A Level Maths and Further Maths - OCR€¦ · AS and A Level Maths • Pure maths looks very...
Transcript of A Level Maths and Further Maths - OCR€¦ · AS and A Level Maths • Pure maths looks very...
A level Maths and Further Maths
Will Hornby Subject Development Lead
Development timeline
AS and A Level Maths
• A choice of specifications… • Mathematics A, developed by OCR • Mathematics B (MEI), developed in collaboration with MEI.
Overview • The grade-set will stay the same: A* - E for A level and A - E for AS
level.
• AS and A level qualifications are to be linear. The AS level qualifications will be stand-alone; students may or may not take AS level on the way to A level.
• The AS content will be a subset of the A level content. AS and A level qualifications must be co-teachable, so that AS and A level Mathematics can be taught together in year 12 and Further Mathematics can be studied in parallel with Mathematics.
Overview • There will be no coursework in either Mathematics or Further
Mathematics.
• Students will be expected to have experience of a prescribed large data set.
• Technology
– Use of technology must “permeate” the specifications.
– No CAS.
– In the examination students are expected to be able to use built-in
calculator functions to find summary statistics and to obtain probability
values from standard distributions.
Overarching themes
The assessment covers three broad themes across the
entire content in both mathematics and further
mathematics:
1. Mathematical argument, language and proof
2. Mathematical problem solving
3. Mathematical modelling
AS and A Level Maths
Pure Mathematics
approx 2/3
Mechanics
approx 1/6
Statistics
approx 1/6
AS and A Level Maths • Pure maths looks very similar to the current C1-C4 – a slight
emphasis on proof.
• Mechanics also very familiar with kinematics and Newton’s laws,
extending into 2D for A level including projectiles, resolving forces,
friction and static moments.
• Statistics content is very different from current S1 units. • The emphasis is on interpretation of statistical diagrams not drawing
them, along with the interpretation of real data.
• Hypothesis testing using the binomial distribution is in AS; the Normal
distribution is not in AS but is in the full A level.
• The content in current Decision maths units is out, but can appear
as optional content in Further Maths.
OCR AS and A level Mathematics A
Pure
Pure
and
Statistics
Pure
and
Mechanics
Pure
and
Mechanics
Pure
and
Statistics
A Level
AS level
1 hour 30 mins 75 marks
2 hours 100 marks
OCR AS and A level Mathematics B (MEI)
Pure
and
Comprehension
Pure
and
Statistics
Pure
and
Mechanics
Pure
And
Statistics
Pure
and
Mechanics
A Level
1 hour 30 mins 75 marks
2 hours P1+2 100 marks P3 75 marks
AS level
AS Further A Level Further
Further Maths
Pure Maths
50%
Optional Content
50%
Pure Maths
at least
30%
Optional Content
up to 70%
OCR AS Level Further Mathematics A
Pure
Core
Statistics Mechanics
Discrete
Maths
Additional
Pure
Maths
+ Two of...
1 hour 10 mins 60 marks
OCR A Level Further Mathematics A
Pure
Core
Statistics Mechanics
Discrete
Maths
Additional
Pure
Maths
+ Two of...
Pure
Core
1 hour 30 mins 75 marks
OCR AS Level Further Mathematics B (MEI)
Pure
Statistics
a
Mechanics
a
Modelling
with
Algorithms
+ Two of...
Statistics
b
Mechanics
b
Numerical
Methods
1 hour 15 mins 60 marks
OCR A Level Further Mathematics B (MEI)
Pure
+Major Minor
MinorMinorMinor + +
Either
Or
Major: Statistics or Mechanics
Minor: Statistics, Mechanics, Modelling with Algorithms,
Numerical Methods, Pure with Technology,
Extra Pure
Paper Length Option Paper Length Marks
Pure core 2 hours 40 minutes 144 (scaled to 180)
Mechanics major 2 hours 15 minutes 120 marks
Statistics major 2 hours 15 minutes 120 marks
Mechanics minor 1 hour 15 minutes 60 marks
Statistics minor 1 hour 15 minutes 60 marks
Numerical methods 1 hour 15 minutes 60 marks
Modelling with algorithms 1 hour 15 minutes 60 marks
Extra pure 1 hour 15 minutes 60 marks
Further pure with technology
1 hour 45 minutes 60 marks
Further Mathematics Content A Level - Overview
Pure
CoreOptions Options
.
Pure
CoreOptions
Year 1
Year 2 Pure
Core
Further Mathematics Content AS Level (spec A)
Pure
CoreOption 1 Option 2+ .
Further Mathematics Content A Level (Spec A)
Pure
Core
1/2
Option 1
1/4
Option 2
1/4+ .
Further Mathematics Content A Level (Spec A)
Pure
CoreOption 1 Option 2
.
Pure
Core
Option
1
Option
2
Year 1
Year 2
Further Mathematics Content AS Level (Spec B (MEI))
Pure
CoreOption 1 Option 2+ .
Further Mathematics Content A Level (Spec B (MEI))
Pure
Core
1/2
Major
Option
1/3
Minor
Option
1/6
+ .
Further Mathematics Content A Level (Spec B (MEI))
Pure
Core
1/2
Minor
Option
1/6
+ .
Minor
Option
1/6
Minor
Option
1/6
Further Mathematics Content A Level (Spec B)
Pure
CoreMinor
.
Pure
Core
Year 1
Year 2
Major
Further Mathematics Content A Level (Spec B)
Pure
CoreMinor
.
Pure
Core
Year 1
Year 2
Minor
Minor
Large Data Set • Designed to be used in the classroom
• Students will not have access to the large data set in the exam
• Summary data or small sets of data may be provided within the
exam paper.
• Students will not be expected to spend time entering data into a
calculator.
• Some of the questions on the statistics content will be set in the
context of the large data set, providing an advantage to students
who have spent time exploring the data.
Large Data Set Teaching and Learning tasks
(a non-exhaustive list)
1.Exploratory data analysis
2.Modelling
3.Repeated sampling
4.Hypothesis testing
Large Data Set In the exam…..
Questions will be set that give a material advantage to learners who
have studied, and are familiar with, the large data set.
They might include questions/tasks which:
• assume familiarity with the terminology and contexts of the data,
• use summary statistics or selected data from, or statistical diagrams
based on, the prescribed large data set
• are based on samples related to the contexts in the prescribed large
data set,
• require learners to interpret data in ways which would be too
demanding in an unfamiliar context.
Use of Technology
Teaching and Learning tasks
(a non-exhaustive list)
1.Graphing tools
2.Spreadsheets
3.Statistics
4.Mechanics
5.Computer Algebra System (CAS)
Use of Calculators
Non Calculator Questions
CPD Face to Face events – running in the spring term
• Introducing the OCR and OCR (MEI) GCE Maths qualifications (London, Birmingham, Manchester, Newcastle & Exeter – half day am event)
• Introducing the OCR and OCR (MEI) GCE Further Maths qualifications (London, Birmingham, Manchester, Newcastle & Exeter – half day pm event)
Live Online Training Events – running in February & March
• Practical approach to teaching Mechanics • Using a large data set to teach statistics • Using technology in the classroom • Teaching the new Pure Core content for Further Maths in Spec A and Spec B • Teaching the new Statistics content for Further Maths Spec A • Teaching the new Mechanics content for Further Maths Spec A • Teaching the new Discrete Maths content for Further Maths Spec A • Teaching the new Additional Pure content for Further Maths Spec A
Further sessions may be scheduled in the summer term to cater for demand.
Planned Resources • Mapping documents from legacy Specifications to the new AS/A level for Maths and
Further Maths Spec A & B • Large data set resource with activities that have been trialled in the classroom • Using technology resource with activities that have been trialled in the classroom • A guide to bridging the gap between GCSE and AS • Topic exploration packs and lesson elements that focus on new areas of content e.g.
proof, hypothesis testing • Check In Tests – similar in style to GCSE (10 Qs covering AO1, AO2 & AO3) but with
worked solutions rather than answers and RAG grids • A guide to calculator use • Practical Mechanics resource • ‘Formulae you should know’ poster • SAMs commentaries • Maths in context flipped learning resources, covering engineering, computer science,
sciences, economics, social science and more…
ocr.org.uk/maths
ocr.org.uk/alevelmaths
01223 553998
OCR Maths podcast on iTunes
@OCR_Maths
Spec A - AS Pure Core
• Proof • Complex Numbers • Matrices • Further Vectors • Further Algebra
AS level
Spec A - A Level Pure core
• Proof • Complex Numbers • Matrices • Further Vectors • Further Algebra • Series • Hyperbolic Functions • Further Calculus • Polar Coordinates • Differential Equations
A Level
Spec A - Mechanics
• Dimensional Analysis • Work, Energy and Power • Impulse and Momentum • Centre of Mass • Motion in a Circle • Further Dynamics and Kinematics (A Level)
A Level
AS level
Spec A - Statistics
A Level
AS level
• Permutations and Combinations • Discrete Random Variables • Continuous Random Variables (A Level) • Chi-squared Tests • Non-Parametric Tests • Correlation • Linear Regression • Hypothesis Tests • Confidence Intervals (A level) • Linear Combinations of Random Variables
(A level)
Spec A - Discrete Maths
• Pure mathematical Preliminaries • Graphs and Networks • Algorithms • Network Algorithms • Decision Making in Project Management • Graphical Linear Programming • Game Theory • The Simplex Algorithm (A Level)
A Level
AS level
Spec A - Additional pure
• Sequences and Series • Number Theory • Groups • Further Vectors • Surfaces and Partial Differentiation • Further Calculus (A Level)
A Level
AS level
Spec B - AS Pure Core
• Proof • Complex numbers • Matrices and transformations • Vectors and 3-D space • Algebra • Series
A Level
AS level
Spec B - A Level Pure core
A Level
AS level
• Proof • Complex numbers • Matrices and transformations • Vectors and 3-D space • Algebra • Series • Calculus (A-level) • Polar coordinates (A-level) • Hyperbolic Functions (A-level) • Differential equations (A-level)
Spec B - Mechanics a/b/major Mechanics a • Dimensional analysis • Forces • Work, energy and power • Momentum and impulse • Centre of mass (simple shapes) Mechanics b • Momentum and impulse (oblique impact) • Circular motion • Hooke’s law • Centre of mass • Vectors and variable forces
A Level
AS level
Spec B - Statistics a/b/major Statistics a • Discrete random variables • Bivariate data • Chi-squared tests Statistics b • Bayes’ theorem • Continuous random variables • Inference • Simulation
A Level
AS level
Spec B - Numerical Methods
• Use of technology • Errors • Solutions of equations • Numerical differentiation • Numerical integration • Approximation to functions
A Level
AS level
Spec B - Modelling with algorithms
• Algorithms • Networks • Linear Programming
A Level
AS level
Spec B - Further pure with technology
• Investigation of curves • Exploring differential equations • Number Theory
• Based on the current FPT unit (4798) available
since 2012
• Students have access to a computer during the
exam.
• Not computer based testing, students record
answers in a printed answer booklet
• Students will be required to use CAS, spreadsheet
software, and a programming language.
• Many centres currently use Geogebra, and python
A Level
Spec B - Extra pure
Students answer questions on a choice of three from the following six topics • Sets, logic and Boolean algebra • Recurrence relations • Combinatorics • Groups • Matrices and vectors • Multivariable calculus
A Level