ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
2016-2017
Instructional Materials for WCSD Math Common Finals
The Instructional Materials are for student and teacher use and are aligned
to the 2016-2017 Course Guides for the following course:
 Algebra 1 Semester 2 S1 (#7824)
When used as test practice, success on the Instructional Materials does not
guarantee success on the district math common final.
Students can use these Instructional Materials to become familiar with the
format and language used on the district common finals. Familiarity with
standards and vocabulary as well as interaction with the types of problems
included in the Instructional Materials can result in less anxiety on the part
of the students. The length of the actual final exam may differ in length
from the Instructional Materials.
Teachers can use the Instructional Materials in conjunction with the course
guides to ensure that instruction and content is aligned with what will be
assessed. The Instructional Materials are not representative of the depth
or full range of learning that should occur in the classroom.
*Students will be allowed to use a
non-programmable scientific calculator
on Algebra 1 Semester 2 S1 and
Algebra 1 Semester 2 S2 final exams.
Updated 9/15/15
Algebra 1 Reference Sheet
Note: You may use these formulas throughout this entire test.
Linear
Quadratic
𝑦2 − 𝑦1
𝑥2 − 𝑥1
Vertex-Form
𝑦 = 𝑎(𝑥 − h)2 + 𝑘
𝑥1 + 𝑥2 𝑦1 + 𝑦2
𝑀=(
,
)
2
2
Standard Form
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Intercept Form
𝑦 = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)
Slope
𝑚=
Midpoint
Distance
Slope-Intercept Form
𝑦 = 𝑚𝑥 + 𝑏
Exponential
(h, k) Form
Probability
𝑦 = 𝑎𝑏 𝑥−h + 𝑘
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵)
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵|𝐴)
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
Volume and Surface Area
𝑉 = 𝜋𝑟 2 ℎ
4
𝑉 = 𝜋𝑟 3
3
𝑆𝐴 = 2(𝜋𝑟 2 ) + ℎ(2𝜋𝑟)
𝑆𝐴 = 4𝜋𝑟 2
1
1
𝑉 = 𝜋𝑟 2 ℎ
3
1
𝑆𝐴 = 𝜋𝑟 2 + (2𝜋𝑟 ∙ 𝑙)
2
Updated 9/15/15
𝑉 = 𝐵ℎ
3
1
𝑆𝐴 = 𝐵 + (𝑃𝑙)
2
Where 𝐵 =base area
and 𝑃 =base perimeter
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
2016-2017
Multiple Choice: Identify the choice that best completes the statement or answers the question.
1.
1
Which of the following graphs represents 𝑓(𝑥) = 2 |𝑥 − 3| − 2 ?
A.
C.
B.
D.
2. Which of the following functions represent 𝑔(𝑥) and ℎ(𝑥) based on the following
information:
 𝑔(𝑥) is the result of reflecting the graph of 𝑓(𝑥) = |𝑥| over the x-axis, then
translating the function up one unit.

ℎ(𝑥) is the result of translating the graph of 𝑓(𝑥) = |𝑥| up one unit, then reflecting
the function over the x-axis.
A. 𝑔(𝑥) = −|𝑥| + 1
ℎ(𝑥) = −|𝑥| + 1
C. 𝑔(𝑥) = −|𝑥 + 1|
ℎ(𝑥) = −|𝑥 − 1|
B. 𝑔(𝑥) = −|𝑥| − 1
ℎ(𝑥) = −|𝑥| + 1
D. 𝑔(𝑥) = −|𝑥| + 1
ℎ(𝑥) = −|𝑥| − 1
Updated 9/15/15
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
2016-2017
Courses: Algebra 1 Semester 2 S1 (#7826)
3. Which of the following is the solution for x in the equation −2|𝑥 + 3| + 6 = 10 ?
A. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
C. 𝑥 = 1
B. 𝑥 = −5, 𝑥 = −1
D. 𝑥 = −5
4. Which of the following is the solution for x in the equation −3|𝑥 + 4| = −6 ?
5.
A. 𝑥 = −2
C. 𝑥 = −2 and 𝑥 = 6
B. 𝑥 = −6 and 𝑥 = −2
D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
1
If 𝑓(𝑥) = 2|𝑥 + 3| − 4 and 𝑔(𝑥) = 2 𝑥 + 5, use the tables below find the x-value(s)
where 𝑓(𝑥) = 𝑔(𝑥).
𝑓(𝑥) = 2|𝑥 + 3| − 4
𝑥
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
A. 𝑥 = 2, 4, 6
B. 𝑥 = 2, 6
Updated 9/15/15
𝑓(𝑥)
4
2
0
−2
−4
−2
0
2
4
6
8
10
1
𝑔(𝑥) = 𝑥 + 5
2
𝑥
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
C. 𝑥 = −6, 2
D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
𝑔(𝑥)
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
2016-2017
6. Which graph below models the solutions to the equation −3|𝑥 + 2| + 4 = −2𝑥 ?
7.
A.
C.
B.
D.
What is the simplified form of (4𝑔−3 ℎ4 )−3 ?
A.
−12𝑔6
ℎ12
C.
12𝑔9
ℎ
B.
−64𝑔9
ℎ12
D.
𝑔9
64ℎ12
8. Let 𝑓(𝑥) = −3𝑐 1/2 and 𝑔(𝑥) = 2𝑐 15/2 𝑑 −8. Find ℎ(𝑥) = 𝑓(𝑥) ∙ 𝑔(𝑥).
−5𝑐 7
𝑑8
A. ℎ(𝑥) =
−6𝑐 8
𝑑8
C. ℎ(𝑥) =
B. ℎ(𝑥) =
6𝑑 8
𝑐8
D. ℎ(𝑥) = −6𝑐𝑑
Updated 9/15/15
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
9.
What is the simplified form of
A.
9𝑛4 𝑝4
𝑚3
A.
√21
7
B. √63
7
11.
4𝑚𝑛−2 𝑝−4
? (Assume that 𝑚 ≠ 0, 𝑛 ≠ 0, and 𝑝 ≠ 0)
9𝑛8 𝑝4
𝑚5
C.
9𝑛8
B.
𝑚5 𝑝4
10. Simplify: √
36𝑚−4 𝑛6
2016-2017
9𝑚5
D. 8 4
𝑛 𝑝
18
42
C. 3
D. √3
Find the simplified form of the following expression, assuming 𝑥 ≠ 0, 𝑦 ≠ 0, and 𝑧 ≠ 0:
−2
2𝑥 −4 𝑦 5 𝑧 3
( 7 0 )
𝑥 𝑦𝑧
A.
−4𝑧 6
𝑥6𝑦8
C.
𝑥6
4𝑦 8 𝑧 6
B.
𝑥 22
4𝑦 8 𝑧 6
D.
𝑦5𝑧3
4𝑥11
Updated 9/15/15
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
12.
2016-2017
1
0
Which of the following expressions is equivalent to (3−1 𝑥 0 )−2 + (2𝑦 0 )−3 − 5 [3 (3 𝑥 3 ) ]?
A. 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
B. 4
1
8
C. −5
7
8
D. −6
7
8
13. Write a recursive formula for the sequence below, assuming 𝑓(1) is the first term in the
sequence:
3, −6, 12, −24, 48 …
A. 𝑓(1) = −6 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ (−2), for 𝑛 ≥ 2
B. 𝑓(1) = −2 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ 3, for 𝑛 ≥ 2
C. 𝑓(1) = 3 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ (−2), for 𝑛 ≥ 2
D. 𝑓(1) = 3 and 𝑓(𝑛) = 𝑓(𝑛 − 1) − 9, for 𝑛 ≥ 2
14. Write an explicit formula for the geometric sequence given 𝑎3 = 1 and 𝑎5 = 0.25.
Assume the common ratio is positive.
A. 𝑎𝑛 = 8(0.25)𝑛−1
C. 𝑎𝑛 = 0.5(4)𝑛−1
B. 𝑎𝑛 = 4(0.5)𝑛−1
D. 𝑎𝑛 = 0.25(8)𝑛−1
Updated 9/15/15
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
2016-2017
Courses: Algebra 1 Semester 2 S1 (#7826)
15. Determine which of the following equations represent exponential growth or decay.
Equation 1
Equation 2
−𝑥
𝑦 = 1.5
𝑦 = 0.8
Equation 3
𝑥
Equation 4
−𝑥
𝑦 = 2.7𝑥
𝑦 = 0.5
A. Equation 1:
Equation 2:
Equation 3:
Equation 4:
Growth
Growth
Decay
Decay
C. Equation 1:
Equation 2:
Equation 3:
Equation 4:
Decay
Growth
Growth
Decay
B. Equation 1:
Equation 2:
Equation 3:
Equation 4:
Decay
Decay
Growth
Growth
D. Equation 1:
Equation 2:
Equation 3:
Equation 4:
Growth
Decay
Decay
Growth
16. Which of the following represents the function 𝑓(𝑥) = 2𝑥 − 5 ?
A.
C.
B.
D.
Updated 9/15/15
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
2016-2017
Courses: Algebra 1 Semester 2 S1 (#7826)
17.
1 2
Which of the following functions is equivalent to the function 𝑓(𝑥) = (3) ?
A. I, III, V
B. II, IV, VI
C. I, II, VI
D. III, V, VI
I.
𝑔(𝑥) = 3−2
1
9
2 −1
III. 𝑔(𝑥) = ( )
3
II.
𝑔(𝑥) =
IV. 𝑔(𝑥) = 2(−3)
V.
𝑔(𝑥) =
1
6
VI. 𝑔(𝑥) = 9−1
18. The maximum height reached by a bouncing ball is given by ℎ(𝑥) = 10(0.75)𝑥 where h is
measured in feet and x is the bounce number. Describe the domain of this function and what it
means when 𝑥 = 0.
A. The domain is all real numbers. When the bounce number 𝑥 = 0, the height h of the ball
is 10 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and
bounces.
B. The domain is all real numbers. When the bounce number 𝑥 = 0, the height h of the ball
is 7.5 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and
bounces.
C. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the bounce
number x and does not have units. When 𝑥 = 0 the height h of the ball is 10 𝑓𝑒𝑒𝑡, which
represents its original height of the ball before it is dropped and bounces.
D. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the bounce
number x and does not have units. When 𝑥 = 0 the height h of the ball is 7.5 𝑓𝑒𝑒𝑡, which
represents its original height of the ball before it is dropped and bounces.
Updated 9/15/15
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
2016-2017
19. Which of the following best describes the data in the table?
A.
B.
C.
D.
𝑥
1
2
3
4
𝑦
3
9
27
81
Exponential with a growth factor of 3
Linear with a rate of change of 6
Quadratic with a second difference of 12
none of the above
20. Use the table below to help determine which function has the greatest value as x gets larger
and larger.
𝑥
𝑓(𝑥) = 𝑥 + 3
𝑔(𝑥) = 3𝑥
ℎ(𝑥) = 𝑥 3
3
4
5
6
A. 𝑓(𝑥) has the greatest value as x gets larger and larger.
B. 𝑔(𝑥) has the greatest value as x gets larger and larger.
C. ℎ(𝑥) has the greatest value as x gets larger and larger.
D. 𝑖(𝑥) has the greatest value as x gets larger and larger.
Updated 9/15/15
𝑖(𝑥) = 3𝑥
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
2016-2017
Courses: Algebra 1 Semester 2 S1 (#7826)
21. Since the year 2001 the population of community A grows exponentially as illustrated in
the table. The exponential rate of growth is 1.3. What are the units for the rate of growth
in the table?
𝑦𝑒𝑎𝑟
𝑝𝑒𝑜𝑝𝑙𝑒
2001
1200
2002
1560
2003
2028
2004
2636.4
2005
3427.32
2006
4455.52
A. people per year
B. years per people
C. years
D. people
22. If 𝑓(𝑥) = 3 ∙ 4𝑥 and 𝑔(𝑥) = 3 ∙ 2𝑥 , compare the functions and determine which of the
following statements is correct.
A. The x-intercept of 𝑓(𝑥) is greater than the x-intercept of 𝑔(𝑥).
B. The y-intercept of 𝑓(𝑥) is greater than the y-intercept of 𝑔(𝑥).
C. The functions increase at the same rate.
D. The functions have the same y-intercept.
23. What is the solution for x in 4𝑥 = 64 ?
A. 𝑥 = 16
C. 𝑥 = 3
B. 𝑥 = 4
D. 𝑥 = 2
Updated 9/15/15
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
24. What is the solution for x in 52𝑥−9 = 125 ?
A. 𝑥 = 6
C. 𝑥 = 5
B. 𝑥 = 4
D. 𝑥 = 3
25. What is the solution to the system graphed?
A. (2, 4)
B. (4, 2)
C. (1, 2)
D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
26. What is the solution for x in the system?
𝑦=8
{
𝑦 = 2𝑥
A. 𝑥 =
1
3
C. 𝑥 = 1
B. 𝑥 =
1
2
D. 𝑥 = 3
Updated 9/15/15
2016-2017
ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS
Courses: Algebra 1 Semester 2 S1 (#7826)
Algebra 1 Semester 2 S1 Instructional Materials 2016-17Answers
Unit 6
Unit 7
1.
D
7.
D
2.
D
8.
A
3.
A
9.
C
4.
B
10.
A
5.
C
11.
B
6.
B
12.
C
13.
C
14.
B
15.
B
16.
B
17.
D
18.
C
19.
A
20.
D
21.
A
22.
D
23.
24.
25.
26.
C
A
A
D
Updated 9/15/15
2016-2017