Pure 2

Question 1

how can a statement be proven by contradiction?

Answer 1

first assume it is not true i.e. assume the opposite is true
then use logical steps to show this assumption leads to something impossible (contradiction of the assumption or something true)
then conclude the assumption is incorrect so original statement is true

Question 2

how can a rational number be written?
an irrational number cannot be expressed in this form

Answer 2

a/b where a & b are integers

Question 3

how is a single fraction split into partial fractions?

Answer 3

2 (or more) distinct linear factors:
multiple both sides by denominator
substitute values of x to eliminate A, B (or C)
equate coefficients of the same degree of x

repeated linear factor:
A/factor 1 + B/ factor 2 not repeated + C/factor 2 repeated

Question 4

what is an improper fraction?

Answer 4

fraction whose numerator has a degree equal to or greater than the denominator

Question 5

how is an improper fraction converted into a mixed fraction?

Answer 5

algebraic long division
inspection: relationship F(x) = Q(x) x divisor + remainder