# FP1 test paper and mark scheme, December 2014, 2015, 2016

Correct bit-by-bit

Write neatly, give yourself plenty of space, always write each line below the previous line (leaving lots of blank space on the right of the page if necessary), and do big, clear diagrams with a ruler.

Try not to have your working run over from one page to the next. If a question is going to need long working, then start a new page with it. Be concise in your working (this isn’t GCSE: you don’t have to show every tiny step).

Then, if an answer looks wrong, or your working shows something different from the formula you are asked to prove, donâ€™t cross out everything and start again. Continue reading

# FP1 June 2013 “withdrawn” paper and worked answers

This paper was used for a mock exam in April 2015.

# How to solve cubic equations

In FP1 we study how to get two more roots of a cubic equation if we are given one in advance. But life is not always so generous. How do we solve a cubic if we’re given no root in advance? Continue reading

# “Don’t do it as the book says” notes, FP1

Proof by induction

Set out proofs as Step 1 (prove claim true for n=1) and Step 2 (prove claim infectious, i.e. if it’s true for n=k, then it’s true for n=k+1), plus a final line: “Step 1 + Step 2 ⇒ true for all n, by induction”. Continue reading