FP1 Revision Sheet

Basics of all Edexcel FP1 topics.

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  • Created on: 24-11-11 09:40
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Ellie Griffiths ­ FP1 Revision Sheet
Complex numbers:
Complex numbers are in the form a + bi, where a
and b are real numbers:
The complex conjugate of complex number z:
If roots and of a quadratic are complex, they
will be a complex conjugate pair.
If one root of anything is complex, another root
will be its complex conjugate.
Complex numbers in the form z = x + yi may be
represented on an Argand diagram where (x, y)
are Cartesian coordinates.
The modulus of complex number z = x + yi, known
as r or |z| or |x + yi|:
The argument arg z is the angle between the
positive real (x-) axis and the vector
The modulus-argument form of z = x + yi:
For complex numbers z1 and z2:
Interval bisection:
Find an interval in which f(x) changes sign.
Take the mid-point as an approximation.
Repeat using mid-point between previous mid-point and original limit where there is a change of
sign.
Linear interpolation:
Draw a sketch of function f(x) for given interval [a, b]
Join a line between points on curve at x-coordinates a and b. Where this line intercepts the x-axis is
your next approximation.
Use similar triangles to find this point: ratio of heights is same to ratio of bases.
Repeat using approximation and one of the original limits where there is a change of sign between
them. Repeat until answer found to required degree of accuracy.
Netwon-Raphson:

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Ellie Griffiths ­ FP1 Revision Sheet
Parabola:
A parabola is a set of points which are equidistant from the focus S and a line
called the directrix.…read more

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Ellie Griffiths ­ FP1 Revision Sheet
If you have a recurrence relation, check for more than one basic case of n to see if all are true.
Assume that it is true for k equivalents to starting numbers.
eg. Un+2 relation , given u1 and u2, check true for n = 1, 2, 3 and assume true for n = k and n = k + 1.…read more

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