Summary IEB Further Studies Mathematics Paper 1 Notes

IEB: FURTHER STUDIES
MATHEMATICS (P1)

Module 1: SPLIT DOMAIN & COMPOSITE
FUNCTIONS
SPLIT DOMAIN FUNCTIONS
In a split domain function, different ‘rules’ apply to different parts of the domain. Use
the following approach to drawing graphs of split functions:

Indicate the boundaries with dotted lines.

For each interval determine and mark the endpoints at the boundaries; mark any
other important points within the interval (e.g. intercepts with axes, turning
points, etc.) and draw the graph.

Remember to use hollow dots for > and < and solid dots for ≥, ≤ and =

Reminder: For a function, each x-value has only ONE corresponding y-value.

COMPOSITE FUNCTIONS
The composite function f ∘ g(x) – read as “f circle g” or “f of g” – is defined by f(g(x))



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IEB: FURTHER STUDIES MATHEMATICS (P1) 1

, Module 2: TRIGONOMETRY




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Module 3: PARTIAL FRACTIONS
INTRODUCTION DETERMINING PARTIAL
Rational algebraic fractions can be FRACTIONS
either proper or improper: In general use the following procedure:




Algebraic partial fractions only apply to
PROPER FRACTIONS (for improper



IEB: FURTHER STUDIES MATHEMATICS (P1) 2

, fractions first divide out and then
resolve the resulting proper fraction into
partial fractions if necessary).




COVER-UP METHOD

(only works for non-repeated linear
denominators)
…for determining the value of A , since
it is a partial fraction with a non-
repeated linear denominator.




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Module 4: POLYNOMIAL AND RATIONAL
INEQUALITIES
POLYNOMIAL INEQUALITIES RATIONAL INEQUALITIES
NB: For rational inequalities, DON’T
MULTIPLY THROUGH BY THE LCD.
Move everything to the LHS and put
everything over a common denominator
instead.




IEB: FURTHER STUDIES MATHEMATICS (P1) 3