AS/A Level Mathematics a and Further Mathematics Teaching Order Framework Model 2

Teaching Order Framework

Model 2 – Starting Further Maths with the Pure Core

Introduction

This GCE Teaching Order Framework has been designed to help teachers develop schemes of work for delivering the reformed Mathematics and Further Mathematics qualifications in parallel. This document details a possible route for co-teaching H230 OCR AS Level Mathematics A H240 OCR A Level Mathematics A H235 OCR AS Level Further Mathematics A H245 OCR A Level Further Mathematics A This document should be used in conjunction with the full specification documents. One key feature of the OCR A Level Mathematics A and Further Mathematics A specifications is their two-column structure, setting out the required content in a format to clearly show the progression through AS Level and A Level. The Teaching Order Framework is fully customisable so that it can be edited to suit your own particular cohort, however care should be taken to avoid introducing content without the required prerequisite knowledge. The route provided is a ‘best fit’ generic solution, effective for whichever of the Further Mathematics options are taken (centres that do not offer all four Further Mathematics options will have less prior knowledge constraints that will need to be balanced). This document covers the full specification content, but is not designed to constitute a full programme of study. There is flexibility to incorporate periodic review and formative assessment at appropriate times throughout the course. The structure of the Teaching Order Framework has been produced based on the assumption of A Level Mathematics and A Level Further Mathematics being taught as two fully timetabled qualifications, each covered by two teachers. In A Level Mathematics there is an assumption that Teacher A acts as a specialist in statistics and Teacher B acts as a specialist in mechanics (with both teaching aspects of the pure content). In A Level Further Maths there is an assumption that Teachers C and D each deliver one of the four options (with both teaching aspects of the core pure content). Model 2 prioritises the teaching of the Pure Core content in AS Level Further Mathematics and of optional content which is familiar from the legacy specification. In particular it (generally) leaves “new” content until at least the end of the first term.

This has required some restructuring and reordering of the Mathematics content as compared to the Model 1 version of this framework, in particular moving enough of the pure content early in term 1 to facilitate starting Further Mathematics with the Pure Core. A few other small changes have been made to improve the grouping and ordering of the Mathematics content based on feedback from teachers. Download specifications, sample assessment materials, teaching and learning resources at ocr.org.uk/alevelmathematics ocr.org.uk/alevelfurthermaths

Version 1 1 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both applied components] 1/T1 Algebra and Functions Equations of lines The language The language of complex numbers of Matrices 1.02 a, b, c, d, e 1.03 a, b, c 4.02 a, b, c 4.03 a, b, c

2/T1 Polynomial Equations Equations of circles Determinants Basic Operations with complex numbers (Radians) and Inverses 1.02 f, j 1.03 d, e, f 4.02 e, f 4.03 h, j, l, m, n, o, p 3/T1 Proof Vectors Solutions of Solutions of equations simultaneous 1.01 a, b, c 1.10 a, c, d 4.02 g, h, i, j equations 4.03 r 4/T1 Graphs and Transformations Vectors Proof by Argand Diagrams and Loci Induction 1.02 p, q, r, w 1.10 e, f, g 4.02 k, l, o, p 4.01 a

5/T1 Polynomials and Graphs Units and Kinematics Linear Vectors Transformatio 1.02 m, n, o 3.01 a, b 3.02 a, b 4.04 a, c, e, g ns using matrices 6/T1 LDS Introduction and single Kinematic Graphs Invariance Roots of equations variable data and scale 3.02 c 4.05 a, b factors 2.02 a, b 4.03 g, i, k, q

Version 1 2 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 7/T1 Measures of Average and Spread Suvat Equations P & C Energy Mathematical Groups Preliminaries 2.02 f, g 3.02 d 5.01 a 6.02 d, e 8.02 e, 8.03 a, b 7.01 a, b, c

8/T1 Outliers and cleaning data 1st Principles of Applications Energy Mathematical Groups Differentiation of P & C Preliminaries 2.02h, i, j 6.02 i 8.03 c, d 1.07 g, i 5.01 b 7.01 d, e, f, g, I, k 9/T1 Binomial Expansion Differentiation and Chi Squared Momentum Graphs Groups Gradients Contingency 1.04 a 6.03 a, b 7.02 a, b, c, g 8.03 e, f, Tables 1.07 a, b 5.06 a 10/T Probability Gradient Functions and Fitting Restitution Graphs Groups 1 2nd derivatives distributions 1.04 b, 2.03 a, b 6.03 i, j 7.02 d, e, p, q, r 8.03 g, h 1.07 c, d, e 5.06 b, d (ratio and 11/T Discrete distributions (incl Equations of tangents and Probability Dim Analysis Algorithms Properties of 1 Binomial) normal Distributions groups 6.01 a, b, d 7.03 a, b, c 2.04 a, b, c 1.07 m 5.02 a, b, c 8.03 i

12/T Sampling Stationary Points Binomial, Dim Analysis Algorithms Properties of 1 Uniform and sequences 2.01 a, b, c, d 1.07 n, o 6.01 c, e 7.03 j, l Geometric 8.01 a, b, h distributions 1/T2 Inequalities Forces Fitting Resolving forces Graphs Properties of distributions (preliminary work) sequences 1.02 g, h, i 3.03 a, f, g 7.02 j, k 5.06 b, d (Bin, 8.01 c, d U and Geo)

Version 1 3 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 2/T2 More LDS and Bivariate data (1) Newton’s Laws (1) Dependent Impulse Network Fibonnaci and and Algorithms Solving relations 2.02 c, d, e 3.03 b, c, j, r 6.03 e, f Independent 7.04 a 8.01 e, f Variables 3/T2 Bivariate Data (2) Newton’s Laws (2) Linear Restitution Network Vector product and regression Algorithms scalar triple product 2.02 c, d, e 3.03 d 6.03 i, j, k 5.09 b, c, d, e 7.04 b, f 8.04 a, b, c, d

4/T2 Exponentials and Logarithms Newton’s Laws (3) PMCC Work, Energy and Critical Path Number Theory Power Analysis 1.06 a, b, c 3.03 h, i 5.08 a, b, c 8.02 a, b, c, d 6.02 a, b, (i) 7.05 a

5/T2 Exponential Graphs Connected particles SRC Work, Energy and Critical Path Number Theory Power Analysis 1.06 d, e, f 3.03 k, n 5.08 e, g 8.02 e, f, i, j, k 6.02k, l, (i) 7.05 b, c

6/T2 Modelling with exponentials Connecting Kinematics Recap of Recap of Complex numbers and Vectors and Forces Proof and 1.06 g, h, i Matrices

7/T2 Trigonometry Fundamental Theorem of Poisson Uniform motion in a Algorithms Surfaces Calculus circle 1.05 a, b, c 5.02 i, j, k, l, 7.03 d, e, f, g 8.05 a 1.08 a, b 6.05 a

Version 1 4 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 8/T2 Trigonometry Functions Definite Integrals (1) Poisson Uniform motion in a Graphical Sections and 5.02 m , n + circle Linear contours 1.05 f, j, o 1.08 d, e 5.06b, d Programming 6.05 b 8.05 c 7.06 a, c 9/T2 Statistical Hypothesis Testing (1) Definite Integrals (2) Hypothesis Uniform motion in a Graphical Partial Diff tests 5.08d circle Linear 2.05 a, b, c 1.08 d, e 8.05 d Programming 6.05 c 7.06 d 10/T Statistical Hypothesis Testing (2) Constant and variable Hypothesis Motion in a vertical Game Theory Stationary points 2 acceleration tests 5.08f circle 2.05 a, b, c 7.08 a, b, c, e 8.05 e 3.02 d, f 6.05 d

1/T3 Conditional Probability Radians and Non- Hooke’s law Graphs and Finite (modular) Trigonometry parametric Networks arithmetic 2.03 c, d, e 6.02 g, h Tests 1.05 d, e 7.02 f, h, i, 8.02 g 5.07 a, b 2/T3 Algebra and Functions Radians and Single Linear momentum in 2- Graphs and Finite (modular) Trigonometry Sample D Networks arithmetic 1.02 u, v, x hypothesis 1.05 g, h, i, k, o 6.03 c, d 7.02 l, m, n, o 8.02 h tests 3/T3 Series and Sequences Numerical Methods Paired- Oblique impact Network Fermat’s little sample and Algorithms theorem and 1.04 c, d, e, f, g 1.09 a, b, c 6.03 g, h two sample binomial theorem 7.04 c, d, e hypothesis 8.02 l, o test

Version 1 5 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 4/T3 AP and GP Newton-Raphson Test for NEL Network Order identity Algorithms 1.04 h, i, j, k 1.09 d, e 6.03 l 8.02 m, n 5.07 e 7.04 c, d, e

5/T3 Parametric form Moments about a point Proof Exponential form of complex numbers and geometric effects 1.03 g 3.01 c, 3.04 a, b 4.01 b 4.02 d, m

6/T3 Modelling using parametric Modelling Static problems Solutions of Euler’s formula and de Moivre’s theorem equations equations 3.04 c 4.02 n, q, r, s and 1.03 h intersection of planes 7/T3 Normal Distribution Introduction to Differential Continous Centre of Mass of Arrangement Groups Equations random symmetric lamina and Selection 2.04 e, f 8.03 j, k, l variables problems 1.07 t 6.04 a, b 5.03 a 7.01 h, j 8/T3 Normal Distribution Analytical Solutions of Probability Composite Rigid bodies Inclusion- Groups Differential Equations density exclusion 2.04 d, g, h 6.04 c 8.03 m functions principle 1.08 k 5.03 b, c, d 7.01 l

Version 1 6 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both

1/T4 Partial Fractions Proof by Contradiction Summation of Further Vectors series 1.02 k, y 1.01 d 4.04 b, d, f 4.06 a

2/T4 Modulus Function 3D Vectors Method of Further Vectors differences 1.02 l, s, t 1.10 b 4.04 h, i, j 4.06 b

3/T4 Binomial Expansion Further Vectors and Cumulative Work in 2-D Efficiency and Scalar Vector Kinematics distribution complexity of 1.04 c 6.02 c 8.04 e functions Algorithms 1.10 h, 3.02 e 5.03 e, f, 7.03 h, i, 4/T4 Normal and Hypothesis Resolving Forces Cumulative Energy Strategies Surfaces distribution 2.05 d 3.03 e, l 6.02 f 7.03 k, m 8.05 b functions 5.03 g 5/T4 Normal and Hypothesis Forces in Equilibrium Random Conservation of Energy Critical Path Stationary points Variables Analysis 2.05 e 3.03 m, o 6.02 j 8.05 f 5.04 a 7.05 d, e

Version 1 7 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 6/T4 Points of Inflection Resultant Forces in Normal Power Critical Path Tangent planes motion Random Analysis 1.07 f, p 6.02 m 8.05 g Variables 3.03 p, q, s, t, u 7.05 d, e 5.04 b 7/T4 Product and Quotient Rule Area between two curves Polar Hyperbolic functions Coordinates 1.07 q 1.08 f 4.07 a, b 4.09 a, b

8/T4 Chain Rule Integration as limit of a Area Hyperbolic functions sum enclosed by 1.07 r 4.07 c, d polar curve 1.08 g 1.09 f 4.09 c 9/T4 Trigonometry Identities Integration by substitution 5.06 Chi Statics of solids Game Theory Second Order Squared Recurrence 1.05 k. l, m 1.08 h 6.04 d, e 7.08 d, f Tests Relation 5.06 c 8.01 g, i 10/T Trigonometry Identities Motion in two dimensions Differential Volumes of solids of revolution 4 Equations 1.05 n, o, p, q 3.02 e, h, i 4.08 d 4.10 a, c

11/T Further Numerical Methods Projectile Model 2nd order Volumes of solids of revolution defined parametrically 4 homogeneou 1.09 f 3.02 i 4.08 d s differential equations

Version 1 8 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 1/T5 Pearson’s Product Moment Exponential Calculus Central Limit Motion in a Circle Graphical Further Calculus Correlation Theorem review Linear 1.07 j, l, 1.08 c 8.06 a Programming 2.05 f 5.05 a 7.06 b, e, f 2/T5 Hypothesis Testing and Trigonometrical Calculus Population Radial and tangential The Simplex Further Calculus Correlation Mean and components Algorithm 1.07 h, k, q, r 8.06 a Variance 2.05 g 6.05 e 7.07 a, b, c, 5.05 b 3/T5 Functions and Modelling Trigonometrical Calculus Hypothesis Free motion The Simplex Further Calculus Tests Algorithm 1.02 z 1.08 c 6.05 f 8.06 b 5.05 c, 5.07 f 7.07 d

4/T5 Integration of parametric functions Further Kinematics Confidence Linear Motion under The Simplex Further Calculus Intervals variable force Algorithm 1.08 f 3.03 v 8.06 b 5.05 d 6.06 a 7.07 e, f

5/T5 Integration by parts Further Kinematics Differential Inverse Hyperbolic functions Equations 1.08 i, j 3.02 g 4.07 e, f 4.10 b

6/T5 Further Differential equations Further Parametrics 2nd order Further Integration homogeneou 1.07 t, 1.08 k, l 1.03 g, h, 1.07 s, 1.08 f 4.08 g s differential equations

Version 1 9 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 7/T5 Pure Revision Pure Revision 2nd order non- Further Integration homogeneou 4.05 c 4.08 h s differential equations 8/T5 Statistics Revision Mechanics Revision Simple Maclaurin series Harmonic 4.08 a, b Motion 4.10 f 9/T5 Statistics Revision Mechanics Revision Damped Improper integrals Oscillations 4.08 c 4.10 g

10/T Pure Revision Pure Revision Linear Further Calculus 5 Systems 4.08 e, f 4.10 h

1/T6 Pure Revision Pure Revision Core Core Revision Revision

2/T6 Statistics Revision Mechanics Revision Option Option Revision Option Revision Option Revision Revision

Version 1 10 © OCR 2017 wk/ Teacher A Teacher B Teacher C & D Term Maths Maths Further Maths (Each teacher deliveries core pure + 1 (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] applied component) Y532 Stats Y534 Discrete Y535 Add Pure [Students study all core pure + both 3/T6 Statistics Revision Mechanics Revision Core Core Revision Revision

4/T6 Pure Revision Pure Revision Option Option Revision Option Revision Option Revision Revision

5/T6 Pure Revision Pure Revision Core Core Revision Revision