Geometry Review Final Exam

James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.

Bring lunch: 46 males, 254 females

Buy lunch: 176 males, 264 females

The events "male" and "buys lunch" are not independent because

• P(buys lunch I male) = P(male) = 0.4

• P(male I buys lunch) = P(male) = 0.3

• P(buys lunch I male) = 0.3 and P(male) = 0.4

• P(male I buys lunch) = 0.4 and P(male) = 0.3

Bart found 20 quadrilaterals in his classroom. He made a Venn diagram using the properties of the quadrilaterals, comparing those with four equal side lengths (E) and those with four right angles (R).

Given that a randomly chosen quadrilateral has four right angles, what is the probability that the quadrilateral also has four equal side lengths? Express your answer in percent form, rounded to the nearest whole percent.

• 25%

• 33%

• 40%

• 67%

A spiner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive. What is true about spinning the spinner one time? Select three options.

• S = {1, 2, 3, 4, 5, 6, 7, 8}

• If A is a subset of S, A could be {1, 2, 3}.

• If A is a subset of S, A could be {7, 8, 9}.

• If a subset A represents spinning a number less than 4, then A = {1, 2, 3, 4}.

• If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.

Line segment ON is perpendicular to line segment ML.

What is the length of segment NP?

• 1 unit

• 2 units

• 3 units

• 4 units

Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on the line segment GX.

Marco wants to create a new circle using line segment GX as a radius. What will be the area of Marco's new circle?

• $10\pi\ cm^2$

• $16\pi\ cm^2$

• $356\pi\ cm^2$

• $676\pi\ cm^2$

In circle O, what is  $m\angle MAJ$ ?

•  $50\degree$  

•  $55\degree$  

•  $125\degree$  

•  $250\degree$  

What is the measure of arc BEC in circle D?

• $134\degree$

• $150\degree$

• $209\degree$

• $210\degree$

The two square pyramids are similar. The side length of the smaller pyramid is  $\frac{3}{4}$ the side length of the larger pyramid. 

Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid?

•  $\frac{16}{9}$  

•  $\frac{3}{4}$  

•  $\frac{4}{3}$  

•  $\frac{9}{16}$  

The circular base of a cone has a radius of 5 centimeters. The height of the cone is 12 centimeters, and the slant height is 13 centimeter.
What is the approximate surface area of the cone? Use 3.14 for $\pi$ and round to the nearest whole number.

•  $267\ cm^2$  

•  $456\ cm^2$  

•  $283\ cm^2$  

•  $487\ cm^2$  

An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm.

What is the area of the equilateral triangle, rounded to the nearest tenth?

• $2.7\ cm^2$

• $4.1\ cm^2$

• $16.2\ cm^2$

• $24.2\ cm^2$