Download Algebra 3 – Final Exam Review Name

Algebra 3 – Final Exam Review
Name: ___________________________________
I.
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)
II.
Geometry – Chapter 3 (Angle Pairs)
 angle pairs: alternate interior, alternate exterior, same-side interior, corresponding
 slopes of parallel lines, slopes of perpendicular lines
III.
Geometry – Chapter 6 (Ratio and Proportion)
 ratio and proportion (including percent word problems)
 similar figures
IV.
Geometry – Chapter 7 (Right Triangles)
 simplifying square roots and cube roots
 Pythagorean Theorem
 special right triangles (45-45-90, 30-60-90)
V.
Geometry – Chapter 10 (Circles)
 properties of circles
 central angles, inscribed angles, and arcs
 line tangent to a circle
 “megaphone theorem”
 area of a circle
 circumference of a circle
 area of sectors and length of arcs
VI.
Geometry – Measurement (Chapters 11 and 12)
 area and perimeter of various shapes (formula sheet will be provided)
 surface area and volume of various shapes (formula sheet will be provided)
 manipulating equations to determine various measurements
I.
Geometry – Chapter 1 (Intro to Geometry)
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. Two supplementary angles are (3x – 24)  and (12x – 10) . Solve for x.
13. The angles of a triangle measure (4w), (3w + 2), and (2w –7). Find w.
14. If
3x  5 2 x  4

, then solve for x.
5
4
15. The measure of an angle is 40 more than its complement. Find both angles.
Solve for x and find the length of AB:
13.
4x

8


14.
3x + 2

A
B
A
B
80
C
5x + 6


C
48
4x + 2
15.
7x
77
B
A

C
9x – 13
16. 


A
B
C
Solve for x and find mGHK for #17 and #18.
17.
18.
G
K
3x
G
54
6x – 15
J
H
K
14x – 5
H
19. BK is an angle bisector for ABC. Find x, and then find the measure of ABC:
K
A
4x + 25
10x – 11
B
x = _______
mABC = _______
C
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 m1 = 78, what is m2?
24. 3 and 4 are supplementary. If m3 = 65, what is m4?
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!)
II.
Geometry – Chapter 3 (Angle Pairs)
Use the figure at the right to determine whether the angles are:
(C) Corresponding
(AI) Alternate 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: _______
(AE) Alternate Exterior
(CI) Consecutive Interior
a
1
3
9
11
10
12
b
2
4
5
6
7
8
13
14
15
16
c
d
Determine which type of angles they are (corresponding, alternate interior, alternate exterior, same-side
interior), then solve for the variable.
23.
angle pair: ___________________________
(10x – 30)
x = __________
(4x + 12)
24.
angle pair: _________________________
(8x + 6)
(10x – 6)
x = __________
25.
(12y – 62)
angle pair: ________________________
(6y +10)
y = _________
26.
angle pair: ____________________
(4x + 25 )
(8x - 15)
x: _____________
Find the slope of the line that crosses through the given points.
27. (-3, 4) and (-3, 6) m = ________
28. (0, -1) and (-3, 8) m = ________
29. (-7, 4) and (-9, 4) m = ________
30. (-8, -2) and (-1, -9) m = ________
31. What kind of line has a slope of 0?
32. What kind of line has a slope that is undefined?
Determine the slope of the line, write the equation, and graph the line.
33) Table:
Graph:
x
3
0
y
2
4
4
2
-5
Slope: __________
5
-2
-4
Equation: ____________________
34) Table:
Graph:
x y
0 -3
-1 5
4
2
-5
Slope: __________
5
-2
-4
Equation: ____________________
III.
Geometry – Chapter 6 (Ratio and Proportion)
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.
6.
Solve the following proportions. Show all work.
a)
x 5
=
18 2
x = ______
b)
a 1 4

5
10
a = ______
c)
2x  5 x  5

3
4
x = ______
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 = _________
IV.
Geometry – Chapter 7 (Right Triangles)
Simplify each radical.
1. 2 90
2. 5 800
3.
5.
3
20
4. 4 49
54
6.
23 32
Find x using the Pythagorean Theorem. Simplify all radicals. (No decimal answers!)
8
7.
8.
9.
15
x
12
x
10
x
17
8
Use SPECIAL RIGHT TRIANGLES RULES to solve for the missing side lengths. (45-45-90 and 30-60-90)
10.
11.
y
10
x
x
24
y
X= ________
Y=________
X= ________
12.
Y= ________
13.
x
6
y
X= ________
y
x
30

Y=________
45˚
9
X= ________
Y= ________
14.
15.
60°
y
x
x
15
12
X= ________
y
Y=________
X= ________
Y= ________
Tell whether triangles with the following side lengths can exist.
16. 9, 12, 15
17. 14, 21, 30
18. 10, 12, 26
Draw a diagram and solve using the Pythagorean Theorem.
19. 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?
20. The bases on a softball diamond are 60 feet apart. How far is it from home plate to second base?
21. An isosceles triangle has congruent sides of 20 cm. The base is 10 cm. Find the area of the triangle.
22. What is the length of the diagonal of a 10 cm by 15 cm rectangle?
23. The area of a square is 100 square centimeters. Find the length of a side. Find the length of the diagonal.
V.
Geometry – Chapter 10 (Circles)
Find the value of the unknown.
x
1.
5
6
2.
3x + 10
C
7x - 6
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.
3. MN
4. NQ
5. NQR
6. MRP
M
N
7. PN
O
81
8. MNQ
R
73
Q
P
9. QR
10. MR
11. QMR
12. PQ
13. PRN
14. MQN
15. Sector Area = __________
Arc length = __________
16. Sector Area = __________
Arc length = _________
17. Sector Area = __________
Arc length = __________
120˚
60˚
90˚
VI.
Geometry – Measurement (Chapters 11 and 12)
Practice:
Find the perimeter and area of each figure. Be sure to include units.
1.
2.
5 cm
3.
7 in.
8 cm
4.
12 cm
6 in.
P = ___________
P = ___________
P = ___________
A = ___________
A = ___________
A = ___________
13 cm
5.
6.
17 in.
15 in.
17 in.
7 cm
4 cm
5 cm
3 cm
12 cm
16 in.
P = ___________
P = ___________
P = ___________
A = ___________
A = ___________
A = ___________
Find the indicated information for each figure.
7.
Area = _________
8.
Area = _________
9.
Area = _________
10.
Area = _________
Perimeter = __________
34 cm
12 cm
22 cm
12 cm
30 cm
11.
Area = _________
Perimeter = _________
12.
Area = _________
Perimeter = __________
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.
4 in
20.
7m
3 in
12 m
Find the surface area and volume of each figure.
21.
22.
12 in
4m
16 in
6m
12 m
SA = ___________
SA = _________
V = __________
V = __________
23.
24.
4 cm
9 cm
7 in
SA = ___________
SA = _________
V = __________
V = __________
25.
26.
13 in
10 in
10 in
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)