Further Maths As Pure

Question 1

Roots if polynomials usbtjoin, remember when squaring a fraction what are you also squaring

Answer 1

The DENOMINATOR TOO

Question 2

For finding roots, if it’s 3, then you can use factor theorem, otherwise if they give ine comolex snd quadratic what ti do

2) if they just say fund them, what o do)

Answer 2

Use conjugate
Make quadratic
Divide
Solve

2) classic maths, inspect a root divide

Question 3

Remmeber to expand quadratic

Answer 3

Can do sun and product but easier ti factories

Make it Z - 2 sqaured - (I ) 2

Question 4

If it starts on the 2nd term how can you easily adjust it

Answer 4

Just find the first term and find the thing again

Question 5

Always simply the quadratic in summations if you can!

Question 6

Partial fractions, in each case, what must the denominators look like
(So special case for when you can’t split one term in denimiatornjnti linear)

Answer 6

Too must be one order less always than bottom

This only if you can’t split

So is would be Ax +b

Question 7

And what if it’d a cubic / quadratic

Answer 7

This is improper, this will return a linear and a remainder, which can be written in partial fractions

Linear & Ax +B + C/ 1 + D 2nd

Question 8

If the summations is similar to what you know, like from r=2 to n of just r, how to ADJUST so yiu can write that down

Answer 8

We know from r=1 to n, so write this down

Essentially we’ve gone back one step, so muktilky the 1 by n it’s just 1

Okay so we need to subtract the first erm so just subtract 1: