Download Word - The Further Mathematics Support Programme

Further Mathematics Support Programme
MEI FP2 – Scheme of Work Template - 2016-2017
This template is part of a series designed to assist with planning and delivery of further mathematics courses.
It shows how Integral Resources and Live Interactive Lectures can be used to support students and teachers.
Integral
Resources
Integral
Resources
Live Interactive
Lectures
Teacher-level access to the Integral Resources (integralmaths.org/) for
Further Pure and Applied units is available free of charge to all
schools/colleges that register with the Further Mathematics Support
Programme: www.furthermaths.org.uk/
Student-level access to the Integral Resources and the Live Interactive
Lectures for Further Mathematics is available at a moderate cost via:
www.furthermaths.org.uk/lilfm
Integral Resources include a wide range of resources for both teacher and student use in learning and assessment. A selection of these are suggested in the
template below. Sample resources are available via: http://integralmaths.org/help/info.php.
Live Interactive Lectures are available for individual Further Pure and Applied units and take place in the spring and autumn terms. LIL FM is ideal for
schools/colleges teaching Further Mathematics with small groups and/or limited time allocation. It is also useful to support less experienced teachers of
Further Mathematics. See www.furthermaths.org.uk/lilfm
Scheduling will depend on circumstances, but the template below breaks the module down into 12 sections which may be allocated approximately equal
time. Each section corresponds to one Live Interactive Lecture (LIL) and these take place fortnightly to supplement the teaching and tutorial support in
schools/colleges and students' own independent study. FMSP Area Coordinators will be able to offer additional guidance if needed. See
www.furthermaths.org.uk/regions
MEI FP2 – Scheme of Work Template - 2016-2017
Topic
Specification statements
Suggested Integral Resources
Matrices 1: The
determinant and
inverse of a 3 x 3
matrix
 Be able to find the
determinant of any 3x3
matrix and the inverse of a
non-singular 3x3 matrix.
► MEI_FP2
/ ► Matrices
/ ► Matrices 1: The
determinant of a 3 x 3 matrix
 Determinants teaching
resources
 Determinant of a 3x3 matrix
(PowerPoint)
 Additional exercise
Assessment
(Integral
Resources)
Live Interactive
Lecture
Other resources
Matrices 1: The
determinant and
inverse of a 3 x 3
matrix
 Section Test M1
► MEI_FP2
/ ► Matrices
/ ► Matrices 2: The inverse of
a 3 x 3 matrix
Matrices 2:
Matrices and
simultaneous
equations
 Be able to solve a matrix
equation or the equivalent
simultaneous equations, and
to interpret the solution
geometrically.
Matrices 3:
Eigenvalues and
eigenvectors
 Understand the meaning of
eigenvalue and eigenvector,
and be able to find these for
2x2 or 3x3 matrices
whenever this is possible.
 Inverse of a 3x3 matrix
(PowerPoint)
 Additional exercise
► MEI_FP2
/ ► Matrices
/ ► Matrices 3: Matrices and
simultaneous equations
 Additional exercise
► MEI_FP2
/ ► Matrices
/ ► Matrices 4: Eigenvalues
and eigenvectors
 Section Test M2
Matrices 2:
Matrices and
simultaneous
equations
 Section Test M3
Matrices 3:
Eigenvalues and
eigenvectors
nrich: Nine eigen
Matrices 4: The
Cayley-Hamilton
theorem
Complex numbers
1: The polar form
of complex
numbers
Complex numbers
2: De Moivre’s
theorem
 Be able to form the matrix of
eigenvectors and use this to
reduce a matrix to diagonal
form.
 Be able to find powers of a
2x2 or 3x3 matrix.
 Understand the term
characteristic equation of a
2x2 or 3x3 matrix.
 Understand that every 2x2 or
3x3 matrix satisfies its own
characteristic equation, and
be able to use this.
 Understand the polar
(modulus-argument) form of
a complex number, and the
definition of modulus,
argument.
 Be able to multiply and
divide complex number in
polar form.
 Appreciate the effect in the
Argand diagram of
multiplication by a complex
number.
 Understand de Moivre's
theorem.
 Be able to apply de Moivre's
theorem to finding multiple
angle formulae and to
summing suitable series.
 Matrices teaching activities
 Eigenvalues and eigenvectors
matching activity
 Additional exercise
 Section Test M4
► MEI_FP2
/ ► Matrices
/ ► Matrices 5: The CayleyHamilton theorem
Matrices 4: The
Cayley-Hamilton
theorem
 Additional exercise
 Section Test M5
► MEI_FP2
/ ► Matrices
► MEI_FP2
/ ► Complex numbers
/ ► Complex numbers 1: The
polar form of complex numbers
 Matrices topic assessment
Complex
numbers 1: The
polar form of
complex numbers
 Additional exercise
 Section Test CN1
► MEI_FP2
/ ► Complex numbers
/ ► Complex numbers 2: de
Moivre's theorem
 de Moivre’s theorem puzzle
 Additional exercise
Complex
numbers 2: De
Moivre’s
theorem
 Section Test CN2
Complex numbers
3: Complex
exponents and
roots
 Understand the definition ejθ
= cos θ + j sin θ and hence
the form z = r ejθ
 Understand the definition ejθ
= cos θ + j sin θ and hence
the form z = r ejθ
 Know that every non-zero
complex number has n nth
roots, and that in the Argand
diagram these are the
vertices of a regular n-gon.
 Know that the distinct nth
roots of rejθ are
1
𝜃 + 2𝑘𝜋
𝑟 𝑛 (cos (
)
𝑛
𝜃 + 2𝑘𝜋
+ 𝑗𝑠𝑖𝑛 (
))
𝑛
Calculus: The
inverse
trigonometric
► MEI_FP2
/ ► Complex numbers
/ ► Complex numbers 3:
Complex exponents
 Complex numbers teaching
activities
 Exponential and polar form
puzzle
 Additional exercise
Complex
numbers 3:
Complex
exponents and
roots
 Section Test CN3
► MEI_FP2
/ ► Complex numbers
/ ► Complex numbers 4:
Complex roots
 Be able to explain why the
sum of all the nth roots is
zero.
 Be able to represent complex
roots of unity on an Argand
diagram.
 Be able to apply complex
numbers to geometrical
problems.
 Complex numbers teaching
activities
 Additional exercise
 Understand the definitions of
inverse trigonometric
functions.
► MEI_FP2
/ ► Calculus
/ ► Calculus 1: The inverse
trigonometric functions
 Section Test CN4
► MEI_FP2
/ ► Complex numbers
 Complex numbers topic assessment
Calculus: The
inverse
trigonometric
ExamSolutions Integration - two
standard integrals
functions and
integration
 Be able to differentiate
inverse trigonometric
functions.
 Recognise integrals of
functions of the form
1
Polar coordinates:
Polar coordinates
and area of a
sector
 Inverse trigonometric
functions (Geogebra)
 Additional exercise
(𝑎2 − 𝑥 2 )−2 , (𝑎2 +
𝑥 2 )−1 and be able to
integrate associated
functions by using
trigonometrical
substitutions.
 Use trigonometric identities
to integrate functions.
► MEI_FP2
/ ► Calculus
/ ► Calculus 2: Integration
using inverse trigonometric
functions
 Understand the meaning of
polar coordinates (r, θ) and
be able to convert from polar
to Cartesian coordinates and
vice-versa.
 Be able to sketch curves with
simple polar equations.
 Be able to find the area
enclosed by a polar curve.
► MEI_FP2
/ ► Polar coordinates
/ ► Polar coordinates 1: Polar
coordinates and curves
 Inverse trigonometric
functions teaching activities
 Additional exercise
 Exploring polar curves
(Geogebra)
 Additional exercise
functions and
integration
 Section Test C1
 Section Test C2
► MEI_FP2
/ ► Calculus
 Calculus topic assessment
Polar
coordinates:
Polar coordinates
and area of a
sector
 Section P1
► MEI_FP2
/ ► Polar coordinates
/ ► Polar coordinates 2: The
area of a sector
 Polar coordinates teaching
activities
 Additional exercise
 Section P2
► MEI_FP2
/ ► Polar coordinates
Power series:
Maclaurin series
Hyperbolic
functions 1:
Introduction
Hyperbolic
functions 2: Inverse
hyperbolic function
 Be able to find the Maclaurin
series of a function, including
the general term in simple
cases.
 Appreciate that the series
may converge only for a
restricted set of values of x.
 Identify and be able to use
the Maclaurin series of
standard functions.
► MEI_FP2
/ ► Power series
/ ► Power series 1: Maclaurin
series
 Understand the definitions of
hyperbolic functions and be
able to sketch their graphs.
 Be able to differentiate and
integrate hyperbolic
functions.
► MEI_FP2
/ ► Hyperbolic functions
/ ► Hyperbolic functions 1:
Introduction
 Understand and be able to
use the definitions of the
inverse hyperbolic functions.
 Be able to use the
logarithmic forms of the
inverse hyperbolic functions.
 Be able to integrate
1
1
(𝑥 2 + 𝑎2 )−2 , (𝑥 2 − 𝑎2 )−2
and related functions.
 Maclaurin series teaching
activities
 Maclaurin series (Geogebra)
 Additional exercise
 Hyperbolic graphs 1
 Hyperbolic graphs 2
 Additional exercise
► MEI_FP2
/ ► Hyperbolic functions
/ ► Hyperbolic functions 2:
Inverse hyperbolic functions
 Hyperbolic functions
teaching activities
 Hyperbolic dominoes
 Inverse Hyperbolic graphs
 Hyperbolic differentiation
dominoes
 Polar coordinates topic assessment
Power series:
Maclaurin series
nrich - What do
functions do for tiny
x?
nrich - Building
approximations for
sin x
 Section Test S1
► MEI_FP2
/ ► Power series
 Power series topic assessment
Hyperbolic
functions 1:
Introduction
nrich – Hyperbolic
thinking
nrich – Gosh cosh
 Section Test H1
Hyperbolic
functions 2:
Inverse
hyperbolic
function
 Hyperbolic integration
dominoes
 Additional exercise
 Section Test H2
► MEI_FP2
/ ► Hyperbolic functions
 Hyperbolic functions topic assessment
Consolidation and
revision
FMSP - Revision
Videos
The study plans available on Integral Resources refer to the 3rd edition MEI FP2 textbook (ISBN 978 0340 889954). Other textbooks covering this course
may be available, and Integral Mathematics Resources does not endorse any particular set of textbooks.