Download Word - The Further Mathematics Support Programme

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.