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.