Thinking About Circles

  1. Syllabus
  2. Class Test
  3. Outcomes

More About Circular Reasoning

Research

  1. Design Problem
  2. Literature Review
  3. Work Models
  4. Design Patterns
  5. Design Experiments
  6. Lesson Ideas
  7. Montessori Computes
  8. Thinking About Circles

Related Links

Patterns and Design

Montessori

 

Class Test

Below is a reproduction of the Thinking About Circles Prettest given on April 5, 2003. The same questions were used in the posttest on May 17, 2003.

Name ______________________________________          Total Score _________

 

Thinking About Circles Prettest

 

 

This question requires you to show your work and explain your reasoning. You may use drawings, words, and numbers in your explanation. Your answer should be clear enough so that another person could read it and understand your thinking. It is important that you show all your work.
 

1. 

Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities.

KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below.

On the next page, draw a diagram that shows the following.

Highway 7
The location of the two radio stations
The part of Highway 7 where both radio stations can be received


Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received.
 

 



 

 

2. 

The sum of the measures of the 24 angles in a 24-sided regular polygon is 3,960°. What is the measure in degrees of one of the angles?
 

Answer:____________________
 

 


 

 

Stimulus Image

 3. 

In the rectangle above, the intersection of triangle ABC and triangle ADC is which of the following?

A) 

A right angle

B) 

A vertex of the rectangle

C) 

A diagonal of the rectangle

D) 

A pair of parallel sides

E) 

A pair of perpendicular sides

 


 

 

Stimulus Image

 4. 

The sum of the measures of angles 1 and 2 in the figure above is 90°. What is the measure of the angle formed by the bisectors of these two angles?

A) 

60°

B) 

45°

C) 

30°

D) 

20°

E) 

15°

 


 

 

Stimulus Image

 5. 

Point O is the center of the circle above. Line segment AC is a diameter of the circle. Line segment BC does not pass through the center of the circle. Which of the following is true?

A) 

AC is longer than BC.

B) 

BC is longer than AC.

C) 

AC and BC are the same length.

D) 

BC is twice as long as OA.

E) 

The lengths of AC and BC change, depending on how this piece of paper is turned.

 


 

 

 6. 

In which of the following circles is the line segment a diameter?

A) 

B) 

C) 

D) 

E) 

 

 


 

 

Stimulus Image

 7. 

The length of a side of the square above is 6. What is the length of the radius of the circle?

A) 

2

B) 

3

C) 

4

D) 

6

E) 

8

 


 

 

 8. 

Which of the following figures contains line segments that are perpendicular?

A) 

B) 

C) 

D) 

 


 

 

 9. 

If the diameter of a circle is 30 centimeters, what is the radius of the circle?

A) 

10 cm

B) 

15 cm

C) 

60 cm

D) 

90 cm

E) 

180 cm

(National Center for Education Statistics, 2003)