K5FM5 Polynomial roots and finite sums personal learning checklist

Edexcel A-level Further Mathematics · Core Pure · either mandatory paper

Name ____________________ Class __________ Date __________

Tick one box per statement. Red: need help. Amber: partly confident. Green: can do independently.

I can	Red	Amber	Green
Roots and coefficients through quartics
derive and apply coefficient relations to quadratic, cubic and quartic root lists
calculate higher-power and reciprocal expressions with explicit exclusions
evaluate shifted root products by polynomial substitution with degree-sensitive signs
Forming polynomials with transformed roots
form complete cubic and quartic equations under scale-and-shift root changes
Standard finite sums and changed bounds
derive exact polynomial sums from the standard integer, square and cube identities
handle shifted indices, parity subsequences and parameter-dependent summation bounds
Method of differences and partial fractions
derive rational telescoping identities with exact decomposition and complete boundary terms
use polynomial differences to derive finite power sums
distinguish exact finite sums from limits of their partial sums

Next revision priority: __________________________________________________