a level (f)m

what is meant by “necessary”?

it is used when giving the conditions under which a statement is true

⇒

what is meant by sufficient?

when giving conditions under which you can be certain that a statement is true

⇐

what is a converse

think of it as “if … then …”

but the … are swapped to make sense

proof by deduction

logical argument as to why the conjecture must be true

proof by exhaustion

test all the possible cases

proof by counter example

find one case where it isn’t true

index laws: multiplication

a^m x aⁿ = a^m+n

index laws: power to another power

(a^m)ⁿ = a^mn

index laws: division

a^m / aⁿ = a^m-n

index laws: 0

a⁰ = 1

index laws: negative indicies

a^-m = 1 / a^m

index laws: fractional indicies

^m√a = a^1/m

index laws: mixed bases

(a x b)^m = a^m + b^m

strictly greater or less than inequality

hollow circle or line

greater than or equal to

less than or equal to

inequality

filled circle or line

equation of a circle

(x-a)² + (y-b)² = r²