Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Final Exam Review Sheet

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Which description does NOT guarantee that a trapezoid is isoscles?

a. congruent diagonals

b. both pairs of base angles congruent

c. congruent bases

d. congruent legs

____ 2. Which description does NOT guarantee that a quadrilateral is a parallelogram?

a. a quadrilateral with both pairs of opposite sides congruent

b. a quadrilateral with the diagonals bisecting each other

c. a quadrilateral with consecutive angles supplementary

d. quadrilateral with two opposite sides parallel

Short Answer

3. Points B, D, and F are midpoints of the sides of ∆ACE. EC = 30 and DF = 23. Find AC. The diagram is not to

scale.

Name: ________________________ ID: A

2

4. Q is equidistant from the sides of ∠TSR. Find m∠RST. The diagram is not to scale.

5. What is the negation of this statement?

Miguel’s team won the game.

6. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL.

7. DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal.

8. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 20x + 9, and

m∠M = 14x + 15, find m∠K.

9. Find the values of a and b.The diagram is not to scale.

Name: ________________________ ID: A

3

10. If ON = 5x − 5, LM = 4x + 4, NM = x − 9, and OL = 2y − 5, find the values of x and y for which LMNO must

be a parallelogram. The diagram is not to scale.

11. A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length

of the car to the length of the model?

12. 6

a=

18

27

13. 5

7=

m

35

14. 3y − 8

12=

y

5

15. A map of Australia has a scale of 1 cm to 120 km. If the distance between Melbourne and Canberra is 463

km, how far apart are they on the map, to the nearest tenth of a centimeter?

16. On a blueprint, the scale indicates that 6 cm represent 15 feet. What is the length of a room that is 9 cm long

and 4 cm wide on the blueprint?

17. Triangles ABC and DEF are similar. Find the lengths of AB and EF.

Name: ________________________ ID: A

4

18. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.

19.

20. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.

21.

22. The students in Mr. Collin’s class used a surveyor’s measuring device to find the angle from their location to

the top of a building. They also measured their distance from the bottom of the building. The diagram shows

the angle measure and the distance. To the nearest foot, find the height of the building.

Name: ________________________ ID: A

5

23. Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.

24. The radius of the base of a cylinder is 28 cm and its height is 48 cm. Find the surface area of the cylinder in

terms of π .

25. Find the surface area of the cone in terms of π .

26. Find the lateral area of the cone to the nearest whole number.

Not drawn to scale

Name: ________________________ ID: A

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27.

28. Find the length of arc XPY. Leave your answer in terms of π .

29. Find the area of the shaded portion of the figure. Dimensions are in feet. Round your answer to the nearest

tenth..

30. Find the area. The figure is not drawn to scale.

Name: ________________________ ID: A

7

31. Find the area of the circle. Leave your answer in terms of π .

32. Find the area of the figure to the nearest tenth.

33. Find the area of a sector with a central angle of 140° and a diameter of 7.9 cm. Round to the nearest tenth.

34.

35. Find the circumference. Leave your answer in terms of π .

Name: ________________________ ID: A

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36. AB is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest

tenth if necessary. The diagram is not to scale.

37. JK, KL, and LJ are all tangent to O (not drawn to scale). JA = 9, AL = 10, and

CK = 14. Find the perimeter of ∆JKL.

38.

Name: ________________________ ID: A

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39. The radius of circle O is 18, and OC = 13. Find AB. Round to the nearest tenth, if necessary. (The figure is

not drawn to scale.)

Essay

40. From the top of a 210-foot lighthouse located at sea level, a boat is spotted at an angle of depression of 23°.

a. Draw a sketch to represent this situation.

b. Use the angle of depression to find the distance from the base of the lighthouse to the

boat. Explain your steps in finding the distance.

ID: A

1

Final Exam Review Sheet

Answer Section

MULTIPLE CHOICE

1. C

2. D

SHORT ANSWER

3. 46

4. 25

5. Miguel’s team did not win the game.

6. x = 5, NM = 20, OL = 20

7. x = 4, DF = 15, EG = 15

8. 151

9. a = 144, b = 67

10. x = 9, y = 5

2

11. 18 : 1

12. 9

13. 25

14. 40

3

15. 3.9 cm

16. 22.5 ft

17. AB = 10; EF = 2

18. 130

19. 8

20. no; 122

+ 142

≠ 192

21. 60

22. 308 ft

23. w = 7.7, x = 44

24. 4256π cm2

25. 54π cm2

26. 4712 m2

27. 480 cm3

28. 6π m

29. 68 − 16π( ) ft2

30. 18.86 cm2

31. 6.5025π m2

ID: A

2

32. 53.4 in.2

33. 19.1 cm2

34. 165 cm2

35. 28π in.

36. 7

37. 66

38. 10

39. 24.9

ID: A

3

ESSAY

40.

[4] a.

b. tan 23° =210

xUse the tangent ratio.

tan 23°(x) = 210 Multiply each side by x.

tan 23°(x)

tan 23°=

210

tan 23°Divide each side by tan 23°.

x ≈ 494.7 Use a calculator.

The distance from the base of the lighthouse to the boat is about 494.7 feet.

c. Since the measures of the acute angles of a right triangle add to 90°, you can use

the other angle in the triangle to find the distance. The measure of the other

acute angle is 90° – 23°, or 67°.

tan 67° =x

210Use the tangent ratio.

x = 210(tan 67°) Multiply each side by 210.

x 494.7 Use a calculator.

d. The shortest distance from the top of the lighthouse to the boat is the

hypotenuse of the right triangle with legs of length 210 feet and 494.7 feet.

a2

+ b2 = c

2 Pythagorean Theorem

2102

+ 494.72 = c

2 Substitute.

44,100 + 244,728 = c2 Simplify.

288,828 = c2 Simplify.

537.4 ≈ c Use a calculator.

The shortest distance from the top of the lighthouse to the boat is about

537.4 feet.

[3] one mathematical error or correct answers with incomplete explanations

[2] two mathematical errors or correct answers with errors in explanation

[1] correct answers with no explanation