A2 Further Mathematics


Past mock examinations

     
OCR A2 Further Mathematics Formula Booklet
     
U6 FM Mock Teacher Z 19-20 U6 FM Mock Teacher Z 19-20 SOLUTIONS
     
U6 FM Mock (Mechanics/Statistics) 19-20 U6 FM Mock (Mechanics/Statistics) 19-20 SOLUTIONS

Teacher X (Mechanics)

     

Topic X4: Centre of mass

     
Lessons
     
Centre of mass of systems of point masses
     
Centre of mass of standard shapes
     
Centre of mass of composite bodies
     
Centre of mass by integration
     
Equilibrium of a rigid body
     
Topic test preparation
     
X4 (Pre-TT A) Centre of mass
     
X4 (Pre-TT A) Centre of mass MS
     
X4 (Pre-TT B) Centre of mass
     
X4 (Pre-TT B) Centre of mass MS
     
X4 (Post-TT A) Centre of mass
     
X4 (Post-TT A) Centre of mass MS
     
X4 (Post-TT B) Centre of mass
     
X4 (Post-TT B) Centre of mass MS

Topic X5: Variable forces
                & oblique collisions

     
Lessons
     
Work done by a variable force
     
Hooke's law
     
Elastic potential energy and work done
     
Problem solving with work, energy and power
     
Vector form of work done, kinetic energy and power
     
Differential equations with acceleration and velocity
     
Variable forces
     
Impulse-momentum of variable forces
     
Oblique impacts with walls
     
Oblique collisions of two objects
     
Impulsive tension in strings
     
Topic test preparation
     
X4 (Pre-TT A) Variable forces and oblique collisions
     
X4 (Pre-TT A) Variable forces and oblique collisions MS
     
X4 (Pre-TT B) Variable forces and oblique collisions
     
X4 (Pre-TT B) Variable forces and oblique collisions MS
     
X4 (Post-TT A) Variable forces and oblique collisions
     
X4 (Post-TT A) Variable forces and oblique collisions MS
     
X4 (Post-TT B) Variable forces and oblique collisions
     
X4 (Post-TT B) Variable forces and oblique collisions MS

Revision

     
     

Teacher Y (Statistics)

     

Topic Y4: Non-parametric tests
                & continuous random variables

     
Lessons
     
The single-sample sign test
     
The single-sample Wilcoxon signed rank test
     
Matched-pairs (or paired-sample) tests
     
Wilcoxon rank-sum test
     
Normal approximations with Wilcoxon tests
     
Continuous random variables
     
Averages and measures of spread of crv
     
Expectation & variance of functions of random variables
     
Cumulative distribution functions
     
Piecewise-defined probability density functions
     
Continuous uniform distribution
     
Exponential distribution
     
Distributions of related continuous random variables
     
    Worksheet: Distributions of related crv Worksheet MS
     
Goodness-of-fit with continuous distributions
     
Topic test preparation
     
Non-parametric tests and continuous rv (Pre-TT A)
     
Non-parametric tests and continuous rv (Pre-TT A) MS
     
Non-parametric tests and continuous rv (Pre-TT_B)
     
Non-parametric tests and continuous rv (Pre-TT B) MS
     
Non-parametric tests and continuous rv (Post-TT)
     
Non-parametric tests and continuous rv (Post-TT) MS

Topic Y5: Sample means

     
Lessons
     
Adding independent random variables
     
Expectation and variance of the sample mean
     
Unbiased estimates of the mean and variance
     
Linear combinations of normal variables
     
Central Limit Theorem
     
Hypothesis testing for the mean of a large sample
     
Confidence intervals
     
Topic test preparation
     
Y5 Sample means (Pre-TT)
     
Y5 Sample means (Pre-TT) MS
     
Y5 Sample means (Post-TT)
     
Y5 Sample means (Post-TT) MS

Revision

     
     

OCR past papers
and markschemes

     

Sample assessment material (SAM)

     
OCR SAM Pure Paper 1 QP & MS
     
OCR SAM Pure Paper 2 QP & MS
     
OCR SAM Statistics Paper 3 QP & MS
     
OCR SAM Mechanics Paper 4 QP & MS

Practice papers Set 1

     
OCR PP Set 1 Pure Paper 1
     
OCR PP Set 1 Pure Paper 1 MS
     
OCR PP Set 2 Pure Paper 2
     
OCR PP Set 1 Pure Paper 2 MS
     
OCR PP Set 1 Statistics Paper 3
     
OCR PP Set 1 Statistics Paper 3 MS
     
OCR PP Set 1 Mechanics Paper 4
     
OCR PP Set 1 Mechanics Paper 4 MS

Practice papers Set 2

     
OCR PP Set 2 Pure Paper 1
     
OCR PP Set 2 Pure Paper 1 MS
     
OCR PP Set 2 Pure Paper 2
     
OCR PP Set 2 Pure Paper 2 MS
     
OCR PP Set 2 Statistics Paper 3
     
OCR PP Set 2 Statistics Paper 3 MS
     
OCR PP Set 2 Mechanics Paper 4
     
OCR PP Set 2 Mechanics Paper 4 MS

Practice papers Set 3

     
OCR PP Set 3 Pure Paper 1
     
OCR PP Set 3 Pure Paper 1 MS
     
OCR PP Set 3 Pure Paper 2
     
OCR PP Set 3 Pure Paper 2 MS
     
OCR PP Set 3 Statistics Paper 3
     
OCR PP Set 3 Statistics Paper 3 MS
     
OCR PP Set 3 Mechanics Paper 4
     
OCR PP Set 3 Mechanics Paper 4 MS

June 2019

     
June 2019 Pure Paper 1
     
June 2019 Pure Paper 1 MS
     
June 2019 Pure Paper 2
     
June 2019 Pure Paper 2 MS
     
June 2019 Statistics Paper 3
     
June 2019 Statistics Paper 3 MS
     
June 2019 Mechanics Paper 4
     
June 2019 Mechanics Paper 4 MS

November 2020

     
November 2020 Pure Paper 1
     
November 2020 Pure Paper 1 MS
     
November 2020 Pure Paper 2
     
November 2020 Pure Paper 2 MS
     
November 2020 Statistics Paper 3
     
November 2020 Statistics Paper 3 MS
     
November 2020 Mechanics Paper 4
     
November 2020 Mechanics Paper 4 MS

Teacher Z (Pure)

     

Topic Z1: Vectors

     
Lessons
     
Review of AS vectors
     
Equation of a plane
     
Intersection between a line and plane
     
Angle between a line and a plane
     
Angle between two planes
     
Shortest distance between a point and a line
     
Shortest distance between a point and a plane
     
Shortest distance between two skew lines
     
Linear simultaneous equations
     
Intersections of planes
     
Topic test preparation
     
Z1 (Pre-TT A) Vectors Z1 (Pre-TT A) Vectors MS
     
Z1 (Pre-TT B) Vectors Z1 (Pre-TT B) Vectors MS
     
Z1 (Post-TT A) Vectors Z1 (Post-TT A) Vectors MS
     
Z1 (Post-TT B) Vectors Z1 (Post-TT B) Vectors MS

Topic Z2: Complex numbers

     
Lessons
     
Review of AS complex numbers
     
De Moivre's Theorem
     
Complex exponents including Euler's formula
     
Roots of complex numbers
     
Roots of unity
     
Further factorising
     
Geometry of complex numbers
     
Deriving multiple angle formulae
     
Application of multiple angle formulae to polynomial equations
     
Expressing powers of trigonometric functions using multiple angles
     
Trigonometric series
     
Topic test preparation
     
Z2 (Pre-TT A) Complex numbers
     
Z2 (Pre-TT A) Complex numbers MS
     
Z2 (Pre-TT B) Complex numbers
     
Z2 (Pre-TT B) Complex numbers MS
     
Z2 (Post-TT A) Complex numbers
     
Z2 (Post-TT A) Complex numbers MS
     
Z2 (Post-TT B) Complex numbers
     
Z2 (Post-TT B) Complex numbers MS

Topic Z3: Hyperbolics and further calculus

     
Lessons
     
Defining hyperbolic functions
     
Inverse hyperbolic functions
     
Hyperbolic identities
     
Solving harder hyperbolic equations
     
Differentiation of hyperbolic functions
     
Integration of hyperbolic functions
     
Differentiation of inverse trigonometric functions
     
Differentiation of inverse hyperbolic functions
     
Integration involving inverse trigonometric and hyperbolic functions
     
Using partial fractions in integration
     
Maclaurin series
     
Using standard Maclaurin series
     
Improper and infinite integrals
     
Volumes of revolution
     
Mean value of a function
     
Topic test preparation
     
Z3 (Pre-TT A) Hyperbolics and further calculus
     
Z3 (Pre-TT A) Hyperbolics and further calculus MS
     
Z3 (Pre-TT B) Hyperbolics and further calculus
     
Z3 (Pre-TT B) Hyperbolics and further calculus MS
     
Z3 (Pre-TT C) Hyperbolics and further calculus
     
Z3 (Pre-TT C) Hyperbolics and further calculus MS
     
Z3 (Post-TT A) Hyperbolics and further calculus
     
Z3 (Post-TT A) Hyperbolics and further calculus MS
     
Z3 (Post-TT B) Hyperbolics and further calculus
     
Z3 (Post-TT B) Hyperbolics and further calculus MS

Topic Z5A: Polar coordinates

     
Lessons
     
Curves in polar coordinates
     
Some features of polar coordinates
     
Changing between polar and Cartesian coordinates
     
Area enclosed by a curve
     
Area enclosed by 2 curves

Topic Z4: Differential equations

     
Lessons
     
Exact 1st order differential equations
     
The integrating factor
     
Homogenous 2nd order linear differential equations
     
Differential equations involving complex numbers
     
Non-homogenous 2nd_order linear differential equations
     
Forming differential equations
     
Simple harmonic motion
     
Damping and damped oscillations
     
Coupled 1st order differential equations
     
Topic test preparation
     
Z4 (Pre-TT A) Differential equations
     
Z4 (Pre-TT A) Differential equations MS
     
Z4 (Pre-TT B) Differential equations
     
Z4 (Pre-TT B) Differential equations MS
     
Z4 (Post-TT A) Differential equations
     
Z4 (Post-TT A) Differential equations MS
     
Z4 (Post-TT B) Differential equations
     
Z4 (Post-TT B) Differential equations MS

Topic Z5B: Series

     
Lessons
     
Review of AS proof by induction
     
Induction and series
     
Using standard series
     
The method of differences
     
Topic test preparation
     
Z5 (Pre-TT A) Polar coordinates and series
     
Z5 (Pre-TT A) Polar coordinates and series_MS
     
Z5 (Pre-TT B) Polar coordinates and series
     
Z5 (Pre-TT B) Polar coordinates and series MS
     
Z5 (Post-TT A) Polar coordinates and series
     
Z5 (Post-TT A) Polar coordinates and series_MS
     
Z5 (Post-TT B) Polar coordinates and series
     
Z5 (Post-TT B) Polar coordinates and series MS

Revision

     
     

Edexcel past papers MS

     

     
     
     
     

     
     
     
     

     
     
     
     

     
     
     
     


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