Algebra 3 – Final Exam Review Name: ___________________________________

I. Area, Perimeter, Surface Area, Volume (I will give you the formula sheet)

II. Quadrilaterals

squares, rectangles, rhombuses

III. Geometry – Chapter 1 (Intro to Geometry)

point, line, plane, midpoint, distance formula

perpendicular lines, parallel lines

angles (acute, right, obtuse, complementary, supplementary, linear pairs, vertical angles)

IV. Geometry – Chapter 3 (Angle Pairs)

angle pairs: alternate interior, alternate exterior, same-side interior, corresponding

slopes of parallel lines, slopes of perpendicular lines

V. Geometry – Chapter 6 (Ratio and Proportion)

ratio and proportion (including percent word problems)

similar figures

VI. Geometry – Chapter 7 (Right Triangles)

simplifying square roots and cube roots

Pythagorean Theorem

special right triangles (45-45-90, 30-60-90)

right triangle trigonometry (SOHCAHTOA)

VII. Geometry – Chapter 10 (Circles)

properties of circles

central angles, inscribed angles, and arcs

line tangent to a circle

“megaphone theorem”

area of sectors and length of arcs

area of a circle

circumference of a circle

I. Area, Perimeter, Surface Area, Volume (I will give you the formula sheet)

Practice: Find the perimeter and area of each figure. Be sure to include units.

1. 2. 3.

P = ___________ P = ___________ P = ___________

A = ___________ A = ___________ A = ___________

4. 5. 6.

P = ___________ P = ___________ P = ___________

A = ___________ A = ___________ A = ___________

Find the indicated information for each figure.

7. Area = _________ 8. Area = _________

8 cm

5 cm 7 in.

6 in.

12 cm

13 cm

12 cm

17 in. 17 in.

16 in.

15 in. 4 cm 5 cm

3 cm

7 cm

9. Area = _________ 10. Area = _________

Perimeter = __________

11. Area = _________ 12. Area = _________

Perimeter = _________ Perimeter = __________

30 cm

34 cm

12 cm

12 cm

22 cm

Use the given information to determine the missing information. It may be necessary to work backwards

using one of the formulas.

13. A square has a side of length 11 in. What is its perimeter? ______________ Area? _______________

14. A square has a perimeter of 100 cm. What is its area? ________________

15. A rectangle has a perimeter of 32 ft and a base of 9 ft. What is its height? ________________

Find the circumference (C) and area (A) of each circle.

Be sure to include the proper units.

16. C = __________

A = __________

17. The area of the circle is 25 in2.

Circumference = __________

14 mm

Find the area of the shaded region rounded to the nearest hundredth.

18. 19. 20.

Find the surface area and volume of each figure.

21. 22.

SA = ___________ SA = _________

V = __________ V = __________

23. 24.

SA = ___________ SA = _________

V = __________ V = __________

3 in 4 in

12 m

7 m

12 m 6 m

4 m

4 cm

9 cm

16 in

12 in

7 in

25. 26.

SA = ___________ V = _________________

V = _____________

27. If the surface area of a given sphere is 804.25 m3, what is the length of the radius of the sphere? (use the

formula to write an equation and solve for r)

28. If the volume of a given cylinder is 2827.43 in3 and the height of the cylinder is 9 in, what is the length of

the radius? (use the formula to write an equation and solve for r)

10 in

10 in

13 in

II. Quadrilaterals

29. A quadrilateral with diagonals that are perpendicular is called a ________.

a. rectangle b. parallelogram c. rhombus

30. The sum of the measures of the interior angles of a quadrilateral is ______ .

a. 180º b. 200º c. 360º

31. In a parallelogram, the opposite angles are always __________ .

a. complementary b. congruent c. supplementary

Matching: Match the figure with its description:

____ 32. I am not a polygon. A. rhombus

____ 33. My interior angles always add up to 180º. B. circle

____ 34. My opposite sides are always parallel and congruent. C. pentagon

____ 35. I am a figure with four congruent sides. D. triangle

____ 36. I am a figure with five sides. E. parallelogram

Find the value of x in each quadrilateral:

37. x = ______ 38. x = _______

ABCD is a square. DEFG is a rectangle.

(4x + 6)º A B

C D

4x – 10

3x + 4

D E

F G

GEOMTRY REVIEW:

Chapter 1:

Fill in the blank.

1. The point that divides a segment into two congruent segments is a _______________ .

2. The endpoint of the two rays of an angle is called the _______________ .

3. The intersection of two planes is a _______________ .

4. The intersection of two lines is a ________________ .

6. An angle measure that is less than 90 is called _______________ .

7. Two adjacent angles that are complementary form a(n) ___________ angle:

8. Two adjacent angles that are supplementary are known as a __________ ___________ .

10. The lengths of the legs of an isosceles triangle are (3x) and (x + 15). Find x.

11. The measures of two vertical angles are (5y – 21) and (3y + 12). Find y.

12. If 8

2x

7

4x

, then solve for x.

13. The angles of a triangle measure (4w), (3w + 2), and (2w –7). Find w.

14. If 4

4x2

5

5x3

, then solve for x.

15. The measure of an angle is 40 more than its complement. Find both angles.

Solvefor x and find the length of AB:

13. 14.

15. 16.

Solve for x and find mGHK for #17 and #18.

17. 18.

19. BK is an angle bisector for ABC. Find x, and then find the measure of ABC:

x = _______ mABC = _______

A C B

A C B

7x 77

A C B

4x + 2 9x – 13

3x

54 6x – 15 14x – 5

A

B C

K

4x + 25

10x – 11

4x 8

48

A C B

3x + 2 5x + 6

80

G

H

K

G

H K J J

Midpoint and Distance Formulas

20. What is the coordinate of the midpoint between two endpoints at (-5, 2) and (9, -6)?

21. What is the other endpoint if one endpoint is at (3, 6) and the midpoint is at (-2, 2)? (hint: graph)

22. What is the distance between point A (3, 7) and point B (-4, -3)?

(Round to nearest tenth.)

Pairs of Angles.

23. 1 and 2 are complementary. If m1 = 78, what is m2?

24. 3 and 4 are supplementary. If m3 = 65, what is m4?

25. 1 and 2 are complementary. If 1 is four times as large as 2, what are the

measures of each angle? (Hint: set up an equation!)

Chapter 3

Use the figure at the right to determine whether the angles are:

(C) Corresponding (AI) Alternate Interior (AE) Alternate Exterior (CI) Consecutive Interior

(V) Vertical Angles (None) Not Related

1. 1 & 9: _______

2. 15 & 14: _____

3. 3 & 9: _______

4. 6 & 10: _______

5. 16 & 6: _______

6. 12 & 13: _______

7. 4 & 1: _______

8. 11 & 15: _______

9. 5 & 16: _______

10. 2 & 11: _______

Determine which type of angles they are (corresponding, alternate interior, alternate exterior, same-side

interior), then solve for the variable.

23. angle pair: ___________________________

x = __________

a b

c

d

1 2

4 3 8 7

6 5

12 11

10 9

15

14 13

16

(4x + 12)

(10x – 30)

24.

angle pair: _________________________

x = __________

25.

angle pair: ________________________

y = _________

26. angle pair: ____________________

x: _____________

(6y +10)

(12y – 62)

(8x + 6) (10x – 6)

(4x + 25 )

(8x - 15)

Chapter 6

1. The perimeter of a room is 66 feet. The ratio of its length to its width is 6:5. You want to tile the floor with 12 inch square tiles. Find the length and width of the room, and the area of the floor. How many tiles will you need? The tiles cost $1.98 each. What is the total cost to tile the floor?

Find the measure of each angle.

2. The measures of the angles of a triangle are in the ratio 3 : 5 : 7.

3. The ratio of the measures of two complementary angles is 4 : 6.

4. To estimate the height of a tree, Casey waited until the tops of the shadows of the tree and sign coincided.

The sign is 2 m high and the sign and the tree have shadows of 6.4 m and 15.8m, respectively. Find the height

of the tree rounded to the nearest tenth of a meter.

5. Solve the following proportions. Show all work.

a) 18

x =

5

2 x = ______

b) 1 4

5 10

a a = ______

c) 2 5 5

3 4

x x x = ______

6. Suppose on a map, 2.5 inches represents 520 miles. If the distance between Philadelphia and Nashville on the map measures 4.125 inches, find the actual distance between the two cities in miles. (Write a proportion and then solve.)

7. The measures of the angles in a triangle are given in the ratio 4 : 7 : 9. Find the measure of each angle.

9. A rectangle has a perimeter of 56 feet. If the rectangle has a length to width ratio of 4 : 3 , find the

length and width of the rectangle. Then, find the area of the rectangle. Draw figure and show work.

Area = _________

Chapter 7

Chapter 7 Practice Problems:

Simplify each radical.

5. 2 90 6. 5 800

7. 20 8. 4 49

9. 3

2 10. 509

11. 108 27 12. 500 125

Find x using the Pythagorean Theorem. Simplify all radicals. (No decimal answers!)

6. 7. 8.

Use SPECIAL RIGHT TRIANGLES RULES to solve for the missing side lengths. (45-45-90 and 30-60-90)

9. 10.

X= ________ Y=________ X= ________ Y= ________

11. 12.

X= ________ Y=________ X= ________ Y= ________

12 x

8

8

10

x

15

17 x

10 x

y

x 24

y

6 x

y

30

9

x

45˚

y

13. 14.

X= ________ Y=________ X= ________ Y= ________

Tell whether triangles with the following side lengths can exist. If so, is the triangle a right triangle?

15. 9, 12, 15 16. 14, 21, 30 19. 10, 12, 26

Draw a diagram and solve using the Pythagorean Theorem.

21. In your town, there is a field that is in the shape of a right triangle with one leg 35 feet and hypotenuse is 80

feet.

a. Find the perimeter of the field.

b. You are going to plant dogwood trees about every ten feet around the field’s edge. How many trees do you

need?

c. If each dogwood costs $12, how much will the trees cost?

22. The bases on a softball diamond are 60 feet apart. How far is it from home plate to second base?

23. An isosceles triangle has congruent sides of 20 cm. The base is 10 cm. Find the area of the triangle.

60°

12

x

y

15

x y

24. What is the length of the diagonal of a 10 cm by 15 cm rectangle?

25. The area of a square is 100 square centimeters. Find the length of a side. Find the length of the diagonal.

Solve each right triangle using trigonometry (SOHCAHTOA). Then, find the area AND the perimeter of each triangle.

Round all answers to two decimal places.

11. 12.

13. The design for part of a water ride at an amusement park is shown. The ride carries people up a track along ramp

AB. Then, riders travel down a water chute along ramp BC.

a) How high is the ride above point D? (find the length of BD) Show all work.

b) What is total distance from point A to point B to point C? Show all work.

27o

12

51o

10

A

B

D C

35o

50 feet 42 feet

CHAPTER 10

Find the value of the unknown. A and B are points of tangency.

9. 10.

MQ and NR are diameters of Circle O. Determine whether the given arc is a minor arc, major arc, or semicircle. Then find the measure of the arc.

1. MN 2. NQ

3. NQR 4. MRP

5. PN 6. MNQ

7. QR 8. MR

9. QMR 10. PQ

11. PRN 12. MQN

C

x

6

5 3x + 10

7x - 6

M

N

P

O R

Q

81 73

1. Sector Area = ____________

Arc length = __________

2. Sector Area = ____________

Arc length = __________

3. Sector Area = ____________

Arc length = __________

7. The area of a sector is 36π.

The area of the circle is 144π.

Find the measure of the angle that

creates the sector.

8. A cake is cut into 8 equal pieces

and each piece has an arc length

of 6.28 in. Find the diameter.

90˚

120˚

60˚