DRILL 1

Question 1

ABCD is a square with side length 2.

Quantity A	Quantity B
The area of the shaded region	π

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 2

What is the degree measure of the smaller angle formed by the hands of a circular clock when it is 10:00?

Question 3

The area of circle C is 9π.

Quantity A	Quantity B
The radius of circle C	6

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 4

Line segments UV, WX, and YZ are diameters of the circles with centers A, B, and C, respectively. If YZ = 2, then what is the area of the circle with center A?

      4π

      8π

      9π

    16π

    64π

Question 5

Quantity A	Quantity B
The circumference of a circle with a diameter of 6	The circumference of a circle with a radius of 12

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 6

Quantity A	Quantity B
Four times the area of a circular region with a circumference of 4π	The circumference of a circular region with an area of 64π

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 7

An office needs to buy circular pizzas for 20 employees. If each pizza is cut into equal slices, and each slice has a central angle of 40°, what is the minimum number of pizzas that need to be ordered so that each employee gets at least two slices of pizza?

Question 8

Triangle ABC is equilateral. If the circle with center A has a diameter of 6, what is the length of the darkened arc?

    

    π

    6

    6π

    

Question 9

A circle with center C has a radius of 6.

Quantity A	Quantity B
The ratio of the circumference of C to the radius of C	Half the diameter of C

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 10

O is the center of the circle above.

Quantity A	Quantity B
Length of line segment AB	Length of line segment CD

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 11

A circle of radius 3 is inscribed in a square. What is the product of the perimeter and area of the square?

Question 12

In the figure above, a rectangle is inscribed in a circle. Lengths x and y are both integers such that x + y = 10, and 1 < x < y. Which of the following are possible values for the diameter of the circle?

Indicate all such values.

    

    

    

    

    

    

    10

Question 13

The height of a right circular cylinder is increased by p percent and the radius is decreased by p percent.

Quantity A	Quantity B
The volume of the cylinder if p = 10	The volume of the cylinder if p = 20

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 14

The diameters of the semicircles above are 8, and the diameter of the semicircle on the right is perpendicular to those of the other two semicircles. What is the total area of the shaded region?

    12π + 64

    24π + 12

    24π + 48

    32π + 48

    32π + 64

Question 15

Triangle ACE is equilateral with side lengths of 8. Points B and D are the midpoints of line segments AC and CE respectively. Line segment BD is a diameter of the circle with center F. What is the area of the shaded region?

    

    

    

    

    

Question 16

Quantity A	Quantity B
The area of a square with a perimeter of p	The area of a circle with a circumference of p

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.

Question 17

Line AB passes through the center of circle O and through the centers of each of the 3 identical smaller circles. Each circle touches two other circles at exactly one point each.

Quantity A	Quantity B
The circumference of circle O	The sum of the circumferences of the 3 smaller circles

    Quantity A is greater.

    Quantity B is greater.

    The two quantities are equal.

    The relationship cannot be determined from the information given.