Name: ______________________ Class: _________________ Date: _________
ID: A
Algebra 1 - Chapter 11 Practice Test
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
Simplify the radical expression.
____
____
1. −4 160
a. −4 80
2. −2
2p ⋅ 2
b. −4
16
c. −16
10
b. −8
11p
c. −4
44p
d.
10
22
factor 1: 1
factpr 2: 11
common factor: 2
a.
____
44p
d. −8
11p 2
10
81
3.
a.
10
9
b.
10
41
c. 9
10
d.
10
9
Simplify the radical expression by rationalizing the denominator.
____
4
21
4.
a.
4
21
21
b. 4
21
c. 21
4
d.
441
21
Find the length of the missing side. If necessary, round to the nearest tenth.
____
5.
a.
361
b. 19
c. 38
1
d. 14.9
Name: ______________________
____
____
ID: A
6.
a. 15
b. 22.4
c. 17.3
d. 30
7. A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is
140 feet long and the water is 40 feet deep. To the nearest tenth of a foot, how far is the anchor from a
point directly below the boat?
a. 145.6 ft
b. 9,000 ft
c. 18,000 ft
d. 134.2 ft
Determine whether the given lengths can be sides of a right triangle.
____
____
8. 7 cm, 40 cm, 41 cm
a. no
b. yes
9. Find the distance from H(2, 3) to K(4, –3). If necessary, round to the nearest tenth.
a.
6.3
b. 7.1
c. 5.1
d. 40
Find the midpoint of each segment with the given endpoints.
____
10. C(1, –5) and D(–5, 1)
a. (−2, −3)
b. (–2, –2)
c. (3, –2)
2
d. (−2, −2)
Name: ______________________
____
ID: A
11. The King and Taylor families are hiking in a national park. The Kings leave the visitor center and
hike 2 km east and 2 km south. The Taylors leave the visitor center and hike 3 km west and 3 km
north. How far apart are the families?
a. 7.1 km
b. 7.2 km
c. 1.4 km
d. 50 km
Simplify the expression.
____
____
____
12.
6 +2 6
a. 3 6
13. 4 7 + 8 63
a. 76 7
8
14.
6− 3
a.
b.
____
b. −
8
Ê
8 ÁÁÁ
Ë
6 −8
3
6+
6
b. 12
63
3
12
d. −
c. 28
7
d. 28
c.
ˆ
3 ˜˜˜
¯
d.
9
15. Determine whether
a. never
c. 3
a+
8
6 +8
27
3
8
6 +8
3
3
12
63
a = 2a is sometimes, always, or never true.
b. sometimes
c. always
Solve the equation. Check your solution.
____
____
16. 4 = m − 8
a. 6
17.
a.
____
18.
2x + 7 =
a.
____
r + 5 = 11
126
–3
b. 144
c. 2
3
d. 12
b. 6
c. 17
d. 116
b. 5
c. –5
d.
5x − 8
1
5
19. The velocity of sound in air is given by the equation v = 20 273 + t where v is the velocity in meters
per second and t is the temperature in degrees Celsius. Find the temperature when the velocity of
sound in air is 369 meters per second. Round to the nearest degree.
a. 507º
b. 6,535º
c. 7,081º
d. 67º
3
Name: ______________________
ID: A
Solve the equation. Identify any extraneous solutions.
____
20. x =
−3x + 40
a. 8 is a solution to the original equation. The value –5 is an extraneous solution.
b. 5 and 8 are both extraneous solutions.
c. 5 is a solution to the original equation. The value –8 is an extraneous solution.
d. 5 and –8 are solutions.
____
21. Find the domain of y = 4
a.
x ≥ −2
4x + 2 .
1
b. x ≥ −
2
c. x >
Match the function with its graph.
____
22. y =
x −4
a.
c.
b.
d.
4
1
2
d. x ≥
1
2
Name: ______________________
____
____
23. y =
ID: A
x−1
a.
c.
b.
d.
24. Find the value of sin 66°. Round to the nearest ten-thousandth.
a. 0.4067
b. 2.246
c. 0.9135
d. –0.0266
Find the value of x to the nearest tenth.
____
25.
a.
2.9
b. 3.3
c. 9.2
5
d. 5
Name: ______________________
____
ID: A
26. A ranger spots a forest fire while on a 45-meter observation tower. The angle of depression from the
tower to the fire is 12°. To the nearest meter, how far is the fire from the base of the tower?
a. 212 meters
b. 10 meters
c. 216 meters
d. 71 meters
Short Answer
27. Simplify
4
6
by rationalizing the denominator. Show your work.
30
28. The sales of a certain product after an initial release can be found by the equation s = 16 3t + 25,
where s represents the total sales (in thousands) and t represents the time in weeks after release.
a. Make a table of values.
b. Graph the function.
c. Use the graph to estimate the sales 7 weeks after release.
29. Make a table of values and graph the function.
f(x) = x + 4 − 4
6
ID: A
Algebra 1 - Chapter 11 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: C
DIF: L1
REF: 11-1 Simplifying Radicals
OBJ: 11-1.1 Simplifying Radical Expressions Involving Products
STO: CA 1.0, CA 1.1, CA 2.0
TOP: 11-1 Example 1
KEY: radical expressions,Multiplication Property of Square Roots,square root
MSC: NAEP N3a, NAEP N5b, NAEP A3b, NAEP A3c, CAT5.LV19.50, CAT5.LV19.51,
IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.52, TV.LVALG.53
2. ANS: B
DIF: L1
REF: 11-1 Simplifying Radicals
OBJ: 11-1.1 Simplifying Radical Expressions Involving Products
STO: CA 1.0, CA 1.1, CA 2.0
TOP: 11-1 Example 3
KEY: multiplying two radicals,Multiplication Property of Square Roots,radical expressions
MSC: NAEP N3a, NAEP N5b, NAEP A3b, NAEP A3c, CAT5.LV19.50, CAT5.LV19.51,
IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.52, TV.LVALG.53
3. ANS: D
DIF: L1
REF: 11-1 Simplifying Radicals
OBJ: 11-1.2 Simplifying Radical Expressions Involving Quotients
STO: CA 1.0, CA 1.1, CA 2.0
TOP: 11-1 Example 5
KEY: Division Property of Square Roots,radical expressions,fractions within a radical
MSC: NAEP N3a, NAEP N5b, NAEP A3b, NAEP A3c, CAT5.LV19.50, CAT5.LV19.51,
IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.52, TV.LVALG.53
4. ANS: A
DIF: L1
REF: 11-1 Simplifying Radicals
OBJ: 11-1.2 Simplifying Radical Expressions Involving Quotients
STO: CA 1.0, CA 1.1, CA 2.0
TOP: 11-1 Example 7
KEY: radical expressions,rationalize,radicand in the denominator
MSC: NAEP N3a, NAEP N5b, NAEP A3b, NAEP A3c, CAT5.LV19.50, CAT5.LV19.51,
IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.52, TV.LVALG.53
5. ANS: D
DIF: L1
REF: 11-2 The Pythagorean Theorem
OBJ: 11-2.1 Solving Problems Using the Pythagorean Theorem STO: CA 24.2
TOP: 11-2 Example 1
KEY: Pythagorean Theorem,right triangle
MSC: NAEP N3g, NAEP G3d, NAEP G3f, CAT5.LV19.55, IT.LV15.CP, S9.TSK1.NS,
S9.TSK1.GM, S10.TSK1.NS, S10.TSK1.GM, TV.LV19.11, TV.LV19.14, TV.LVALG.53,
TV.LVALG.58
6. ANS: C
DIF: L1
REF: 11-2 The Pythagorean Theorem
OBJ: 11-2.1 Solving Problems Using the Pythagorean Theorem STO: CA 24.2
TOP: 11-2 Example 2
KEY: Pythagorean Theorem,right triangle
MSC: NAEP N3g, NAEP G3d, NAEP G3f, CAT5.LV19.55, IT.LV15.CP, S9.TSK1.NS,
S9.TSK1.GM, S10.TSK1.NS, S10.TSK1.GM, TV.LV19.11, TV.LV19.14, TV.LVALG.53,
TV.LVALG.58
1
ID: A
7. ANS: D
DIF: L2
REF: 11-2 The Pythagorean Theorem
OBJ: 11-2.1 Solving Problems Using the Pythagorean Theorem STO: CA 24.2
TOP: 11-2 Example 2
KEY: Pythagorean Theorem,right triangle,problem solving,word problem
MSC: NAEP N3g, NAEP G3d, NAEP G3f, CAT5.LV19.55, IT.LV15.CP, S9.TSK1.NS,
S9.TSK1.GM, S10.TSK1.NS, S10.TSK1.GM, TV.LV19.11, TV.LV19.14, TV.LVALG.53,
TV.LVALG.58
8. ANS: A
DIF: L1
REF: 11-2 The Pythagorean Theorem
OBJ: 11-2.2 Identifying Right Triangles STO: CA 24.2
TOP: 11-2 Example 3
KEY: right triangle,converse of the Pythagorean Theorem,converse,Pythagorean Theorem
MSC: NAEP N3g, NAEP G3d, NAEP G3f, CAT5.LV19.55, IT.LV15.CP, S9.TSK1.NS,
S9.TSK1.GM, S10.TSK1.NS, S10.TSK1.GM, TV.LV19.11, TV.LV19.14, TV.LVALG.53,
TV.LVALG.58
9. ANS: A
DIF: L1
REF: 11-3 The Distance and Midpoint Formulas
OBJ: 11-3.1 Finding the Distance Between Two Points
TOP: 11-3 Example 1
KEY: distance formula,graphing
MSC: NAEP M1e, CAT5.LV19.55, IT.LV15.CP, S9.TSK1.NS, S9.TSK1.GM, S10.TSK1.NS,
S10.TSK1.GM, TV.LV19.11, TV.LV19.14, TV.LVALG.53, TV.LVALG.58
10. ANS: B
DIF: L1
REF: 11-3 The Distance and Midpoint Formulas
OBJ: 11-3.2 Finding the Midpoint of a Line Segment
TOP: 11-3 Example 3
KEY: midpoint,midpoint formula
MSC: NAEP M1e, CAT5.LV19.55, IT.LV15.CP, S9.TSK1.NS, S9.TSK1.GM, S10.TSK1.NS,
S10.TSK1.GM, TV.LV19.11, TV.LV19.14, TV.LVALG.53, TV.LVALG.58
11. ANS: A
DIF: L2
REF: 11-3 The Distance and Midpoint Formulas
OBJ: 11-3.1 Finding the Distance Between Two Points
TOP: 11-3 Example 1
KEY: distance formula,word problem,problem solving
MSC: NAEP M1e, CAT5.LV19.55, IT.LV15.CP, S9.TSK1.NS, S9.TSK1.GM, S10.TSK1.NS,
S10.TSK1.GM, TV.LV19.11, TV.LV19.14, TV.LVALG.53, TV.LVALG.58
12. ANS: A
DIF: L1
REF: 11-4 Operations With Radical Expressions
OBJ: 11-4.1 Simplifying Sums and Differences
STO: CA 1.0, CA 1.1
TOP: 11-4 Example 1
KEY: like radicals,combining like radicals
MSC: NAEP A3b, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.11,
TV.LV19.14, TV.LV19.52, TV.LVALG.53
13. ANS: C
DIF: L1
REF: 11-4 Operations With Radical Expressions
OBJ: 11-4.1 Simplifying Sums and Differences
STO: CA 1.0, CA 1.1
TOP: 11-4 Example 2
KEY: like radicals,combining like radicals,radical expressions
MSC: NAEP A3b, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.11,
TV.LV19.14, TV.LV19.52, TV.LVALG.53
14. ANS: D
DIF: L2
REF: 11-4 Operations With Radical Expressions
OBJ: 11-4.2 Simplifying Products and Quotients
STO: CA 1.0, CA 1.1
TOP: 11-4 Example 5
KEY: radical expressions,rationalize,conjugates
MSC: NAEP A3b, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.11,
TV.LV19.14, TV.LV19.52, TV.LVALG.53
2
ID: A
15. ANS: B
DIF: L2
REF: 11-4 Operations With Radical Expressions
OBJ: 11-4.1 Simplifying Sums and Differences
STO: CA 1.0, CA 1.1
KEY: like radicals,reasoning,always sometimes never,reasoning
MSC: NAEP A3b, CAT5.LV19.54, IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.11,
TV.LV19.14, TV.LV19.52, TV.LVALG.53
16. ANS: B
DIF: L1
REF: 11-5 Solving Radical Equations
OBJ: 11-5.1 Solving Radical Equations
TOP: 11-5 Example 1
KEY: radical,radical equation,solving equations
MSC: CAT5.LV19.50, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17,
TV.LV19.52, TV.LVALG.56
17. ANS: D
DIF: L1
REF: 11-5 Solving Radical Equations
OBJ: 11-5.1 Solving Radical Equations
TOP: 11-5 Example 1
KEY: radical,radical equation,solving equations
MSC: CAT5.LV19.50, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17,
TV.LV19.52, TV.LVALG.56
18. ANS: B
DIF: L1
REF: 11-5 Solving Radical Equations
OBJ: 11-5.1 Solving Radical Equations
TOP: 11-5 Example 3
KEY: radical,radical equation,solving equations,equations with radical expressions on both sides
MSC: CAT5.LV19.50, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17,
TV.LV19.52, TV.LVALG.56
19. ANS: D
DIF: L1
REF: 11-5 Solving Radical Equations
OBJ: 11-5.1 Solving Radical Equations
TOP: 11-5 Example 2
KEY: radical,radical equation,solving equations,word problem,problem solving
MSC: CAT5.LV19.50, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17,
TV.LV19.52, TV.LVALG.56
20. ANS: C
DIF: L1
REF: 11-5 Solving Radical Equations
OBJ: 11-5.2 Solving Equations With Extraneous Solutions
TOP: 11-5 Example 4
KEY: solving equations,radical equation,extraneous solutions
MSC: CAT5.LV19.50, IT.LV15.CP, S9.TSK1.PRA, S10.TSK1.PRA, TV.LV19.16, TV.LV19.17,
TV.LV19.52, TV.LVALG.56
21. ANS: B
DIF: L1
REF: 11-6 Graphing Square Root Functions
OBJ: 11-6.1 Graphing Square Root Functions
STO: CA 17.0
TOP: 11-6 Example 1
KEY: radical expressions,graphing,function,square root,domain
MSC: CAT5.LV19.54, IT.LV15.DI, TV.LV19.14, TV.LV19.16, TV.LVALG.56
22. ANS: B
DIF: L1
REF: 11-6 Graphing Square Root Functions
OBJ: 11-6.2 Translating Graphs of Square Root Functions
STO: CA 17.0
TOP: 11-6 Example 3
KEY: translation,square root,graphing
MSC: CAT5.LV19.54, IT.LV15.DI, TV.LV19.14, TV.LV19.16, TV.LVALG.56
23. ANS: D
DIF: L1
REF: 11-6 Graphing Square Root Functions
OBJ: 11-6.2 Translating Graphs of Square Root Functions
STO: CA 17.0
TOP: 11-6 Example 4
KEY: translation,square root,graphing
MSC: CAT5.LV19.54, IT.LV15.DI, TV.LV19.14, TV.LV19.16, TV.LVALG.56
24. ANS: C
DIF: L1
REF: 11-7 Trigonometric Ratios
OBJ: 11-7.1 Finding Trigonometric Ratios
TOP: 11-7 Example 2
KEY: sine,cosine,tangent,trigonometric ratios,calculator
MSC: NAEP M1f, NAEP M1m, CAT5.LV19.46, CAT5.LV19.55, CAT5.LV19.56, IT.LV15.CP,
TV.LV19.10, TV.LV19.13, TV.LV19.14, TV.LVALG.53, TV.LVALG.58
3
ID: A
25. ANS: C
DIF: L1
REF: 11-7 Trigonometric Ratios
OBJ: 11-7.1 Finding Trigonometric Ratios
TOP: 11-7 Example 3
KEY: tangent,sine,cosine,trigonometric ratios,right triangle
MSC: NAEP M1f, NAEP M1m, CAT5.LV19.46, CAT5.LV19.55, CAT5.LV19.56, IT.LV15.CP,
TV.LV19.10, TV.LV19.13, TV.LV19.14, TV.LVALG.53, TV.LVALG.58
26. ANS: A
DIF: L1
REF: 11-7 Trigonometric Ratios
OBJ: 11-7.2 Solving Problems Using Trigonometric Ratios
TOP: 11-7 Example 5
KEY: angle of elevation,trigonometric ratios,tangent,word problem,problem solving
MSC: NAEP M1f, NAEP M1m, CAT5.LV19.46, CAT5.LV19.55, CAT5.LV19.56, IT.LV15.CP,
TV.LV19.10, TV.LV19.13, TV.LV19.14, TV.LVALG.53, TV.LVALG.58
SHORT ANSWER
27. ANS:
4 6
30
=
=
=
=
=
=
=
4
6
⋅
30
4
180
900
30
30
4
180
30
4 36 ⋅ 5
30
4⋅6 5
30
24 5
30
4 5
5
DIF: L2
REF: 11-1 Simplifying Radicals
OBJ: 11-1.2 Simplifying Radical Expressions Involving Quotients
STO: CA 1.0, CA 1.1, CA 2.0
TOP: 11-1 Example 7
KEY: rationalize,radical expressions,radicand in the denominator,Division Property of Square Roots
MSC: NAEP N3a, NAEP N5b, NAEP A3b, NAEP A3c, CAT5.LV19.50, CAT5.LV19.51,
IT.LV15.AM, S9.TSK1.NS, S10.TSK1.NS, TV.LV19.52, TV.LVALG.53
4
ID: A
28. ANS:
a.
Week
Sales
1
53
2
64
3
73
4
80
5
87
b.
c. about $100,000
DIF:
OBJ:
TOP:
KEY:
MSC:
L2
REF: 11-6 Graphing Square Root Functions
11-6.1 Graphing Square Root Functions
STO: CA 17.0
11-6 Example 2
graphing,square root,multi-part question,word problem,problem solving
CAT5.LV19.54, IT.LV15.DI, TV.LV19.14, TV.LV19.16, TV.LVALG.56
5
ID: A
29. ANS:
x
f(x)
−4
−4
−3
−3
−2
−2.6
−1
−2.3
DIF:
OBJ:
KEY:
MSC:
L2
REF: 11-6 Graphing Square Root Functions
11-6.2 Translating Graphs of Square Root Functions
STO: CA 17.0
square root,graphing,translation
CAT5.LV19.54, IT.LV15.DI, TV.LV19.14, TV.LV19.16, TV.LVALG.56
6