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 (Statistics).
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 | 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 |
