FP1 REVISION SHEET
TOPIC
COMPLEX NUMBERS
Find imaginary roots of a quadratic
Multiply out complex numbers (2 + 3i)(5-6i)
Find complex conjugate
Given the complex roots, find the quadratic equation
Divide complex numbers
Find modulus and argument and show on Argand diagram
Write complex number in the form r(cos Ѳ + i sin Ѳ)
Use the properties of modulus: |z1z2| = |z1| |z2|
Use the properties of argument: arg (z1z2) = arg z1 + arg z2
Find square roots of complex numbers
Solve higher order polynomials (cubics and quartics)
MATRICES
Know when you can multiply two matrices
Know how to multiply two matrices
Use matrices to describe linear transformations
Find the matrices that represent given tranformations
Find the transformation associated with a given matrix
Use matrix products to represent combinations of
transformations
Find the determinant of a matrix
Find the inverse of a matrix
Know the terms singular and non-singular
Prove the result (AB)-1 = B-1 A-1
Use inverse matrices to reverse a transformation
Use the determinant to find the area scale factor
Use inverse matrices to solve simultaneous equations
SERIES
Use sigma notation to denote series
Use and know the formula for Σr
Use Σr2 and Σr3
Write solutions in fully factorised form
Sum more complex series, e.g. Σr(2r + 1)(r – 2)
PROOF BY INDUCTION
Set out solutions correctly with all the relevant comments
Use induction to prove results about series
Use induction to prove results about recurrence formulae
Use induction to prove results about matrices
Use induction to prove results about divisibility
NUMERICAL METHODS
Use the sign change method
Solve equations using interval bisection
Solve equations using linear interpolation
Solve equations using the Newton-Raphson process
COORDINATE SYSTEMS
Understand parametric equations and how to use them
Use properties of parabolas to solve problems
Use properties of hyperbolas to solve problems
Find equations of normals and tangents
Solve problems, e.g. finding triangle areas, intersections, etc.
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