AS Further Mathematics Specification Specification for first teaching in 2017
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Students must be able to use the following formulae and identities for AS and A-level further mathematics, without these formulae and identities being provided, either in these forms or in equivalent forms. These formulae and identities may only be provided where they are the starting point for a proof or as a result to be proved.
has roots
for and
A straight line graph, gradient passing through has equation
Straight lines with gradients and are perpendicular when = 1
General term of an arithmetic progression:
General term of a geometric progression:
In the triangle ABC
Sine rule: = =
Cosine rule:
Area
Circumference and Area of circle, radius and diameter :
Pythagoras’ Theorem: In any right-angled triangle where , and are the lengths of the sides and is the hypotenuse:
Area of a trapezium = , where and are the lengths of the parallel sides and is their perpendicular separation.
Volume of a prism = area of cross section length
For a circle of radius , where an angle at the centre of radians subtends an arc of length and encloses an associated sector of area :
For two complex numbers and :
Loci in the Argand diagram:
is a circle radius centred at
arg is a half line drawn from at angle to a line parallel to the positive real axis.
Exponential form:
For a 2 by 2 matrix the determinant
the inverse is
The transformation represented by matrix AB is the transformation represented by matrix B followed by the transformation represented by matrix A .
For matrices A , B :
( AB )–1 = B –1 A –1
For + + = 0 with roots and :
For + + + = 0 with roots , and :
cosh
sinh
tanh
Area under a curve
Volumes of revolution about the and axes:
Simple Harmonic Motion:
Scalar product of two vectors a and b is
where is the acute angle between the vectors a and b .
The equation of the line through the point with position vector a parallel to vector b is:
r = a +
The equation of the plane containing the point with position vector a and perpendicular to vector n is:
( r – a ) . n = 0
Weight = mass
Friction:
Newton’s second law in the form:
For motion in a straight line with variable acceleration:
The mean of a set of data:
The standard Normal variable: where