Teddington School Sixth Form

Transcription

1 Teddington School Sixth Form AS / A level Maths Induction and Key Course Materials

2 Introduction The Mathematics Department at Teddington School is delighted that you would like to continue your studies in mathematics by applying for A-Level at Teddington. This booklet is to help support you from the start of the course. It contains a description of topics you will be studying in year 12 and 13. There is also a pre-course Transition Booklet (available on the website) which must be completed over the Summer and which you will be expected to hand in in your first lesson back in September. Course: We study the Edexcel syllabus for Mathematics From September 2017 a new linear syllabus has been introduced for A level mathematics. This means that all your exams will be at the end of Year 13. You may sit an A/S exam in mathematics at the end of Year 12. This is a stand-alone qualification and is not treated as part of your A level. The assessment at the end of Year 13 will be in three exam papers: Paper 1: Pure Mathematics 33%, 2 hours, 100 marks Any pure content can be assessed on either paper Paper 2: Pure Mathematics 33%, 2 hours, 100 marks Paper 3: Statistics and Mechanics 33%, 2 hours, 100 marks Section A: Statistics (50 marks) Section B: Mechanics (50 marks) Calculator: The new A-level specification requires a calculator that can access probabilities from standard statistical distributions. This will almost certainly mean that you will need to buy a new calculator to study A- level Mathematics. It is not necessary to buy a graphical calculator. The Casio FX-991EX ClassWiz has all the functions you will need. Other suitable calculators may also become available over the next few months. As these calculators can be quite expensive please speak to us if you have any concerns about buying the correct calculator.

3 A level Maths Wider Reading You should start reading around the subject while you are studying to get a flavour of the wider world of maths. None of the books on the list below are textbooks and most are fairly light reading. We do not suggest that you read them all or that you limit yourself to books on the list. Copies of several of the titles listed below are in the main school library. If you are looking for something accessible, Alex Bellos and Ian Stewart have both written several books which are easy to get started with and do not assume any great mathematical knowledge. 1. Alex s Adventures in Numberland, Alex Bellos 2. Mathematics and the Imagination, Edward Kasner 3. The Music of the Primes, Marcus du Sautoy 4. The Simpsons and their Mathematical Secrets, Simon Singh 5. Mathematician s Delight, WW Sawyer 6. From Here to Infinity, Ian Stewart Equations that Changed the World, Ian Stewart 8. Fermat s Last Theorem, Simon Singh 9. A Short History of Nearly Everything, Bill Bryson (more science than maths) 10. The Hitchhiker s Guide to the Galaxy and the Restaurant at the End of the Universe, Douglas Adams (not really about maths at all but has some sideways glances at probability and numbers in restaurants and how they might be used to fly space ships...) If you come across any other books you particularly like, let us know! We look forward to welcoming you in September. The Mathematics Department.

4 Year 12: Pure Mathematics Algebra and Functions Algebraic expressions basic algebraic manipulation, indices and surds Quadratic functions factorising, solving, graphs and the discriminants Equations quadratic/linear simultaneous Inequalities linear and quadratic (including graphical solutions) Graphs cubic, quartic and reciprocal Transformations transforming graphs f(x) notation Coordinate Geometry in the (x, y) plane Straight-line graphs, parallel/perpendicular, length and area problems Circles equation of a circle, geometric problems on a grid Further Algebra Algebraic division, factor theorem and proof The binomial expansion Trigonometry Trigonometric ratios and graphs Trigonometric identities and equations Vectors (2D) Definitions, magnitude/direction, addition and scalar multiplication Position vectors, distance between two points, geometric problems Differentiation Definition, differentiating polynomials, second derivatives Gradients, tangents, normals, maxima and minima Integration Definition as opposite of differentiation, indefinite integrals of x n Definite integrals and areas under curves Exponentials and Logarithms: Exponential functions and natural logarithms

5 Statistics Statistical Sampling Introduction to sampling terminology; Advantages and disadvantages of sampling Understand and use sampling techniques; Compare sampling techniques in context Data Presentation and Interpretation Calculation and interpretation of measures of location; Calculation and interpretation of measures of variation; Understand and use coding Interpret diagrams for single-variable data; Interpret scatter diagrams and regression lines; Recognise and interpret outliers; Draw simple conclusions from statistical problems Probability Mutually exclusive events; Independent events Statistical Distributions:

6 Use discrete distributions to model real-world situations; Identify the discrete uniform distribution; Calculate probabilities using the binomial distribution (calculator use expected) Statistical hypothesis testing Language of hypothesis testing; Significance levels Carry out hypothesis tests involving the binomial distribution Mechanics / Quantities and units in Mechanics Introduction to mathematical modelling and standard S.I. units of length, time and mass Definitions of force, velocity, speed, acceleration and weight and displacement; Vector and scalar quantities Kinematics 1 (constant acceleration) Graphical representation of velocity, acceleration and displacement Motion in a straight line under constant acceleration; suvat formulae for constant acceleration; Vertical motion under gravity Forces & Newton s laws Newton s first law, force diagrams, equilibrium, introduction to i, j system Newton s second law, F = ma, connected particles (no resolving forces or use of F = μr); Newton s third law: equilibrium, problems involving smooth pulleys Kinematics 2 (variable acceleration) Variable force; Calculus to determine rates of change for kinematics Use of integration for kinematics problems i.e. r vd t, v adt

7 Year 13: Pure Mathematics Proof: Examples including proof by deduction* and proof by contradiction Algebraic and partial fractions Simplifying algebraic fractions Partial fractions Functions and modelling Modulus function Composite and inverse functions Transformations Modelling with functions, trigonometric, exponential and reciprocal functions Series and Sequences Arithmetic and geometric progressions (proofs of sum formulae ) Sigma notation Recurrence and iterations The Binomial Theorem Expanding (a + bx) n for rational n; knowledge of range of validity Expansion of functions by first using partial fractions Trigonometry Radians (exact values), arcs and sectors Small angles Secant, cosecant and cotangent (definitions, identities and graphs); Inverse trigonometrical functions; Inverse trigonometrical functions Compound* and double (and half) angle formulae (with geometric proofs) R cos (x ± α) or R sin (x ± α) Proving trigonometric identities Solving problems in context (e.g. mechanics) Parametric Equations Definition and converting between parametric and Cartesian forms Curve sketching and modelling Proof: Examples including proof by deduction* and proof by contradiction Algebraic and Partial Fractions Simplifying algebraic fractions Partial fractions Functions and Modelling Modulus function Composite and inverse functions Transformations

8 Modelling with functions, for example trigonometric, exponential, reciprocal etc Series and Sequences Arithmetic and geometric progressions (proofs of sum formulae ) Sigma notation Recurrence and iterations The Binomial Theorem Expanding (a + bx) n for rational n; knowledge of range of validity Expansion of functions by first using partial fractions Trigonometry Radians (exact values), arcs and sectors Small angles Secant, cosecant and cotangent (definitions, identities and graphs); Inverse trigonometrical functions; Inverse trigonometrical functions Compound and double (and half) angle formulae, including geometric proofs R cos (x ± α) or R sin (x ± α) Proving trigonometric identities Solving problems in context (e.g. mechanics) Parametric Equations Definition and converting between parametric and Cartesian forms Curve sketching and modelling Statistics Regression and Correlation Change of variable Correlation coefficients. Statistical hypothesis testing for zero correlation Probability Using set notation for probability. Conditional probability Questioning assumptions in probability The Normal Distribution Understand and use the Normal distribution Use the Normal distribution as an approximation to the binomial distribution. appropriate distribution Statistical hypothesis testing for the mean of the Normal distribution Selecting the

9 Mechanics Moments: Forces turning effect Forces at any Angle Resolving forces Friction forces (including coefficient of friction µ) Applications of Kinematics: Projectiles Applications of Forces Equilibrium and statics of a particle (including ladder problems) Dynamics of a particle Further Kinematics Constant acceleration (equations of motion in 2D; the i, j system) Variable acceleration (use of calculus and finding vectors and at a given time)