Mathematics 30-2 Unit 1 Quiz Logical Reasoning February 20, 2015Name:

1. The Fibonacci Sequence is a pattern of numbers (1, 1, 2, 3, 5, 8, …) and appears repeatedly in nature. Visually, we can arrange the numbers as a series boxes added in such a way that two boxes add to create the next larger box. Drawing a continuous curve diagonally from corner to corner in successive boxes creates a spiral shape.

Examples of the sequence can be seen in the lengths of the bones in our fingers to the structure of nautical shells and leaves.

Continuing the pattern of 1, 1, 2, 3, 5, 8, …, determine the next two numbers in this sequence. The next two numbers, written in sequence one after the other are:

____ ____ ____ ____

2. Consider the pattern “Ace of Hearts, Two of Clubs, Three of Diamonds, Four of Spades.” Would the “Jack of Diamonds” fit this pattern? Justify your answer. (2 marks)

3. A Pythagorean Triple is a set of three integer (i.e. no decimals) numbers that work in the Pythagorean Theorem:

�Pythagorean Triples are listed in the order “a - b - c” such as “4 - 3 - 5” which means that in this triple a = 4, b = 3 and c = 5. The first four Pythagorean Triples in one particular family of triples are listed in the table below.

Extending to the next Pythagorean Triple, value that would appear where “n” is located in the table would be:

____ ____ ____ ____

4. A child’s worksheet checks for pattern recognition.

If the pattern of these questions continue onto a fifth question, then the answer to that fifth question would contain which shape?

a2 + b2 = c2

a b c

4 3 5

8 15 17

12 35 37

16 63 65

20 m n