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

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

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

& oblique collisions

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

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

& continuous random variables

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

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

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

Y5 Sample means (Pre-TT)

Y5 Sample means (Pre-TT) MS

Y5 Sample means (Post-TT)

Y5 Sample means (Post-TT) MS

and markschemes

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

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

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

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 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 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

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

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

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

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

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

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

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

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

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

Review of AS proof by induction

Induction and series

Using standard series

The method of differences

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

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