Algebraic Methods Flashcards

1
Q

What should you do when simplifying an algebraic fraction

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

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

A

You can use long division

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

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

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What must you do for mathematical proof

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What should you do to prove an identity

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

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

A

Deduction and exhaustion

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

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

A

Counter - example

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is deduction

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is exhaustion

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is counter - example

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly