Algebraic Methods

Question 1

What should you do when simplifying an algebraic fraction

Answer 1

Factorise the numerator and denominator where possible and then cancel common factors

Question 2

What do you use to divide a polynomial by (x +- p) where p is a constant

Answer 2

You can use long division

Question 3

If f(x) is a polynomial the factor theorem states what

Answer 3

If f(p) = 0, then (x - p) is a factor of f(x)

If (x - p) is a factor of f(x), then f(p) = 0

Question 4

What must you do for mathematical proof

Answer 4

State any information and assumptions you are using

Show every step of your proof clearly

Make sure that every step follows logically from the previous step

Make sure you have covered all possible cases

Write a statement of proof at the end of your working

Question 5

What should you do to prove an identity

Answer 5

Start with the expression on one side of the identity

Manipulate that expression algebraically until it matches the other side

Show every step of your algebraic working

Question 6

What are the two ways to prove a mathematical statement is true

Answer 6

Deduction and exhaustion

Question 7

What is the way to prove a mathematical statement is not true

Answer 7

Counter - example

Question 8

What is deduction

Answer 8

This means starting from known facts or definitions, then using logical steps to reach the desired conclusion

Question 9

What is exhaustion

Answer 9

This means breaking the statement into smaller cases and proving each case separately

Question 10

What is counter - example

Answer 10

A counter - example is one example that does not work for the statement. You do not need to give more than one example, as one is sufficient to disprove a statement