NAME: ____________________                                                               DATE: ____________

 

 

Geometry in Nature

End of Unit Exam

 

 

For problems 1 – 3, write out the terms of the sequences from the explicit formula.  5 points each

 

1.    

 

 

 

 

 

2.    

 

 

 

 

 

3.    

 

 

 

 

 

For problems 4 – 6, find the explicit formula from the given sequence.  5 points each

 

4.     4, 6, 13.5, 20.25, 30.375, 45.5625

 

 

 

5.     3, 5, 7, 9, 11, 13

 

 

 

6.     55, 89, 144, 233, 377, 610, 987

 

7.     If a shape ÒmatchesÓ itself only once in a full rotation, it has rotational symmetry.  5 points
 

True / False (circle one).

 

 

8.     This shape is made up of five identical squares. 

 

Draw one more square so that the new shape has exactly one line of symmetry.         

 

Find two different ways to do it on the following figures:  10 points

 

 

9.     Which of the following letters of objects possess rotational symmetry?  5 points
(Circle ALL that apply)

(a) Letter F

(b) Equilateral triangle

(c) Letter X

(d) A rectangle

(e) A square

(f) Letter W

(g) Letter Q

 

 

10.  In the figure shown below, consider the transformation that consists of a reflection through line m, followed by a rotation on 90¡ clockwise around point P.

 

 

(a) Show the position of the letter A shape under this transformation. (Draw it on the figure above making sure I can tell what you intend your answer to be.  5 points

 

(b) Find a transformation or sequence of transformations that undoes what this transformation did.  In other words, what transformation will send the A you drew back to the A in the original position.  5 points

 

 

 

11.  What are the properties of fractals? (Circle one)  5 points

(a) Self-symmetry

(b) Recursion

(c) Infiniteness

(d) Only a and c are correct.

(e) All of the above

 

 

12.  The following table shows iteration results from the Sierpinski Triangle:

 

Stage

# of Shaded Triangles

Number of Unshaded Triangles

0

1

0

1

3

1

2

9

4

3

27

13

4

81

40

 

(a) What is the n-th term formula for shaded triangles? (Show your thought process)  5 points

 

 

 

 

 

(b) What is the n-th term formula for unshaded triangles? (Show your thought process)

5 points

 

13.  Determine which polygon the tessellation was made from by connecting congruent points.  5 points

 

 

 

14.  Show that a 30¡-60¡-90¡ triangle is a rep-3 tile.  5 points

 

 

 

 

 

 

 

 

 

 

 

 

 

15.  Show that a right triangle whose legs measure 2 cm and 4 cm is a rep-5 tile.  5 points

 

 

 

 

 

 

 

 

16.  One property of golden rectangles is that their

 

(a)   If we want to create a golden rectangle with width 9 cm, what would the length be?

5 points

 

 

 

 

 

 

 

 

 

(b)  Draw this rectangle.  5 points

 

 

 

 

 

 

 

 

 

 

Total Score  ______ / 100