C4 Summary Revision Table

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  • Created on: 05-09-13 11:50
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Core 4 Summary Revision Table
Algebra & Functions Binomial Series Trigonometry
Remainder Theorem ­ when a From C2 the Binomial Expansion is developed to : Solving equations (in degrees or radians) and
polynomial f(x) is divided by ax+b, proving identities using compound and multiple
angle identities.
then = R, where R is where n is not a positive integer, and is only valid for
the remainder. 1<x<1 ie |x|<1
Factor Theorem ­ if axb is a To obtain the binomial expansion where n is fractional or
negative, and state the valid interval.
factor of f(x) then Expansion of by first factorising to
Simplifying Rational Functions
Note: the above are in the formula booklet, but
you need to know or work out the following :
ie where both f(x) and Use of binomial expansion to find a numerical
p(x) are polynomials. approximation.
Expressing algebraic fractions in Use with partial fractions to expand a rational function
partial fractions, including where
there is a repeated factor in the
Harmonic Form
Expressing a function in the
where R > 0 and is acute

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Hence, to solve equations in the form
and find maximum and
minimum values for such functions
Exponential Models Further Calculus Vectors
From coordinates (a, b, c) to
Solving problems relating to Differentiation Methods :
exponential growth and decay
models : Solving problems involving Implicit functions
eg eg in the form Position Vector : or
Solving problems involving the
Exponential Function, Solving problems involving parametric equations, Direction vector :
given by: eg in the form Resultant vector :
Modulus or Magnitude of a vector, v:
,…read more

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Applications of differential equations, involving
Growth and Decay functions, whereby differential
equations are of the form: where is a scalar
or r = a +(b a)
Determining points on the line, by
substitution, and intersection of lines, by
solving simultaneous equations. Also,
parallel and skew lines (ie no point of
Determining the perpendicular distance
from a point to a line (shortest distance).…read more



An excellent summary sheet of core 4 theory and formulae.  Thoroughly reccommended.

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