509028
Description
Mathematics:
Further Pure 3
- Differential Equations
- Find the complementary function for a
1st or 2nd order differential equation
- The general solution is the sum
of the complementary function
and a particular integral
- Use substitutions in differential equations
- Find an integrating factor
- Use to find a general solution
- Use to find a general solution
- Understand the meaning of...
- Complementary function
- Particular integral
- Complementary function
- Find a particular integral for
a linear differential equation
- Find coefficients given a particular integral
- Find coefficients given a particular integral
- Find a particular solution
and interpret in terms of
the problem modelled
- Find the complementary function for a
1st or 2nd order differential equation
- Vectors
- Use equations of lines and
planes to solve problems...
- Determine whether a line lies in a plane, is
parallel to a plane, or intersects a plane and find
the point of intersection of a line and a plane
- Find the line of intersection
of two non-parallel planes
- Find the perpendicular
distance from a point to a
plane and from a point to a line
- Find the angle between a line and a plane and the angle between two planes
- Find the shortest distance between two skew lines
- Determine whether a line lies in a plane, is
parallel to a plane, or intersects a plane and find
the point of intersection of a line and a plane
- Vector product of two vectors
- In geometrical terms
- In geometrical terms
- Understand the symbols
used in expressing vectors
- Use equations of lines and
planes to solve problems...
- Complex Numbers
- Use de Moivre's theorem to express trigonometrical
ratios of multiple angles in terms of powers of
trigonometrical ratios of the fundemental angle
- Understand de Moivre's theorem in terms
of the geometrical effect of multiplication
and division of complex numbers
- Use expressions for sin and cos in exponential form
- Find and use the nth roots of unity
- Multiply and divide two complex
numbers expressed in polar form
- Understand geometrically
- Understand geometrically
- Use de Moivre's theorem to express trigonometrical
ratios of multiple angles in terms of powers of
trigonometrical ratios of the fundemental angle
- Groups
- Show whether a given
structure is, or is not, a group
- Use algebraic methods to
establish properties in groups
- Define group
- Understand 'order' and determine
the order of elements in a group
- Subgroups and subsets
- Apply Lagrange's theorem
- Recall the meaning of the term 'cyclic''
- Understand isomorphism
- Show whether a given
structure is, or is not, a group
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