Chapter 1 Algebraic Methods - Year 2

Question 1

What are the 1st step for algebraic fractions?

Answer 1

Multiply both sides by the denominator of the initial fraction

Question 2

After the first step, what are the 2 methods for partial fractions?

Answer 2

Method 1 - substitution
You look at the factors and pick a number which will make everything except 1 variable 0
Then you repeat this for all of the variables (normally A,B,C…)

Method 2 - comparing coefficients
You expand the brackets (in your head or in reality)
Then you know that the x term must = the other x term etc
Then solve the equations simultaneously

Question 3

What are the 2 special cases you need to deal with in partial fractions?

Answer 3

Reated linear factors
Improper fractions

Question 4

What does a repeated linear factor mean?

Answer 4

You have a factor eg (x+1) repeated (squared)

Question 5

How do you do partial fractions with a repeat linear factor?

Answer 5

You add another squared factor to it
See example

Question 6

What is an improper fraction (in terms of this topic)?

Answer 6

A fraction which has the largest degree on the variable at the top

Or

The degrees are the same

Question 7

How do you do partial fractions on an improper fraction?

Answer 7

Method 1: Use long division to get the answer

Method 2: do the normal method

(Sometimes there will be a much quicker way)

Question 8

What are 3 common mistakes/tips for partial fractions?

Answer 8

1) it is useful to always right out the 1st step of the partial fractions (see diagram A)
2) the auestion will often say write so and so in the form: . Make sure to give the answer in that form not just stating A=2 and B=-1
3) if you have A=1/2 or B=4/7 you just write it in the form