TEST 1

Question 1

Golden Rule/ Fibonacci Sequence

Answer 1

The rule for generating success of numbers in the sequence is to add up the previous two terms.
1, 1, 2, 3, 5, 8, 13, 21…

Question 2

Checking Bar Codes

Answer 2

(3n) + n + (3n)…. needs to = 0

Question 3

Coding Checks

Answer 3

(7xn) + (3xn) + (9xn)… needs to equal 0

Question 4

Rational Number

Answer 4

A number that can be written as a fraction a/B or -A/B in which a and B are natural numbers or a=0

Question 5

Converting to Base 10

Answer 5

5 4 3 2 1 0

1 0 1 0 1 0

Question 6

1 to 1 Correspondence

Answer 6

To collections who’s objects can be paired evenly

Question 7

Prove the Cube Root of 5 to be Irrational

Answer 7

Suppose 5=(a/b)^3 where a and B are in their lowest terms. Then we can multiply b^3 to each side in order to get 5b^3=a^3. When we tried to solve this equation we get 5b^3=125a^3 ———–> b^3=25a^3. Both A and B must have a factor five but a and B have no common factors greater than one. This is a contradiction therefore proving that the cube root of 5 is irrational.

Question 8

Prove that there is an Infinite Number of Primes

Answer 8

Suppose that there are only a finite amount primes.what save their are n of them. If we tried to get a new number we can use
P=p1 x p2 x p3 x … x pn +1
P has to equal and numbered larger than any prime. Since p1 - pn are all the available primes then P cannot be a prime and could be divisible by one of the pimes available. Thus making it impossible for there to be a finite number of primes.