CE Additional Mathematics-A Summary
Part 1- Revision Notes
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Differentiation
When
x gets very close to the value a, the
value of f(x) gets very close to b, we
write
f(x) has a limiting value b when x approaches a.
Some
properties of limit:
1.
2.
3.
if
Derivatives
1)
derivative of a constant
2)
the power rule
n
is any real number
3)
4)
The sum rule
5)
The product rule
6)
The quotient rule
if
g(x)
0
7)
The chain rule
F(x) is an antiderivative of f(x) if F?x) = f(x)
Rules
for integration
Probability-
Experiments, Sample Spaces, and Events
Example:
Daniel wants to toss a coin and
observe whether it falls ˇ§headsˇ¨ or ˇ§tailsˇ¨.
We
call this activity an experiment
(an activity with observable results).
ˇ§Headsˇ¨
and ˇ§tailsˇ¨ are the two outcomes
(the results of the experiment). H
denotes the outcome ˇ§headsˇ¨ and T
denotes the outcome ˇ§tailsˇ¨.
The sample
space (the set consisting of all possible outcomes of an experiment)
is given by {H, T} = S.
The
events (subsets of a
sample space of an experiment) of the experiment, the subsets of S,
are {H}, {T}, {H,
T} and Æ.
The empty set, Æ,
is called the impossible event. There is no element (outcome) in Æ.
The
union of the two events E
and F is the event EÈF
(the set of outcomes of E and/or F)
The intersection of the two events E and F is the event EÇF (the set of outcomes of E and F)
The
complement of an event E
is the event
(the set of all the outcomes in the
sample space S that are not
in E)