Download Algebra II Practice Test CH1 25 49 7 5 35 5 7 5

Algebra II Practice Test CH1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Write the set in set-builder notation.
____
a. ÏÔ x| − 3 ≤ x < 4 ¸Ô
c. ÏÔ x| − 3 < x < 4 ¸Ô
ÔÌÓ
Ô˝˛
ÔÌÓ
Ô˝˛
b. [–3, 4)
d. [–3, 4]
2. What statement can be determined from the diagram?
____
a. Every square is a rhombus.
c. No parallelogram is a rhombus.
b. Every rhombus is a square.
d. No parallelogram is a square.
3. Which example shows that the Associative Property does not hold for division?
a. (24 ÷ 3) ÷ 2 ≠ 24 ÷ (3 ÷ 2)
c. 81 ÷ 3 ÷ 3 ≠ 81 ÷ (3 ÷ 3)
18
÷
(3
÷
6)
≠
18
÷
(6
÷
3)
b.
d. (48 − 12) − 4 ≠ 48 − (12 − 4)
____
4. Simplify the expression
a. 5
7
b.
____
2
25
49
5. Simplify
a.
b.
35
5
7
35
50 .
98
c. 25
49
d. 5
7
7
by rationalizing the denominator.
5
c.
7
5
d. 7
5
____
____
____
____
2
2
6. Simplify the expression s − 3s + t + 5s .
a. 5s2 − 3s + t
b. 3s2 + t
c. 2s2 + t
d. 6s2 − 3s + t
7. Murphy’s motorcycle gets 55 miles per gallon of gas on the highway and 45 miles per gallon in the
city. The motorcycle holds 8 gallons of gas. Write and simplify an expression for the total number
of miles Murphy can travel if he has a full tank of gas but uses 2 gallons on the highway and the
rest in the city.
a. 10x + 36; 270 miles
c. 36x + 10; 110 miles
b. 10x + 36; 380 miles
d. 36x + 10; 420 miles
8. Write the expression (5xy)4 in expanded form.
a. (5xy)(5xy)(5xy)(5xy)
c. 20xy
b. (5xy) + (5xy) + (5xy) + (5xy)
d. 4(5xy)(5xy)(5xy)(5xy)
9. Give the domain and range of the relation.
x
2
8
0
–3
____
y
5
17
0
–5
a. D: {–3, 0, 2, 8}; R: {–5, 0, 5, 17}
b. D: {–5, 0, 5, 17}; R: {–3, 0, 2, 8}
c. D: {2, 8, –3, 5, 17, –5}; R: {0}
d. D: {–3, 2, 8}; R: {–5, 5, 17}
10. Use the vertical-line test to determine whether the relation is a function. If not, identify two points
a vertical line would pass through.
a. Yes, the relation is a function.
b. No, the relation is not a function.
(0, 4) and (0, –4)
____
____
____
11. Which is an element of the range of the graphed function?
a. 3
c. 4
b. 2
d. 0
12. For f(x) = −5x − 2, evaluate f(5).
a. 23
c. –27
b. –15
d. –32
13. Use a table to perform a vertical stretch of f(x) = x by a factor of 3. Graph the transformed function
on the same coordinate plane as the original function.
a.
c.
b.
____
d.
14. In the deep ocean, the length of a wave in meters is related to the period of the wave in seconds.
Graph the relationship between wave period and wavelength and identify which parent function
best describes it. (Hint: Although time cannot be negative, the negative portion of this function has
been provided for you.)
Wave period
(sec)
–1
1
2
3
5
a.
Wavelength (m)
1.56
1.56
6.24
14.04
39
Linear c.
parent function
Quadratic
parent function
b.
____
Cubic d.
Square-
parent function
root parent function
15. For which function is 3 NOT an element of the range?
a. y = −2x + 4
c. y = 3
5
b. y = x
d. y = −(−x)2
Numeric Response
16. By the Pythagorean Theorem, the length d of a diagonal of a rectangle is given by d =
Find the length of diagonal MO to the nearest tenth.
17. What is the value of 3x(y − 6)2 when x = 9 and y = 3?
Matching
Match each vocabulary term with its definition.
a. principal root
b. radicand
c. radical symbol
d. power
e. like radical terms
l2 + w 2 .
f. rationalize the denominator
g. cube root
____
____
18. a method of rewriting a fraction by multiplying by another fraction that is equivalent to 1 in order
to remove radical terms from the denominator
19. the positive square root of a number, indicated by the radical sign
____
____
____
20. the symbol
used to denote a root
21. radical terms having the same radicand and index
22. the number or expression under a radical sign
Match each vocabulary term with its definition.
a. domain
b. x-axis
c. range
d. relation
e. dependent variable
f. independent variable
g. y-axis
h. function
____
____
____
____
____
23.
24.
25.
26.
27.
a type of relation that pairs each element in the domain with exactly one element in the range
a set of ordered pairs
a variable whose value depends on the value of the input, also known as the output of a function
the set of output values of a function or relation
the set of input values of a function or relation
Algebra II Practice Test CH1
Answer Section
MULTIPLE CHOICE
1. ANS: A
Use inequalities to rewrite the set in set-builder notation. Use a less than or equal sign when the
endpoint is included in the set (closed circle) or a less than sign if the endpoint is not included in
the set (open circle).
Feedback
A
B
C
D
Correct!
Use set-builder notation, not interval notation.
The left endpoint should be included in the set.
Use set-builder notation, not interval notation, and do not include the right
endpoint in the set.
PTS: 1
DIF: Average
REF: Page 9
OBJ: 1-1.3 Translating Between Methods of Set Notation
NAT: 12.1.1.d
TOP: 1-1 Sets of Numbers
2. ANS: A
Since the region representing squares is entirely within the region representing rhombi, every
square is a rhombus.
Feedback
A
B
C
D
Correct!
According to the diagram, some rhombi are not squares.
According to the diagram, some parallelograms are rhombi.
According to the diagram, some parallelograms are squares.
PTS: 1
DIF: Advanced
NAT: 12.1.5.f
TOP: 1-1 Sets of Numbers
3. ANS: A
This example, (24 ÷ 3) ÷ 2 ≠ 24 ÷ (3 ÷ 2), shows that the Associative Property does not hold for
division. In the Associative Property, numbers are regrouped.
Feedback
A
B
C
D
Correct!
This example shows the Commutative Property, not the Associative Property.
In the Associative Property, numbers are regrouped.
The question asks for an example using division, not subtraction.
PTS: 1
DIF: Advanced
TOP: 1-2 Properties of Real Numbers
4. ANS: D
NAT: 12.1.5.e
50 =
98
2 ⋅ 25 =
2 ⋅ 49
25 =
49
25 = 5
49 7
Feedback
A
B
C
D
First divide out any factors common to the numerator and the denominator.
Factor the numerator and the denominator. Divide out any common factors and
look for perfect square factors.
Take the square root of the numerator and the denominator.
Correct!
PTS:
OBJ:
TOP:
5. ANS:
1
DIF: Basic
REF: Page 22
1-3.2 Simplifying Square-Root Expressions
1-3 Square Roots
A
7 =
5
=
=
7
5
ÊÁ
ÁÁ
ÁÁ
ÁË
35
25
35
5
5
5
ˆ˜
˜˜
˜˜
˜¯
NAT: 12.5.3.c
Multiply by a form of 1 to get a perfect-square
radicand in the denominator.
Simplify the denominator.
Feedback
A
B
C
D
Correct!
A quotient with a square root in the denominator is not simplified.
Rationalize the denominator by finding the appropriate form of 1 to multiply by.
First, multiply by a form of 1 to get a perfect-square radicand in the
denominator. Then, simplify the denominator.
PTS:
OBJ:
TOP:
6. ANS:
1
DIF: Average
REF: Page 23
1-3.3 Rationalizing the Denominator
1-3 Square Roots
D
2
Identify like terms.
s − 3s + t + 5s2
2
Combine like terms.
6s − 3s + t
NAT: 12.5.3.c
Feedback
A
B
C
D
A term that is written without a coefficient has a coefficient of 1.
Combine only the like terms.
Combine only the like terms.
Correct!
PTS: 1
DIF: Basic
REF: Page 28
OBJ: 1-4.3 Simplifying Expressions
NAT: 12.5.3.c
TOP: 1-4 Simplifying Algebraic Expressions
7. ANS: B
Let x be the number of gallons used on the highway, so 8 − x is the remaining number of gallons to
be used in the city.
55x + 45(8 − x)
= 55x + 360 − 45x
= 10x + 360
Distribute 45.
Combine like terms.
Substitute 2 for x, as this is given as the number of gallons used on the highway.
10(2) + 360 = 380
Feedback
A
B
C
D
Calculate for total gas used.
Correct!
The trip includes both city and highway travel.
Be sure to clearly define your variable for either city or highway gallon use.
PTS: 1
NAT: 12.5.2.b
8. ANS: A
(5xy)4
= (5xy)(5xy)(5xy)(5xy)
DIF: Average
REF: Page 29
OBJ: 1-4.4 Application
TOP: 1-4 Simplifying Algebraic Expressions
The base is 5xy and the exponent is 4.
5xy is a factor 4 times.
Feedback
A
B
C
D
Correct!
Use the base as a factor, not as an addend.
Write the base four times.
Write the base four times.
PTS: 1
DIF: Basic
REF: Page 34
OBJ: 1-5.5 Writing Exponential Expressions in Expanded Form
NAT: 12.1.1.f
TOP: 1-5 Properties of Exponents
9. ANS: A
The domain is the set of all x-values. The range is the set of all y-values.
Feedback
A
B
C
D
Correct!
The domain is the set of all x-values. The range is the set of all y-values.
The domain includes only the x-values.
The domain is the set of all x-values.
PTS: 1
DIF: Basic
REF: Page 44
OBJ: 1-6.1 Identifying Domain and Range
NAT: 12.5.1.g
TOP: 1-6 Relations and Functions
KEY: domain | range | function | relation
10. ANS: B
If any vertical line passes through more than one point on the graph of a relation, the relation is not
a function.
This relation is not a function. A vertical line at x = 0 would pass through (0, 4) and (0, –4).
Feedback
A
B
A vertical line can pass through more than one point on this graph.
Correct!
PTS: 1
DIF: Basic
REF: Page 46
OBJ: 1-6.3 Using the Vertical-Line Test NAT: 12.5.1.e
TOP: 1-6 Relations and Functions
11. ANS: D
The range is the set of y-coordinates on the graph. According to the graph, the range is y < 1.
Feedback
A
B
C
D
The range includes only the y-coordinates on the graph.
The range includes only the y-coordinates on the graph.
The range includes only the y-coordinates on the graph.
Correct!
PTS: 1
DIF: Advanced
TOP: 1-6 Relations and Functions
12. ANS: C
f(x) = −5x − 2
f(5) = −5(5) − 2
f(5) = −27
NAT: 12.5.1.g
Substitute 5 for x.
Simplify.
Feedback
A
B
C
D
Substitute the value of x in the function, and then simplify.
Substitute the value of x in the function, and then simplify.
Correct!
Substitute the value of x in the function, and then simplify.
PTS:
OBJ:
KEY:
13. ANS:
1
DIF: Basic
1-7.1 Evaluating Functions
function | input | output | evaluate
D
REF: Page 51
NAT: 12.5.2.b
TOP: 1-7 Function Notation
Stretching a function vertically means y-coordinates will change and move away from the x-axis,
relative to the original function. Use a table to determine points for the stretched function.
x
1
–1
0
2
y
1
–1
0
2
3y
3
–3
0
6
Feedback
A
B
C
D
To stretch the function multiply each y-coordinate by 3.
To stretch the function multiply each y-coordinate by 3.
A vertical stretch should move the y-values farther from the x-axis.
Correct!
PTS:
OBJ:
TOP:
14. ANS:
1
DIF: Average
REF: Page 61
1-8.3 Stretching and Compressing Functions
1-8 Exploring Transformations
C
NAT: 12.5.2.d
The graph is most like a parabola, so the graph resembles the shape of the quadratic parent
function.
Feedback
A
B
C
D
The negative data mirrors the positive side of the graph.
The negative portion of the cubic function curves down, but data shows a curve
upwards.
Correct!
The square root function curves in the opposite direction that the data indicates.
PTS: 1
NAT: 12.5.1.h
DIF: Average
REF: Page 69
OBJ: 1-9.3 Application
TOP: 1-9 Introduction to Parent Functions
15. ANS: D
3 is NOT an element of the range of a function if no value of x returns the value 3.
If y = 3, then the range is only the number 3 and 3 is an element of the range.
If y = x5, then the range is all real numbers and 3 is an element of the range.
If y = −2x + 4, then the range is all real numbers and 3 is an element of the range.
If y = −(−x)2, then for any value of x, y ≤ 0. To see this clearly, make a table.
x values
y values
−2
−1
0
1
2
2
2
2
−(2) = −4
−(1) = −1
−(0) = 0
2
−(−1) = −1 −(−2)2 = −4
Thus, 3 is NOT an element of y = −(−x)2 .
Feedback
A
B
C
D
The range of the function is all real numbers and includes the given number.
The range of the function is all real numbers and includes the given number.
The range of the function is exactly the given number.
Correct!
PTS: 1
DIF: Advanced
NAT: 12.5.1.d
TOP: 1-9 Introduction to Parent Functions
NUMERIC RESPONSE
16. ANS: 10.8
PTS: 1
17. ANS: 243
DIF:
Advanced
NAT: 12.5.3.c
TOP: 1-3 Square Roots
PTS: 1
DIF: Average
NAT: 12.5.3.c
TOP: 1-4 Simplifying Algebraic Expressions
MATCHING
18. ANS:
TOP:
19. ANS:
TOP:
20. ANS:
TOP:
21. ANS:
TOP:
22. ANS:
TOP:
F
PTS:
1-3 Square Roots
A
PTS:
1-3 Square Roots
C
PTS:
1-3 Square Roots
E
PTS:
1-3 Square Roots
B
PTS:
1-3 Square Roots
1
DIF:
Basic
REF: Page 22
1
DIF:
Basic
REF: Page 21
1
DIF:
Basic
REF: Page 21
1
DIF:
Basic
REF: Page 23
1
DIF:
Basic
REF: Page 21
23. ANS:
TOP:
24. ANS:
TOP:
25. ANS:
TOP:
26. ANS:
TOP:
27. ANS:
TOP:
H
PTS: 1
1-6 Relations and Functions
D
PTS: 1
1-6 Relations and Functions
E
PTS: 1
1-7 Function Notation
C
PTS: 1
1-6 Relations and Functions
A
PTS: 1
1-6 Relations and Functions
DIF:
Basic
REF: Page 45
DIF:
Basic
REF: Page 44
DIF:
Basic
REF: Page 52
DIF:
Basic
REF: Page 44
DIF:
Basic
REF: Page 44