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Further Mathematics Support Programme AQA S2 – Scheme of Work Template - 2016-2017 This template is part of a series designed to assist with planning and delivery of further mathematics courses. It shows how Integral Resources and Live Interactive Lectures can be used to support students and teachers. Integral Resources Integral Resources Live Interactive Lectures Teacher-level access to the Integral Resources (integralmaths.org/) for Further Pure and Applied units is available free of charge to all schools/colleges that register with the Further Mathematics Support Programme: www.furthermaths.org.uk/ Student-level access to the Integral Resources and the Live Interactive Lectures for Further Mathematics is available at a moderate cost via: www.furthermaths.org.uk/lilfm Integral Resources include a wide range of resources for both teacher and student use in learning and assessment. A selection of these are suggested in the template below. Sample resources are available via: http://integralmaths.org/help/info.php. Live Interactive Lectures are available for individual Further Pure and Applied units and take place in the spring and autumn terms. LIL FM is ideal for schools/colleges teaching Further Mathematics with small groups and/or limited time allocation. It is also useful to support less experienced teachers of Further Mathematics. See www.furthermaths.org.uk/lilfm Scheduling will depend on circumstances, but the template below breaks the module down into 7 sections which may be allocated approximately equal time. Each section corresponds to one Live Interactive Lecture (LIL) and these take place fortnightly to supplement the teaching and tutorial support in schools/colleges and students' own independent study. FMSP Area Coordinators will be able to offer additional guidance if needed. See www.furthermaths.org.uk/regions AQA S2 – Scheme of Work Template - 2016-2017 Topic Specification statements Suggested Integral Resources Discrete random variables Discrete random variables and their associated probability distributions. Mean, variance and standard deviation. Mean, variance and standard deviation of a simple function of a discrete random variable. ► AQA_S2 / ► Discrete random variables / ► Discrete random variables 1: Introduction Additional exercise Assessment (Integral Resources) Live Interactive Lecture Other resources Discrete random variables nrich: Data matching Making statistics vital: DRVs from a bag Section Test D1 Making statistics vital: DRV Venn diagram ► AQA_S2 / ► Discrete random variables / ► Discrete random variables 2: Expectation and variance Discrete random variables 1 (PowerPoint) Discrete random variables 2 (PowerPoint) Additional exercise Making statistics vital: The four-sided dice Making statistics vital: Double or add Section Test D2 ► AQA_S2 / ► Discrete random variables / ► Discrete random variables 3: Functions of a random variable Notes and examples Section Test D3 ► AQA_S2 / ► Discrete random variables Discrete random variables topic assessment The Poisson distribution Continuous random variables Conditions for application of a Poisson distribution. Calculation of probabilities using formula. Use of Tables. Mean, variance and standard deviation of a Poisson distribution. Distribution of sum of independent Poisson distributions. ► AQA_S2 / ► The Poisson distribution / ► The Poisson distribution 1: Introduction Differences from discrete random variables. Probability density functions, cumulative distribution functions and their relationship. The probability of an observation lying in a specified interval. Median, quartiles and percentiles. Mean, variance and standard deviation. Mean, variance and standard deviation of a simple function of a continuous random variable. Rectangular distribution. ► AQA_S2 / ► Continuous random variables / ► Continuous random variables 1: Probability density The Poisson distribution Making statistics vital: Poisson or not? Making statistics vital: Adding two Poisson distributions Poisson dominoes Poisson matching activity Exercise Making statistics vital: Parameter gaps Section Test P1 ► AQA_S2 / ► The Poisson distribution Notes and examples The Poisson distribution topic assessment Continuous nrich: pdf matcher random variables Section Test CRV1 ► AQA_S2 / ► Continuous random variables / ► Continuous random variables 2: Mean and variance Notes and examples ► AQA_S2 / ► Continuous random variables / ► Continuous random variables 2: Mean and variance Section Test CRV2 Notes and examples Estimation: The t distribution Confidence intervals for the mean of a normal distribution with unknown variance. ► AQA_S2 / ► Estimation / ► Estimation 1: Confidence intervals with the t-distribution Notes and examples Hypothesis testing 1: One and two tailed tests Hypothesis testing 2: Using t and z statistic Null and alternative hypotheses. One tailed and two tailed tests, significance level, critical value, critical region, acceptance region, test statistic, Type I and Type II errors. Tests for the mean of a distribution using a normal approximation. Tests for the mean of a normal distribution with known variance. Tests for the mean of a normal distribution with unknown variance. ► AQA_S2 / ► Hypothesis testing / ► Hypothesis testing 1: Hypothesis tests for the mean Section Test CRV3 ► AQA_S2 / ► Continuous random variables Continuous random variables topic assessment Estimation: The t distribution Section Test E1 ► AQA_S2 / ► Estimation Estimation topic assessment Hypothesis testing 1: One and two tailed tests Hypothesis test for the mean (Geogebra) Errors in hypothesis testing (Geogebra) Notes and examples Making statistics vital: Generating random numbers Making statistics vital: Sample mean gap-filler Section Test H1 ► AQA_S2 / ► Hypothesis testing / ► Hypothesis testing 2: Further hypothesis tests for the mean Making statistics vital: Sampling Hypothesis testing 2: Using t and z statistic Section Test H2 ► AQA_S2 / ► Hypothesis testing Contingency tables Introduction to χ distribution. Use of ∑((𝑂𝑖 − 𝐸𝑖 )2 )/𝐸𝑖 as an approximate χ2 statistic. Conditions for approximation to be valid. Test for independence in contingency tables. 2 ► AQA_S2 / ► Contingency tables / ► Contingency tables 1: Testing for independence Hypothesis testing topic assessment Contingency tables Additional exercise Section Test CT1 ► AQA_S2 / ► Contingency tables Making statistics vital: Defining the chi-squared distribution Making statistics vital: Chi-squared and percentages Contingency tables topic assessment Consolidation and revision FMSP - Revision Videos The study plans available on Integral Resources refer to Advancing Maths for AQA: Statistics 2 (ISBN 9780435513399) and Advanced Maths for AQA: Statistics S2 (ISBN 9780199149865). Other textbooks covering this course may be available, and Integral Mathematics Resources does not endorse any particular set of textbooks.