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

maths@ocr.org.uk

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