and solving equations using logs.

Differentiation - exponential functions, derivative of 1n x, a quotient and trigonometric ratios.

Integration - integrating e x, by substitution and by parts including the use of the chain rule.

Solids of revolution - revolutions about the x-axis and the y-axis.

Numerical methods - the mid-ordinate rule, Simpson`s Rule.

Proof - disproof, direct proof and proof by contradiction.

**Pure Core 4**

Rational expression - simplifying, using the remainder theorem, further division and partial fractions.

Parametric equations - converting between parametric and cartesian equations, circles and ellipse.

The Binomial Theorem - extending into negative and fractional indices, using partial fractions to obtain expansions.

Trigonometric Formulae - addition formulae, solution of equations.

Differential equations - forming a differential equation, separating the variables, exponential growth and decay.

Differentiation - implicit differentiation.

Integration - using partial fractions, definite integrals, using trig identities.

Vectors - vectors in 2D and 3D, vector equation of a line, intersecting lines, angles between lines, shortest distance between a line and a point.

**Decision Mathematics**

Algorithms - sorting algorithms, flow diagrams, trace tables.

Graphs and networks.

Minimum connector problems - Prim`s algorithm, Kruskal`s algorithm.

Shortest path problems - Dijkstra`s algorithm.

Matching - bipartite graphs, alternating paths, matching augmentation algorithm.

Route inspection - Chinese Postman algorithm.

The travelling salesperson problem - lower and upper bounds, nearest neighbour algorithm.

Linear programming - constraints, objective lines, feasible regions.

**Statistics 1 (OPTION 1) **

Collecting and processing data - sampling.

Variance and standard deviation - measures of spread, scaling, frequency distributions.

Probability - outcomes and events, tree diagrams, conditional probability.

Binomial distribution - Pascal`s triangle, combinations, cumulative binomial tables.

Normal distribution - proportions, the normal curve, using tables.

Estimation - sampling, distribution of the mean, central limit theorem.

Confidence intervals.

Linear regression - least squares, scaling, residuals.

Correlation - measuring correlation, scaling, interpretation.

**Mechanics 1 (OPTION 2) **

Kinematics in 1D - velocity and displacement, graphs of motion, area under a velocity-time graph, constant acceleration questions.

Kinematics in 2D - resultant displacement, position vectors, velocity and acceleration in 2D.

Forces - forces as vectors, resolving forces, weight, tension and thrust, friction.

Momentum - mass and momentum, conservation of momentum.

Newton`s Laws of Motion - force, mass and acceleration, solving problems in 1D, vertical motion, resolving forces, inclined surfaces.

Projectiles - vertical motion under gravity and motion

## Entry requirements

Candidates should hold a minimum of 5A*-C GCSE grades (or the new Grades 4 - 9), in addition candidates should hold a grade A (Grade 7) or higher in mathematics. This is a 2 year full time course and candidates will be expected to complete the full course.

## Assessment

Pure Core 1 Module: 33% of AS - 1 hour 30 minute examination.

Pure Core 2 Module: 33% of AS - 1 hour 30 minute examination.

Option 1 - Decision Module: 33% of AS - 1 hour 30 minute examination.

Option 2 - Mechanics 1 Module: 33% of AS - 1 hour examination + 1 coursework task.

Pure Core 3 Module: 33% of A2 - 1 hour 30 minute examination.

Pure Core 4 Module: 33% of A2 - 1 hour 30 minute examination.

Statistics 1 Module: 33% of A2 - 1 hour 30 minute examination.

## Financial information

No compulsory examination, tuition or material fees will be charged. It is essential however, that each student owns a scientific calculator in order to access the materials on offer.

## Future opportunities

Many students go on to take higher education courses making full use of `A` Level Maths and the skills developed whilst on the course.

A wide range of options including Medicine, Engineering, Law, Business, Social and Political Sciences, Natural Sciences and of course Mathematics itself.

## Further information

Homework is an essential part of the learning process and as such will be set by each of the three teachers every week. Support is given for the completion of homework, coursework and revision purposes. Whilst optional, all teachers encourage all students
to attend revision sessions in order to improve their skills base.

The Maths Faculty also have there own website where you can access the Specifications for this course. It is constantly being updated with new worksheets and syllabuses that students can download.

View Maths Website: www.mathsfaculty.co.uk

## How to apply

You can apply for this course through UCAS Progress. Add this course to your favourites so you can start making an application.