Geometry/Trig

Name:_______________________________________

Date:________________________

Practice Final Exam #1

Directions: Answer all of the following questions to the best of your ability. Show all work for each

question. Partial credit can be awarded to correct work that is shown. All questions in Part I will be worth

2 points. All questions in Part II will have the point value next to the question. Do not leave any questions

blank. Good Luck, and take your time!

Part I – Multiple Choice

1. Find the perimeter of the following rectangle.

a. 10 units2

b. 14x units

c. 10x units

d. 14x units2

2. Given a cone with a diameter of 18 inches, and a height of 10 inches, what is the total volume of the

cone in terms of pi.

a. 270 in3

b. 1080 in3

c. 270 in2

d. 180 in3

3. Find the midpoint of segment CD where C (5, 1) and D (8, 3). a. (13, 4) b. (1.5, 1) c. (6.5, 2) d. (8, 3)

4. What type of triangle is this according to its angles?

a. Acute

b. Obtuse

c. Scalene

d. Isosceles

5. Name the angle pair relationship shown in the following diagram.

a. Complementary angles

b. Supplementary angles

c. Angles at a point

d. Congruent angles

Geometry/Trig

6. What is the slope of the line that passes through the points (-4, 5) and (-2, 0)

a. -

b.

c. -

d. 5

7. Consider the triangle to the right. What is the measure of angle ACB?

a. 55

b. 180

c. 110

d. 70

8. If the scale factor (k) of dilation is 6, the pre-image will…

a. Be enlarged

b. Shrink

c. Remain the same because dilations are rigid motions

d. Translate 5 units

9. If you were to reflect the point M(-4, 3) over the line y = 0, what are the coordinates of M’ (use of the

coordinate plane is optional.

a. (-4, -3)

b. (4, 3)

c. (-3, 4)

d. (3, 4)

10. Which ratio represents the sine of angle A in the right triangle below? (2 points)

a.

b.

c.

d.

Geometry/Trig 11. In triangle PSR, p = 50, s = 80, and m R = 20 . Which equation can be used to determine the value of r?

(Hint: Draw a picture first)

a. ( )( ) ( )

b. ( )( ) ( )

c. ( )

( )( )

d. ( )( ) ( )

12. The graph of which of the following equations has an amplitude of 2 and period of ? (2 points)

a. ( )

b.

( )

c. ( )

d. (

)

Part II – Short Answer 13. Are the following lines parallel, perpendicular, or neither? A line that passes through (7, -4) and (3, 5)

and a line that passes through the points (-2, 4) and (7, 8). State the slope of each of the lines, and

justify your response. [4 points]

14. a. What type of angle pair relationship is shown? (What type of angles are these?) [1 point]

b. Solve for the value of x. [2 points]

Geometry/Trig

15. a. In the following figure below, ABCD is a rectangle and a semicircle O has a radius of 4cm. What is

the area of the figure, in terms of . [5 points]

b. Find the perimeter of the figure above in terms of .[5 points]

16. What is the probability of throwing a dart, and having it land in the outer shaded ring of the target

below? Keep all area calculations in terms of pi. [4 points]

17. Does the following triangle contain a right angle? Please explain why or why not. [4 points]

Geometry/Trig

18. A soup can is in the shape of the accompanying cylinder. Calculate the amount of material that it takes

to make the curved surface of the container. Leave your answer in terms of pi. [3 points]

19. Use the diagram to help you answer parts a-e. The diagram includes parallel lines cut by a transversal.

a) Given the diagram below, name a pair of alternate interior angles. (1 point)

b) Name a pair of same side exterior angles. (1 point)

c) What type of special angle pair are and ? (1 point)

d) You are given that m 1=71o. What is the m 7? (1 point)

e) You are given that 1 = 7x+20 and 8 = 9x – 2. What is the m 8? (3 points)

f) You are given that 2 = 16x and 6 = 10x+45. Solve for x. (2 points)

Geometry/Trig

20. Write the equation of the perpendicular bisector of the line segment whose endpoints are

(-6, 1) and (10, -7). [6 points]

21. a. Phil buys chocolate in the shape of a rectangular prism. The dimensions of the prism are 10 inches

by 2 inches by 7 inches. How much space is inside this package (round your answer to the nearest

cubic inch)[3 points]

b. Monica buys chocolate in the shape of a cylinder. The cylinder has a radius of 2 inches and a height

of 10 inches. How much space is inside this package? (round your answer to the nearest cubic

inch).

[3 points]

c. Which container holds more chocolate (Phil’s or Monica’s) [1 point]

d. Determine to the nearest cubic inch, how much more chocolate does the larger package hold?

[1 point]

Geometry/Trig 22. Solve for the measures of 1, 2, and 3. Show all of your work clearly! (3 points)

m 1 = ______________________

m 2 = ______________________

m 3 = ______________________

23. a) Graph △JKL with vertices J(-4, 1), K(-3, 5) L (-1, 1). b) State and graph the coordinates of the image after a transformation of .

J’( )

K’( )

L’( )

Geometry/Trig 24. Write a rule using appropriate notation for the rotation that took place below.

25. Solve for x in the following diagram. Round your answer the nearest hundredth. (3 points)

26. A person casts a 144 inch shadow on a sunny day, as shown in the diagram. If the angle of elevation from the tip of the shadow to the top of the person’s head is 30 , what is the height of the person to the neatest tenth of an inch. (3 points)

Geometry/Trig

27. Convert the following radian measure to degrees (2 points)

radians

28. In the accompanying diagram of and side BC = 25.

29.

a. Solve for x. Round to the nearest 100th.

29 The diagram below shows displays triangle ABC. b. Find the missing side to the nearest tenth of a meter.

Geometry/Trig 30. Given triangle QRS, m Find the measurement of to the

nearest degree.

31. Given the following function, find the amplitude, frequency, period, and vertical shift. (4 points)

(

)

32. Graph the following function Show all work and critical values! (5 points)

( )

Amplitude:_________________ Frequency:_________________

Period: ____________________ Vertical Shift:_______________