External Evaluation of the European Baccalaureate (Annexes)

ANALYSIS
Real
functions
of a real
variable
Continuity
and limits
of complex numbers
• Complex conjugates
• Operations on complex
numbers
• Reciprocal of non-zero
complex number
• Square roots of a
complex number
• Solution of quadratics
with complex coefficients
• Geometric representation
of a complex number
• Trigonometric form
• Modulus of a complex
number, of a product and
of a quotient
• Argument of a non-zero
complex number, of a
product, of a quotient
• Powers, nth roots
• De Moivres theorem
• Definition of a real function
• Domain of a function
• Zeros of a function, sign of a
function
• Even and odd functions
• Periodic functions
• Composition of two functions
• Inverse of a bijection
• Increasing and decreasing
functions, constant, monotonic,
over an interval. Local and
global extrema
• Graph of a function
Year 7
• Apply the above to absolute
value, polynomials, rational
functions and those involving
square roots
• Circular functions
• Natural logarithm functions
• Exponential function with base
e
• Functions obtained by addition,
multiplication , division or
composition
• Notion of continuity of a
function at a point
• Continuity of a function from
the right
• Continuity of a function over an
open interval
• Statement without proof of
theorems concerning continuity
– of the absolute value of a
continuous function
51
numbers
• Complex conjugates
• Operations on complex numbers
• Argand diagram
• Two square roots of complex numbers
• Illustrate simple equations and
inequalities involving complex
numbers by means of loci in an
Argand diagram
FP2
• Multiplication and division of two
complex number expressed in polar
form
• Understand De Moivres theorem
• Find and use nth roots of unity
• Use expression for sine θ and Cos θ in
expressing powers of sine θ and Cos θ
in terms of multiple angles and
summing series
C1
• Understand and use the relationship
between the graphs of y = f(x), y=a f(x),
y=f(x) +a y = f( x + a), y = f(ax) express in
terms of translations, reflections and
stretches
C3
• Understand terms function, domain, 1 to
1 function, inverse function an
composition of functions
• Identify the range of a functions
• Illustrate in graphical terms the relation
between 1 to 1 functions and its inverse
• Understand the meaning of |x|
• Understand the relationship between the
graphs of y=f(x) and y=|f(x)|
• Use and recognise the compositions of
transformations of graphs
• Understand the properties of exponential
and logarithmic functions and their
graphs
• Understand exponential growth and
decay