External Evaluation of the European Baccalaureate (Annexes)

STUDY OF
REAL
FUNCTIO
NS OF A
REAL
VARIABLE
INTEGRAT
ION
GEOMETR
Y IN 3-D
Vectors in
• Increase and decrease of a
function
• Asymptotes on the graph of a
function
• Concave/convex nature of the
graph of a function, points of
inflection; tangents at such
points
• Applications of these ideas to
the study of polynomial,
rational, circular functions
Year 7
• Integral of a function defined
on a closed and bounded
interval
• Graphical interpretations of
such integrals as area
• Properties of integrals
• Mean value of a function on an
interval
• Indefinite integrals of a function
continuous over an interval
• Evaluation of integrals by the
following methods:
• Integration by inspection
• Integration by parts
• Integration by substitution
• Applications of these methods
to the functions studied
previously
• Application of the theory of
integration to finding plane
areas and volumes of
revolutions generated by
rotation around the x axis
• First order differential
equations with variables
leading to the form y’.f(x)= g(x)
• Points, lines, planes, spheres
• Vectors in 3-D definition
• Sum and product of vectors
• Vector equation of line
53
rate of change as a differential equation
• use and initial condition to find a
particular solution of a differential
equation
• interprets the solution of a differential
equation in the context of a problem
modelled by the equation
C2
• Understand indefinite integration as the
reverse process of differentiation
• Solve problems involving the evaluation
of a constant of integration
• Evaluate definite integrals
• Use integration to find the area of a
region bounded by a curve
• Use the trapezium rule to estimate the
area under a curve
C3
• Integrate eⁿ and 1/x with constant
multiples, sums and differences
• Integrate expressions involving a linear
substitution
• Use definite integration to find the volume
of revolution
C4
• Integrate rational functions by means of
decomposition into partial fractions
• Recognise an integrand of the form k
f’(x)
o f(x)
• Recognise when an integrand can be
usefully regarded as a product
• Use a given substitution to simplify and
evaluate either a definite or indefinite
integral
• Find by integration a general form, of a
solution for a differential equation where
the variables are separable
C4
• Use standard notation for vectors
• Carry out addition and subtraction of