# A2 Further Mathematics

## Past mock examinations

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

### Teacher X (Mechanics)

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#### Topic X4: Centre of mass

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

#### Topic X5: Variable forces                 & oblique collisions

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

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### Teacher Y (Statistics)

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#### Topic Y4: Non-parametric tests                 & continuous random variables

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

#### Topic Y5: Sample means

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

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### OCR past papers and markschemes

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#### Sample assessment material (SAM)

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

#### Practice papers Set 1

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

#### Practice papers Set 2

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

#### Practice papers Set 3

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

#### June 2019

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

#### November 2020

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

### Teacher Z (Pure)

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#### Topic Z1: Vectors

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

#### Topic Z2: Complex numbers

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

#### Topic Z3: Hyperbolics and further calculus

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

#### Topic Z5A: Polar coordinates

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

#### Topic Z4: Differential equations

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

#### Topic Z5B: Series

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

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### Edexcel past papers MS

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