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Structured Mathematics
PURE MATHEMATICS C2
(September 2004 version, based on IPM)
Assessment format
Examination
1h 30 mins (72 marks)
Section A: 8-10 questions, each worth no more than 5 marks, total: 36 marks.
Section B: 3 questions, each worth about 12 marks, total: 36 marks.
Coursework
None
Topic
Competence
Book Reference
Understand the
meaning of the word
logarithm.
Understand the laws of
logarithms and how to
apply them.
Know the value of log a a
and log a 1
Know how to convert
from index form to
logarithmic form and
vice versa.
Know the function
y  a x and its graph.
Be able to solve
equations of the form
ax  b .
Know how to reduce the
equations y=axn and
y=abx to linear form
and, using experimental
data, to draw a graph to
find values of a, b and n.
p410
definition
p414
17C q1,2
p410
definition
p414
17C q3
ALGEBRA
Logarithms
Structured Mathematics C2 (September 2004)
page 1/5
Progress
SEQUENCES
AND SERIES
Definitions of
sequences
Arithmetic series
Geometric series
Know what a sequence
of numbers is and what
are meant by finite and
infinite sequences.
Know that a sequence
can be generated using
a formula for the kth
term, or a recurrence
relation of the form
ak 1  f (ak ) .
Know what a series is,
and the difference
between convergent
and divergent series.
Be familiar with 
notation.
Know and be able to
recognise the
periodicity.
Know what is meant by
an arithmetic series &
sequences.
Be able to use the
standard formulae
associated with
arithmetic series.
Know what is meant by
a geometric series.
Be able to use the
standard formulae
associated with
geometric series.
Know the condition for a
geometric series to be
convergent and be able
to find the sum to
infinity.
Be able to solve
problems involving
arithmetic and
geometric series.
Structured Mathematics C2 (September 2004)
p235
9A q1,4
p235
9A q1,4
p241
9B q1
p235
9A q4
p245
9C q1
p245
9C q2,3
p250
9D q1
p250
9D q2,3
p257
9E q1
p257
9E q10,14
page 2/5
TRIGONOMETRY
Basic trigonometry
Know how to solve rightangled triangles using
trigonometry.
The sine, cosine
Be able to use the
and tangent
definitions of sin  and
cos for any angle.
Know the graphs of
sin  , cos and tan
for all values of  , their
symmetries and
their periodicities
Know the values of
sin  , cos and tan
when  is 0°, 30°, 45°,
60°, 90° and 180°.
Identities
Be able to use
sin 
tan  
(for any
cos 
angle).
Be able to use the
identity
cos 2   sin 2   1 , and
the equivalent forms.
Be able to solve simple
trigonometric equations
in given intervals.
Area of a triangle
Be able to use the fact
that the area of a
triangle is given by
1
ab sin C .
2
The sine and cosine Know and be able to
rules
use the sine and cosine
rules.
Radians
Understand the
definition of a radian
and be able to convert
between radians and
degrees.
Be able to find the arc
length and area of a
sector of a circle, when
the angle is given in
radians.
Structured Mathematics C2 (September 2004)
P347
14A q3
P347
14A q1
P353
14B q2
P353
14B q3
P353
14B q5
P353
14B q2
P66
2C q3
P61
2B q1, 2
P70
2D q1, 2
P71
2D q4, 6
page 3/5
CALCULUS
The basic process
of differentiation.
Applications of
differentiation to the
graphs of functions
Integration as the
inverse of
differentiation
Know that the gradient
of a curve at a point is
given by the gradient of
the tangent at the point.
Know that the gradient
of the tangent is given
by the limit of the
gradient of a chord.
Know that the gradient
dy
function
gives the
dx
gradient of the curve
and measures the rate
of change of y with
respect to x.
Be able to differentiate
y  kx n where k is a
constant, and the sums
of such functions.
Be able to find second
derivatives.
Be able to use
differentiation to find
stationary points on a
curve: maxima, minima
and points of inflection.
Understand the terms
increasing function and
decreasing function.
Be able to find the
equation of a tangent
and normal at any point
on a curve.
Know that integration is
the inverse of
differentiation.
Be able to integrate
functions of the form
kx n where k is a
constant and n ≠ -1 and
the sum of such
functions.
Know what are meant
by indefinite and definite
integrals.
Be able to evaluate
definite integrals.
Structured Mathematics C2 (September 2004)
P171
6B
q8a,b,c,d,g,
h
P163
6A q5
(except h, i,
l)
P163
6A, q11
P181
6C q3
P181
6C q5
P171
P193
6B
q8a,b,c,d,g,
h,j
q9a,b,f,g
7A
q10a,b,c,d,i,
j
7A, q1
P205
7B, q1a-f
P195
page 4/5
Integration to find
the area under a
curve.
Be able to find a
constant of integration
given relevant
information.
Know that the area
under a graph can be
found as the limit of a
sum of areas of
rectangles.
Know that an
approximate value of a
definite integral can be
obtained using the
trapezium rule, and
comment sensibly on its
accuracy.
Be able to use
integration to find the
area between a graph
and the x-axis.
P195
7A,
q10a,b,c,d,I,
j
P487
20B q2
P205
7B q24
CURVE
SKETCHING
Stationary points
Be able to use
stationary points when
curve sketching.
Stretches
Know how to sketch
curves of the form
y  af ( x) and y  f (ax) ,
given the curve
of y  f ( x) .
Textbook: “Introducing Pure Mathematics” R Smedley & G Wiseman (IPM)
[WG: 09/95; PJM: 10/96; PJM: 10/97; DJR: 05/00; ET:04/02; HR: 08/04; TEK
04/05]
Structured Mathematics C2 (September 2004)
page 5/5