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Summer Mathematics Packet
For Incoming Algebra 1
(2016-2017 School Year)
This packet must be turned into your Algebra 1 teacher by the second day of instruction in
August 2016! Failure to turn in this packet will result in a grade penalty of 10 points per day.
Every problem in the packet must be completed with work shown where applicable. If you fail
to show work the packet will not be accepted and you will automatically receive a 10 point
deduction along with the advice to turn in the packet the next school day. On the third day of
instruction you will take your first Algebra 1 Exam, make sure you are prepared by
completing this packet and understanding how to perform all operations without the aid of a
video, teacher, friend, etc…
No Exceptions, No Excuses, & No Sad Stories!
Inside this mathematics packet you will find a wide range of concepts. If you believe these
concepts are too difficult it is your responsibility to find help prior to the packet due date. Ask
your 8th Grade Math or future Algebra teacher for help or look for video tutorials on You-Tube
or Khan Academy. There is an abundance of self-help videos, your Algebra teacher will not
accept that you are unable to find assistance for the following concepts:
Verbal & Algebraic expression
Order of operations
Distributive Property
Solve 1 step, 2 step, and multi-step equations and inequalities
Laws of Exponents
Scientific Notation
Proportion and Similarity
Percent: percent of change, markup, discount and tax
Linear Equations: slope, graphing, and writing linear equations
The Pythagorean Theorem
Find the area of, formula will not be provided for your exam:
o Circle
o Triangle
o Square
o Rectangle
o Trapezoid
Find the volume of, formula will not be provided for your exam:
o Cylinder
o Sphere
o Cone
o Rectangular prism
©M 42J0w1o5e RKcuRtFaO JS6o2fvt8wGaIrieV mLWLQCR.A 1 PADl5lT GraiKg8hktHsp iraeJsbe4rYvPeOdt.A R SMxaddNei XwGiYtrhR uIBn1faidnfiTtiem RP9rJeL-fAqlYgPeyb8rPan.K Worksheet by Kuta Software LLC
Summer PacketID: 1
Name___________________________________
Period____Date________________©l Y260V1D56 CKxurtSav 3SwoLfNtMwWaorreO RLTL8Cq.d 7 TAWltlS 4rhiJgIhYtNs8 erae0sQelrzvWeNdb.W
Incoming Algebra 1 Scholars
Write each as an algebraic expression.
1) 8 more than x
A)
8 −
x B)
x
2
C)
x + 8 D)
x
8
Write each as a verbal expression.
2)
62
A) 6 squared
B) 2 times 6
C) the quotient of 2 and 6
D) 6 more than 2
Evaluate each expression.
3) 21 decreased by 16
A) 336 B) 13
C) 5 D) 46
4) 11 more than 2
A) 13 B) −9
C) 38 D) 4
5)
3 ×
3 × 4
A) 33 B) 40
C) 38 D) 36
6)
(
3 + 3) ÷ (
1 + 1) + 3
A) 8 B) 9
C) 7 D) 6
Evaluate each using the values given.
7)
a +
b ÷ 3; use
a = 4, and
b = 3
A) 7 B) 5
C) 4 D) 8
-1-
©N s2t04185j 9KTuwtXao ASSoNfSt3wwaVr9eN FL4LECy.o b iAOl6lx qrPiTgJhMtDsi irKeksPejrpvde8dC.4 M CM6aUdoeE Kw6iCtOhg qIHn9fZiqnMiMtMef VP4ryet-lAKlKgteWbGrRa5.q Worksheet by Kuta Software LLC
Simplify each expression.
8)
−2
x − 7
x
A)
9
x + 10 B) −13
x
C) −15
x D) −9
x
9)
−4(
−7 − 9
n)
A)
26 + 32
n B)
28 + 32
n
C)
28 + 36
n D)
−4
n + 28
10)
9(
−8
r − 9) − 4
r
A)
−86
r − 81 B)
−76
r − 81
C)
−7 − 10
r D)
−86
r − 87
11)
−4(
−4
x + 1) −
9(
1 − 4
x)
A)
52
x − 13 B)
37
x − 42
C)
−79
x + 31 D)
−79
x + 37
Solve each equation.
12) −4 =
n +
15
A) {11} B) {−60}
C)
{
−4
15} D) {−19}
13)
9 +
a
7 = 3
A) {7} B) {12}
C) {−18} D) {15}
14)
−5
v + 8
v = −3
A) {4} B) {−5}
C) {−1} D) {−16}
15)
7(
−3
x + 7) − 5
x = −159
A) {−12} B) {1}
C) {8} D) {−10}
16)
−4(
2
x + 6) −
4(
1 − 2
x) = −28
A) {7}
B) {11}
C) { All real numbers. }
D) {−10}
-2-
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Draw a graph for each inequality.
17)
r > 3
A) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
B) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
C) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
D) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
Solve each inequality and graph its solution.
18)
4
k < 24
A)
k < 20 : 16 18 20 22 24
B)
k > 20 : 16 18 20 22 24
C)
k > 96 : 92 94 96 98 100 102
D)
k < 6 : 4 6 8 10 12
19)
p
4 + 2 ≤ 0
A)
p ≤ −8 : −14 −12 −10 −8 −6 −4
B)
p ≥ −4 : −8 −6 −4 −2 0 2
C)
p ≤ −4 : −8 −6 −4 −2 0 2
D)
p ≥ −14 : −18 −16 −14 −12 −10 −8
20) 36 ≤
4 +
4
x
A)
x ≥ 8 : 2 4 6 8 10 12
B)
x ≤ 8 : 2 4 6 8 10 12
C)
x ≤ 8 : 2 4 6 8 10 12
D)
x ≤ 8 : 2 4 6 8 10 12
21)
4
x +
6(
2
x − 7) < 86
A)
x < −17 : −22 −20 −18 −16 −14
B)
x < −32 : −40 −38 −36 −34 −32 −30
C)
x < 8 : 4 6 8 10 12
D)
x < −17 : −22 −20 −18 −16 −14
Simplify. Your answer should contain only positive exponents.
22)
6
m3 ⋅
2
m3
A) 28
m7 B) 12
m6
C) 5
m5 D) 18
m6
23)
4
r3
5
r3
A)
3
r2
7B)
1
2
C)
4
5D)
r
2
-3-
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24)
(
3
x4)2
A) 64
x8 B) 8
x6
C) 36
x6 D) 9
x8
Write each number in scientific notation.
25) 0.072
A)
7.2 ×
10−2
B)
7.2 ×
102
C)
0.072 ×
102
D)
0.72 ×
102
Write each number in standard notation.
26)
4.8 ×
10−5
A) 0.0000048
B) 0.000000048
C) 0.00000048
D) 0.000048
State if each pair of ratios forms a proportion.
27)
3
2 and
6
4
A) Yes B) No
Solve each proportion.
28)
7
4 =
x
9
A) {8.2} B) {6}
C) {15.75} D) {7.8}
-4-
©2 S26041M5A bKMuWtCaO 5SjomfCtswhaQroeU ULnLhCj.k a oArlml9 FrzipgLhGtpsk HrneQs9eOr7vmekdZ.i S WM1aadueh rwribtdhD 3IenyfwiJnXiEt6eD OPIrpe2-RAAlggBeRbBrea2.T Worksheet by Kuta Software LLC
Each pair of figures is similar. Find the missing side.
29) 12
32
3
x
A) 32 B) 2
C) 128 D) 8
Find each percent change. Round to the nearest tenth of a percent. State if it is an increase or decrease.
30) From 60 to 47
A) 127.7% decrease
B) 21.7% decrease
C) 13% decrease
D) 81.3% increase
Solve each problem.
31) 84 is what percent of 103?
A) 1.23% B) 0.82%
C) 81.6% D) 122.6%
32) 71% of 127.6 is what?
A) 179.7 B) 9059.6
C) 86.2 D) 90.6
33) 5 is 14% of what?
A) 0.7 B) 4.8
C) 35.7 D) 476
Find each percent change. Round to the nearest tenth of a percent. State if it is an increase or decrease.
34) From 73 to 100
A) 27% decrease
B) 127% increase
C) 137% increase
D) 37% increase
-5-
©H w20071N5K UKYudtIa6 gShoifLtnw7auroeB 0LDLZCW.0 b OAyldlq TrDisgOhGtBsG Jr0emspegr6vJevdC.Z H KMeazd2e5 lwxiOtlhu qITn6fuiMnhibtDea CPtrlew-aAslngredb3rCa8.Z Worksheet by Kuta Software LLC
Find the selling price of each item.
35) Cost of a purse: $145.00
Markup: 30%
A) $174.00 B) $166.75
C) $188.50 D) $43.50
36) Original price of a cell phone: $169.95
Discount: 10%
A) $186.94 B) $152.95
C) $17.00 D) $152.96
37) Original price of a shirt: $24.99
Tax: 4%
A) $26.24 B) $25.99
C) $23.99 D) $1.00
Find the slope of each line.
38)
x
y
A)
−5
3B)
5
3
C)
−3
5D)
3
5
39)
y = 1
A)
−2
5B)
2
5
C) 0 D) Undefined
Find the slope of the line through each pair of points.
40) (16, 0), (−15, 10)
A)
10
31B)
31
10
C)
−10
31D)
−31
10
-6-
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Write the slope-intercept form of the equation of each line given the slope and y-intercept.
41) Slope =
−7
4, y-intercept = −5
A)
y =
−5
x −
7
4
B)
y =
−5
4
x −
7
4
C)
y =
1
2
x −
7
4
D)
y =
−7
4
x − 5
Write the slope-intercept form of the equation of each line.
42)
15
x − 7
y = −49
A)
y =
7
x +
15
7
B)
y =
15
7
x + 7
C)
y =
−7
x +
15
7
D)
y =
3
7
x +
15
7
Find each missing length to the nearest tenth.
43)
11.9
5.3
A) 169 B) 10.3
C) 17.2 D) 13
44)
4.2
10.5
A) 92.2 B) 9.6
C) 6.3 D) 56.3
-7-
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45)
4.8
13.5
A) 14.3 B) 17.3
C) 14.6 D) 204.5
Find the area of each.
46)
7.5 yd
11 yd
A) 50.65 yd² B) 41.25 yd²
C) 20.6 yd² D) 82.5 yd²
47)
2 m
2 m
A) 4 m² B) 10.2 m²
C) 2 m² D) 6.6 m²
48)
8 ft
9.9 ft
A) 39.6 ft² B) 79.2 ft²
C) 73 ft² D) 158.4 ft²
49) 2.6 cm
6 cm
7 cm
A) 32.3 cm² B) 14.4 cm²
C) 57.6 cm² D) 28.8 cm²
50)
3.2 cm
9 cm
11 cm
A) 32 cm² B) 127.8 cm²
C) 63.9 cm² D) 58.2 cm²
-8-
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Find the area of each. Round your answer to the nearest tenth.
51)
6 cm
A) 20.1 cm² B) 113.1 cm²
C) 128.7 cm² D) 5 cm²
Find the circumference of each circle. Round your answer to the nearest tenth.
52)
7 cm
A) 45.2 cm B) 44.6 cm
C) 51.5 cm D) 44 cm
Find the area of each. Round your answer to the nearest tenth.
53)
16 mi
A) 232.4 mi² B) 248.9 mi²
C) 201.1 mi² D) 308 mi²
-9-
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Find the circumference of each circle. Round your answer to the nearest tenth.
54)
22 mi
A) 69.1 mi B) 20.8 mi
C) 23.3 mi D) 28.3 mi
Find the volume of each figure. Round to the nearest tenth.
55) 12 in
12 in
12 in
12 in
6 in
A) 864 in³ B) 1503.4 in³
C) 375.9 in³ D) 751.7 in³
56)
2 ft
2 ft
A) 28.4 ft³ B) 25.1 ft³
C) 23.6 ft³ D) 47.2 ft³
57)
10 cm
6 cm 8 cm
8 cm
A) 93.6 cm³ B) 64 cm³
C) 108.8 cm³ D) 54.4 cm³
58)
5 cm5 cm
5 cm
A) 54.6 cm³ B) 27.3 cm³
C) 41.7 cm³ D) 47.1 cm³
59) Kayla won 55 pieces of gum playingbasketball. After giving some away she only
has 40 remaining. How many did she give
away?
60) Abhasra won 63 lollipops playing horseshoesat the county fair. At school she gave two to
every student in her math class. She only has 3
remaining. How many students are in her
class?
-10-
