A Level Maths. Course Guide

Size: px

Start display at page:

Download "A Level Maths. Course Guide"

Joseph Anthony
5 years ago
Views:

1 A Level Maths Course Guide

2 AS and A Level Maths Course Guide Welcome to A Level Maths. In this course you will develop your mathematical skills from GCSE, and will learn many new and powerful techniques that can be used in many other areas such as Science, Pharmacy, Finance, and Computer Programming to name but a few. This course also gives you the building blocks for any further study in a course that depends heavily on mathematical ideas, for example Physics, Engineering, and of course Maths! Course Overview In Year 12 you will study two modules: Pure Maths and Applied Maths (Statistics and Mechanics). In Year 13 you will study the same again, but obviously to a greater depth. Your A Level grade will be determined from all of your modules studied, and will be assessed via two Pure Maths papers and one Applied Maths paper. A calculator is allowed for each paper. There is no coursework; all of the units are 100% exam. You will sit two Pure Maths exams and one Applied Maths exam at the end of Year 13. Each exam is two hours in length and each counts as 1/3 towards your overall grade. Year 12 In Year 12, you will be taught by two teachers; one teaching predominantly Pure Maths, and the other teaching predominantly Applied Maths (there is some cross-over between the units). For Pure Maths, you will be expected to provide your own folder. Your teacher will provide you with extensive class notes which will guide you through the course, and plenty of supporting exercises that will help you to practise the basics, and develop your problem-solving skills. Able students can expect to be stretched by some optional, very demanding exercises. You must bring your full folder to each lesson, as you will constantly need to refer to earlier topics. You will also be issued with an exercise book for starter activities, as it is essential that basics are practised throughout the course, and this will help to avoid clutter in your folder. It is essential that you bring a calculator to each lesson, as you will be expected to use it in each lesson. For Applied Maths, it would be a good idea to have a separate folder. You will study two topics: Mechanics and Statistics. In Mechanics you will study physics problems by using Newton s laws of motion. In Statistics you will recap ideas on handling data and probability from GCSE, and you will meet the very important concept of Hypothesis Testing. The emphasis in this is on problem-solving. A greater proportion of time therefore will be spent on problem-solving, and you will not be provided with a set of class notes. You will also have access to a large data set provided by the exam board. You will not be expected to do coursework, but familiarity with this data set will be of benefit for the final exam. A Level Maths moves considerably more rapidly than GCSE, but we are sensitive to the differing needs of pupils, and recognise that not all students will progress through the course at the same speed. We do not therefore devote a set amount of time to each module; some modules will be completed very quickly, but some will need a greater amount of time for key ideas to sink in. You will also be expected to complete some of your learning independently. All MCHS Maths staff are very

3 supportive, and you should ask them for help whenever necessary. Your teacher will tell you when support is available. At the end of each module you will be given an assessment. This will be marked with feedback on a PLC which will tell you which areas you were good at, and which need further improvement. You will receive a WWW and an EBI. The EBI will typically be further exercises on areas that you found difficult, or extension work for those who performed well in all areas. Longer modules may involve two assessments. There will be regular tests and exams which will be marked and graded according to A Level grade boundaries. These will form the basis of your reports. Pure Maths Year 12 This course offers some bridging material from GCSE to A Level study, and ensures that you are able use these ideas fluently before moving on to more advanced topics. Towards the end of the course you will meet calculus. This is a powerful technique that deals with how things change, and forms the basis of many applied topics, particularly the maths underlying Physics. The course is split into 9 units. Unit 1 (Proof): - The structure of mathematical proof and its associated language. Proof by deduction, proof by exhaustion, proof by counter-example, proof by contradiction. A lot of these ideas will be met throughout the A Level course. Unit 2 (Algebra and Functions): - Recaps and develops algebraic skills from GCSE such as simplifying, brackets, factorising, indices, surds. A lot of emphasis will be placed on self-study, with support if needed. - Recaps and develops quadratic equations (factorising, using the formula, completing the square) - linear and non-linear simultaneous equations, linear and quadratic inequalities, and using the discriminant to determine the number of solutions to a quadratic - Simplifying algebraic fractions, division of algebraic expressions, Factor-Remainder Theorem. Factorising cubics. - Sketching graphs, including proportionality. Transformations of graphs. Use of graphs to solve equations and inequalities Unit 3 ( Coordinate Geometry) - Gradient and intercept. Equation of a line in various forms. Parallel and perpendicular lines. Solving problems. - Equation of a circle, tangents, chords, diameter Unit 4 (Series): - The binomial theorem, understanding factorial notation, ncr, expanding (a +b) n and (1 + x) n Unit 5 (Trigonometry): - Prove and use trigonometric identities to simplify expressions and solve equations. Determine all possible solutions using a CAST diagram or a graph.

4 Unit 6 (Differentiation): - Understand what differentiation means, and understand the notation. Find gradients of curves, and the equation of the tangent and the normal. Find rates of change, and the second differential. Determine criteria for a function to be increasing/ decreasing/ stationary. Classify stationary points. Solve problems involving maxima and minima Unit 7 (Integration): - Understand that integration is the inverse of differentiation. Find the indefinite integral of expressions involving indices. Find f(x) given f (x) and a coordinate. Use integration to find the area bounded by a curve and the x axis, a curve and a line, or two curves. Understand the meaning of negative area. Unit 8 (Vectors): - Recap basic definitions of vectors and use to prove geometric theorems. Apply to real-world examples, eg Mechanics Unit 9 (Exponentials and logarithms): - Definition of a logarithm, logarithm laws, solving equations - Define the exponential function e x. Find the inverse lnx. Sketch graphs and transform them, eg f(x) + 3, and solve equations - Use logarithms to turn non-linear graphs into linear graphs, and use to solve problems, eg half-life of a radioactive substance. Supporting texts: You will be provided with extensive and detailed course notes Applied Maths Year 12 Note: at first glance it appears that there is far less work to do on Mechanics, but this is misleading. You will have met a lot of the statistical methods before in GCSE, but a lot of the Mechanics will be new to you, so you can expect to spend longer on each module. Mechanics Unit 1 (Kinematics): - Understand the associated language, eg position, distance, displacement, speed, velocity etc and their associated units - Use distance/ time and speed/ time graphs to solve problems - Solve problems involving constant acceleration, and prove the suvat formulas - Solve problems involving varying acceleration using calculus - Use vectors for all the above problems Unit 2 (Forces and Newton s Laws) - Understand how to draw clear diagrams representing forces, and using Newton s first law - Solve problems using Newton s second law: F = ma - Understand the difference between weight and mass, and solve problems using vertical motion - Use Newton s third law to solve problems where forces are in equilibrium - Use vectors for all the above problems.

5 Statistics Unit 1 (Statistical sampling): - Use different sampling techniques, eg random sampling, stratified sampling etc, and understand the advantages/ disadvantages of different methods Unit 2 (Data presentation and interpretation): - Construct and interpret diagrams for single variable data, eg box and whisker plots, histograms, cumulative frequency diagrams, stem and leaf diagrams. Link to probability distributions. - Construct diagrams for bivariate data, eg scatter diagrams. Understand correlation, and the fact that it does not imply causation. Plot the regression line and use to solve problems. Understand the dangers of extrapolation. - Understand measures of central tendency eg mean, median, mode of discrete/ continuous data. Draw inferences from these - Understand measures of spread, eg variance, standard deviation, percentile ranges. Use linear interpolation to estimate percentiles. Draw inferences from these - Use strategies to identify outliers, and understand how to clean data Unit 3 (Probability): - Understand mutually exclusive/ independent events. - Use tree diagrams, Venn diagrams and set notation. Unit 4 (Statistical distributions): - Understand discrete and continuous distributions - Calculate probabilities using the binomial distribution Unit 5 (Hypothesis testing): - Understand and apply the language of hypothesis testing using the binomial distribution - Null hypothesis H 0, Alternative hypothesis H 1, significance level, test statistic, 1 and 2 tail test, critical value, critical region, p-value - Hypothesis test for a proportion of the population - Make inferences using hypothesis testing, and understand Type 1 errors. Supporting text: Statistics and Mechanics Year 1/AS (Pearson), Large Data Set (Edexcel) Year 13 Year 13 Maths follows much the same format as Year 12 Maths in terms of assessment and timings, but you can expect to meet a higher degree of challenge at this level In Core 3 and Core 4, you will further develop some of the ideas introduced in AS, such as differentiation, integration and trigonometry, and you will further develop your precision, eg the construction of proofs and formal definitions of functions. For Applied Maths, you will look at more complicated mechanical systems by using further techniques, and you will look at the very important Normal Distribution in Statistics. You will be provided with a course booklet detailing topics to be covered next year. Mr C Starr

Probability and Statistics Curriculum Pacing Guide

Probability and Statistics Curriculum Pacing Guide Unit 1 Terms PS.SPMJ.3 PS.SPMJ.5 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods