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A level Mathematics Year 12 & 13

Specification

Edexcel - The specification and assessment structure can be found at the link: https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html

Methods of Teaching & Learning

In Mathematics you will learn predominately via a whole class interactive teaching style similar to that experienced at GCSE.  There will be an increased opportunity to share in discussion and present solutions. You will be taught by two teachers, with one concentrating on the pure/mechanics and the other on the pure/statistics.  The homework will be set frequently requiring a quick turn round to support learning ready for the next lesson.  Mathematics is expected to appear in only one block.  This means some setting can and will take place, enabling the teachers to pitch the teaching at the appropriate level.

Qualities and Qualifications Needed to Study Mathematics

It is expected that boys will have at least grade 6 and preferably 7 (if they have studied in a low set at GCSE then a strong commitment will need to have been demonstrated.)

Why Study Mathematics? 

Mathematics is of great value and interest in its own right; in addition, it supports many other areas of study at A Level and beyond; for example: Geography, Economics, Computing, Design and Technology, and the Sciences. It is also a subject which is greatly valued by employers. 

The Course

We will be following the A Level Mathematics course with the Edexcel board which leads to the following possible examinations.

Year 12 AS Level Mathematics

Paper 1  – 2 hour Pure Paper

Paper 2 – 1 hour Statistics and Mechanics paper

These examinations will only be taken in exceptional circumstances.

Year 13 A Level Mathematics

Paper 1 – 2 hour Pure Paper

Paper 2 – 2 hour Pure Paper

Paper 3 – 2 hour Statistics and Mechanics paper

There is a no opportunity to re-sit exams, as the AS and A level are completely independent qualifications

The Pure Mathematics contains all the methods and ideas that are essential for a wide range of applications. The Mechanics and Statistics modules cover the foundations of two important areas of application.

Students who have been taught in the top set in year 11 may wish to consider doing Mathematics and Further Mathematics.  Students who have been taught in the second set in year 11 may wish to consider doing Mathematics and AS Further Mathematics, the details for both courses follow.

A LEVEL FURTHER MATHEMATICS

Specification

Edexcel - The specification and assessment structure can be found at the link: https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html#tab-AlevelFurtherMathematics

Methods of Teaching & Learning

In Further Mathematics you will learn predominately via a whole class interactive teaching style similar to that experienced at GCSE.  There will be an increased opportunity to share in discussion and present solutions. You will be taught by three teachers, with two concentrating on the Pure and Decision and the other on the Mechanics and Statistics.  The homework will be set regularly and frequently requiring a quick turn round to support the students learning ready for the next lesson. Those interested in AS level Further Mathematics will be taught for 14 hours a fortnight and should be considered by students in set 1, 2 and 3 in year 11. Those interested in an A Level in Further Mathematics will be taught for 15 hours a fortnight for two years and should be considered by students in set 1 and the top end of set 2.

Qualities and Qualifications Needed to Study Further Mathematics

Pupils aiming for an 8 or 9 at GCSE with an interest in Mathematics or Science should seriously consider A Level or AS level Further Mathematics as one of their 3, 3 1/2 or 4 A Levels. If a student wishes to study the A Level in Further Mathematics and they are not in set 1 or 2 in year 11 then they would need to follow a catch up programme after completing their GCSE’s and before commencing the course.

Why Study Further Mathematics?

In addition to those already mentioned for Mathematics; Further Mathematics is for the ablest students aiming for the top; at school, university, and beyond. It is a means of standing out from the crowd when 40% of students taking A Level Mathematics, nationally, gain an A or an A* grade. In addition, it is essential for studying Mathematics or Computer Science at Oxbridge and a considerable advantage if applying for Natural Sciences or when applying to good Universities for any Mathematics rich course.

The Course

The course with the Edexcel board leads to the following examinations.

Year 13 AS Further Mathematics Exams

Paper 1 – 1 ½ hour Pure Paper.

Paper 2 – 1 ½ Applied Paper option in Mechanics.

Year 13 A level Further Mathematics

Paper 1 – 1 ½ hour Pure Paper.

Paper 2 – 1 ½ hour Pure Paper.

Paper 3 – 1 ½ hour option Paper (Mechanics).

Paper 4 – 1 ½ hour option Paper (Mechanics).

Below are some comments made by pupils at the end of their first term studying Further Mathematics.

“The course is difficult, but also enjoyable. I find the group makes a good working environment.”
“Not quite as difficult as I had expected.”
“I have found the work more challenging than Maths which has resulted in my having to spend more time on the work to grasp the concepts.”

Note: If you need further advice about the range of Mathematics courses available, Mr Brook or any other of the Mathematics staff will be pleased to help.

Year 12

  Topic Further details about the topic Skills
Autumn Term
1
Ch1: Algebraic Expressions

Ch2: Quadratics

Ch3: Equations and Inequalities

Ch4: Graphs and Transformations

Ch5: Straight line Graphs
Ch1: Index Laws, Expanding brackets, Factorising, Surds, Rationalising Denominators

Ch2: Solving Quadratics, Completing the Square, Functions, Graphs, The Discriminant, Modelling

Ch3: Linear Simultaneous Equations, Quadratic Simultaneous Equations, Graphs, Linear and Quadratic inequalities, Graphs of inequalities

Ch4: Cubic, Quadratic and Reciprocal Graphs, points of intersection, translating graphs, stretching graphs, Transforming functions.

Ch5: Equation of a straight line, parallel and perpendicular lines, length and area, modelling with straight lines.

 

2

Ch6: Circles

Ch7: Algebraic Methods

Ch8: The Binomial expansion

Ch9: Trigonometric ratios

Ch10: Trigonometric identities and equations

Ch6: Midpoints and perpendicular bisectors, Equation of a circle, Intersection of straight lines and circles, Tangent and Chords. Circles and Triangles.

Ch7: Algebraic fractions, Dividing polynomials, The Factor Theorem, Proof.

Ch8: Pascal’s Triangle, Factorial notation, The Binomial expansion, Binomial estimation.

Ch9: The Cosine rule, Sine Rule, Area of a Triangle, Solving problems, Graphs of Trigonometric functions, Transforming Trigonometric graphs.

Ch10: Angles in four quadrants, Exact Trigonometric ratios, , Trigonometric identities, Solving trigonometric equations.

 
Spring Term
1

Ch11: Vectors

Ch12: Differentiation

Ch13: Integration

Ch14: Exponentials and Logarithms

Ch11: Vectors, Representing Vectors, Magnitude and direction, Position Vectors, Solving Geometric problems, Modelling with Vectors.

Ch12 Gradients of Curves, Finding the derivative, differentiating quadratics, Differentiating functions with more than one term, Gradients, Tangents, Normals, increasing and Decreasing functions, Stationary points, Modelling with differentiation

Ch13: Indefinite integrating, Finding functions, Definite integrals, Area under a curve, Areas between curves and lines.

Ch14: Exponential function, Exponential modelling, Logarithms, Laws of logarithms, solving equations using logarithms, working with Natural Logarithms, Logarithms and non-linear data.

 
2

AS Applied

Ch1: Data Collection

Ch2: Measures of Location and Spread

Ch3 Representations of Data

Ch4: Correlation

Ch5: Probability

Ch6: Statistical distributions

Ch7: Hypothesis Testing

Ch8: Modelling in Mechanics

Ch9: Constant Acceleration

Ch10: Forces and Motion

Ch11: Variable acceleration

Ch1: Populations and samples. Sampling, Non-Random samples, Types of Data, The large Data set.

Ch2: Measures of central tendency, Other measures of location, Measures of spread, Variance and Standard deviation, coding.

Ch3: Outliers, Box plots, Cumulative frequency, Histograms, comparing data.

Ch4: Correlation, Linear Regression

Ch5: Calculating Probabilities, Venn Diagrams, Mutually exclusive and independent events, Tree diagrams.

Ch6: Probability distributions, The binomial Distribution, Cumulative probabilities

Ch7: Hypothesis testing, Finding critical values, One-tailed tests, Two-tailed tests.

Ch8: Constructing a model, Quantities and units, working with vectors.

Ch9: Displacement time graphs, Velocity, time graphs, Constant Acceleration formulae, Motion under gravity

Ch 10: Force Diagram, Forces and acceleration, Motion in 2D, Connected particles, Pulleys.

Ch11: Function of time, using differentiation/max and Min problems, Using integration.

 

Summer Term
1

A2 Applied

Ch1: Regression Correlation and hypothesis testing

Ch2: Conditional probability

Ch3: The normal Distribution

Ch4: Moments

Ch5: Forces and friction

Ch6: Projectiles

Ch7: Applications of Forces

Ch8: Further Kinematics

Ch1: Exponential Models, Measuring correlation, Hypothesis testing

Ch2: Set Notation, Conditional probability, Venn diagrams, Tree Diagrams

Ch3: The Normal Distribution, The inverse Normal distribution function, The Standardised Normal distribution, Finding μ and σ, Approximating a Binomial distribution, Hypothesis testing with the normal distribution

Ch4: Moments, Equilibrium, Centres of Mass, tilting.

Ch5: Inclined planes, Friction

Ch6: Horizontal and vertical components, Projection at an angle, Projectile motion formulae.

Ch7: Static particles, modelling with statics, Friction and Statics, Dynamics and inclined planes, connected particles.

Ch8: Vectors and kinematics, Vectors and projectiles, Variable acceleration in one and two dimensions

 

2

Revision

A2 Pure

Ch1 Algebraic methods

Ch5 Radians

End of year Exam

Ch1: Proof by contradiction, Algebraic fractions, Partial fractions, Algebraic division

Ch5: Radian Measure, Arc Length, Area of Segments and sectors, Solving Trigonometric equations, Small angle approximations

 

Year 13

  Topic Further details about the topic Skills
Autumn Term
1

Ch2 Functions and Graphs

Ch3 Sequences and Series

Ch4 Binomial Expansion

Ch6 Trigonometric Functions

Ch7 Trigonometry and modelling

Ch2: Modulus Functions, Composite Functions, Inverse Functions, combining transformations, Solving modulus problems.

Ch3: Arithmetic Sequences and Series, Geometric sequences and series, Sum to infinity, Sigma notation, Recurrence relations, Modelling with series

Ch4: Binomial expansions, Using partial fractions

Ch6: Sec, Cosec and Cot Graphs, Trigonometric Identities, Inverse Trigonometric functions.

Ch7: Addition formulae, Double angle formulae, Solving trigonometric equations, Proving Trigonometric identities, Modelling with Trigonometric  functions.

 
2

Ch8 Parametric equations

Ch9 Differentiation

Ch10 Numerical methods

Ch11 Integration

Ch12 Vectors

Ch8: Parametric equations, curve sketching, points of intersection, modelling.

Ch9: Differentiating Sin x, Cos x, Exponentials and logarithms. The Chain rule, the product rule, the Quotient Rule, Differentiating Trigonometric functions, parametric differentiation, Implicit differentiation, Using second derivatives, Rates of change.

Ch10: Locating roots, Iteration, The Newton Raphson method, Applications to modelling.

Ch11: Integrating standard functions, using trigonometric identities, reverse chain rule, substitution, Parts, Partial fractions. Trapezium Rule, differential equations.

Ch12: 3D coordinates, Vectors in 3D, solving geometric problems, applications to mechanics.

 
Spring Term
1

Finish syllabus if necessary and then revise

Revision of skills for Mock Exams

 

2

Revision

Past paper practice  
Summer Term
1

Revision

Past paper practice

 

Assessments

Resources Topic Type of assessment
CAT 1 All content taught up to this point Past paper questions
CAT 2

All content taught up to this point

Past paper questions
CAT 3 All content taught up to this point

Past paper questions

CAT 4

All content taught up to this point

Past paper questions
CAT 5

All content taught up to this point

Mock Examination

Main Resources

Resource Details Term
Set texts
EDEXCEL Mathematics for year 1 and AS
EDEXCEL Mathematics for year 2 and A level
(Hodder)
 

A2 Core for Edexcel

Edexcel AS and Modular Maths S1

 

Support materials

Please see link on Maths home page

 
Recommended Websites

Website links

All
Equipment Pen, pencil, full geometry set and Casio scientific calculator All

Enrichment opportunities

Activity Day and time or term
Maths Challengers Club Friday lunchtime
Senior Maths Challenge November
Senior House Maths Challenge October
Senior Team Maths Challenge November
Mentoring Year 11 students By invitation from September to May

Where Next