Algebra 1 Summer Skills Packet
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Transcript of Algebra 1 Summer Skills Packet
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8/12/2019 Algebra 1 Summer Skills Packet
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(For Students Entering Algebra I-Fall 2014)
Medford Public Schools
Department of Mathematics
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edford Public Schools489 Winthrop Street, Medford, Massachusetts 02155
Carolyn A. Joy [email protected]
K-12 Director of Mathematic s and Science 781-393-2214
June 13, 2014
Dear Student/Parent/Guardian:
Welcome to your Summer Mathematics Review Packet. In order to help you/your child meet
with success in Algebra I, you are being provided with a packet of mathematics problems
that include topics that have been studied in middle school. In todays environment of
rigorous academic standards with the newly implemented Common Core, students will need
to have an understanding of core topics in order to progress and move forward in theirmathematical learning. This packet is intended to help you retain the basic skills you have
learned.
If you need to review howto complete the work, there are excellent, easy-to-understand set
of tutorials on line. Most of the tutorials are under 10 minutes long. You will see referencesto different sites as you progress through the packet. The sitewww.khanacademy.orgis very
popular with many topics you can scroll down and click on ORuse a search box search for
video or topic. Enter the topic you are working on for the day and you will get a list of
video tutorials to choose from. Watch as many as you need to help you complete the packetproblems. There is also an opportunity to ask questions and get some online feedback. You
will find useful information there if you take the time to read it.
It is suggested that you work on the packet at the rate of about 2-3 pages per week throughoutthe summer. At this rate, you will have it completed in time for the start of school. Your
algebra teacher will give you instructions on the due date, how you will receive credit and
any consequences for not completing the packet. Please remember, the packet is designed tohelp you as you transition to high school algebra.
All work should be neatly shown on the packet. You should show ALL steps in yourprocess, including work in which you may have used a calculator. If you need to do work on
separate paper, make sure you include the title of the page and the problem number.
Good luck as you enter high school.
Sincerely,
Carolyn A. Joy, DirectorMs. Elizabeth Burns, teacher
Ms. Rebecca Jacobs, teacher
Ms. Megan LeClair, teacher
mailto:[email protected]:[email protected]://www.khanacademy.org/http://www.khanacademy.org/http://www.khanacademy.org/http://www.khanacademy.org/mailto:[email protected] -
8/12/2019 Algebra 1 Summer Skills Packet
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Algebra 1 Name:_____________________________
Summer Packet
2014 Middle School:_____________________________
Order of OperationsNeed a refresher? Order of Operations Video:
https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/order-of-operations
1. Determine which step you would do first in the following problems. The first problem has been done for
you.
a) 14 + 7 40 87
7 40because it is the first
multiplication when reading left to
right.
b) 50 5 + (7 2) 9 + 4 c) (11 5)2 + 7 + 36 9
d) 16 8 + 27 35 5 e) 76 + 14 2 8 f) 14 8 + 5 9 + 27 3
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2. Simplify the expression. The first problem has been done for you.
a) (34 4) 3 6
30 3 6
30 3 36
10 36
26
b) (2 + 2)+(12 6) c) (96 6) (9 + 6)
d) (10 + 5)+(15 3) e) (74 + 3) 7 f) (65 5) (15 + 5)
g) (26 8) 10 h) 4(12 + 4)+ 5 i) (30 2) 22
Order of Operations Extra Practice:
https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/e/order_of_operations_2
https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/e/order_of_operations
https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/e/order_of_operations
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Operations with Integers
3. Solve each problem; use the number line if needed. The first problem has been done for you.
a)
8 +(6)= 2
b)
(11) (8)=
c)
12 + (6)=
d)
14 (1)=
e)
(5)+(14)=
f)
1 8 =
g)
86 =
h)
9 + 7 =
i)
414 =
j)
2639 =
k)
677798 =
l)
4 (8) =
4. Solve each problem. The first problem has been done for you.
a) 45 (9)= 5 b) 6 2 = c) 5 8 =
d) 9 8 = e) 9 1 = f) 24 8 =
Operations with Integers Extra Practice:
http://cdn.kutasoftware.com/Worksheets/PreAlg/Dividing%20Integers.pdf
http://cdn.kutasoftware.com/Worksheets/PreAlg/Multiplying%20Integers.pdf
http://cdn.kutasoftware.com/Worksheets/PreAlg/Dividing%20Integers.pdf
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Operations with Rational NumbersNeed a refresher? Operations with Rational Numbers Video:
https://www.khanacademy.org/math/arithmetic/fractions/fractions-unlike-denom/v/adding-and-subtracting-fractions
https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/v/multiplying-negative-and-positive-fractions
https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/conceptual-understanding-of-dividing-fractions-
by-fractions
5. Perform the indicated operation on the rational number. The first problem has been done for you.
a)6
7
7
21=
18
21
7
21=
11
21
b)2
3
3
10=
c)2
3
8
42=
d)12
14
4
8=
e) 13
54
1
9=
f) 1
4
4
20=
g) 5
6
2
4=
h) 10
22
5
11=
i)5
8
1
6
=
=5
8
6
1=
5 6
8 1
=30
8 =
15
4
j)1
3
1
4
=
k)1
2
2
3
=
l)3
6
1
2
=
m)5
7
1
3=
n)3
5
7
10=
o)1
2
5
7=
p)1
3
1
2=
Operations with Rational Numbers Extra Practice:
https://www.khanacademy.org/math/arithmetic/fractions/fractions-unlike-denom/e/adding_and_subtracting_fractions
https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/e/multiplying_fractions
https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/e/dividing_fractions_2
http://cdn.kutasoftware.com/Worksheets/PreAlg/Add%20and%20Subtracting%20Fractions%20and%20Mixed%20Numbers.pdf
http://cdn.kutasoftware.com/Worksheets/PreAlg/Multiplying%20and%20Dividing%20Fractions%20and%20Mixed%20Numbers.pdf
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Evaluating Expressions with Given Values
Need a refresher? Evaluating Expressions with Given Values Video:
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-evaluating-
expressions/v/variables-and-expressions-1
6. Find the value of the given expression. The first problem has been done for you.
a)
3 + 5 , = 1, = 23(1)+ 5(2)
3 + 10
7
b)
4 + 21 , = 7, = 7c)
2 +6
,3 = 2, = 6
d)
( 2)+ 3,
= 1, = 1
e)
)6 ,( = 9, = 2 f)3 + + , = 5, = 2
Evaluating Expressions with Given Values Extra Practice:
http://cdn.kutasoftware.com/Worksheets/PreAlg/Evaluating%20Variable%20Expressions.pdf
http://cdn.kutasoftware.com/Worksheets/PreAlg/Evaluating%20Variable%20Expressions.pdf
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Number Sense
Need a refresher? Number Sense Video:
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/comparing-decimals-1-example
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/ordering-decimals-example
7. Fill in the place holder with, or =. The first problem has been done for you.
a)
4.5 > 4.5
b)
0.707________07.07
c)
18.2________18.0
d)
3.21________ 3.12
e)
0.3________ 0.33
f)
0.06________0.6
8. Arrange and write the decimals in increasing order. The first problem has been done for you
a)
14.367, 28.7784, 213.22, 361.238, 5.2, 5.33
361.238, 28.7784, 5.33, 5 .2, 14.367, 213.22
b)
11.111, 111.11, 1.11, 11.1, 11.1, 1.11
c)
8.1, 67.3, 82.55, 121.91, 2.2, 46.76
Number Sense Extra Practice:
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/comparing-decimals-1-example
https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/ordering-decimals-example
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Properties of Real Numbers
Need a refresher? Properties of Real Numbers Video:
https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/commutative-law-of-addition
9. Choose the best answer about properties of real numbers. The first problem has been done for you.
a) Which property is used in the following
expression?(6 9) 9 = 9 (8 6)
a) Associative Property of Addition
b) Distributive Property of Multiplication
c) Commutative Property of Addition
d) Associative Property of Multiplication
b) The value of any nonzero number will be changed
by_____________
a) Multiplying by zero
b) Adding zero
c) Multiplying by one
d) Dividing by one
c) Which property of addition is used in the
following?2 + 9) + 4 = 2 + (9 + 4)
a) Identity Propertyb) Associative Property
c) Distributive Property
d) Commutative Property
d) Which is an example of the Associative Property
of Addition?
a) 6 + (6)= 0b) (3 + 9) + 7 = 3 + (9 + 7)c) 3 + 2 = 2 + 3
d) 5 + 0 = 5
e) Which is an example of the Identity Property of
Addition?
a) 9 + 0 = 9b) 7 + 6 = 6 + 7c) 8 1 = 8
d) (6 + 2)+ 3 = 6 + (2 + 3)
f) Which equation shows the Commutative Property
of Multiplication?
a) 7 4 = 4 7b) 6 9 5 9 =(6 5) 3c) 3 3 = 3 + 3 + 3
d) 8 1 = 8
g) Which property would you use to simplify thefollowing expression?3( + 9)a) Associative Property
b) Commutative Property
c) Distributive Property
d) Multiplication Property of Zero
h) Which operation will not change the value of anynonzero number?
a) Dividing by zero
b) Multiplying by one
c) Multiplying by zero
d) Adding one
10. Find the property used in each question. The first problem has been done for you.
a)
4 + 9 = 9 + 4
Commutative Property of Addition
b)
2 1
2
= 1
c)
9 (8 + 2)= 9 8 + 9 2
d)
11 (7 5)=(11 7) 5
e)
2 + 0 = 2
f)
6 + 4 = 4 + 6
g)
5 1 = 5
h)
3 + 3 = 0
i)
15 + 0 = 15
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Properties of ExponentsNeed a refresher? Properties of Exponents Video:
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-1
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-2
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-properties-involving-
quotients
https://www.khanacademy.org/math/pre-algebra/exponents-radicals/negative-exponents-tutorial/v/negative-exponents
If there is a negative it is NOT being raised to that power unless
there are parenthesis.
Example:1 = 1, 2 = 1, (7) = 1
11. Evaluate the exponents. The first problem has been done for you.
a)
(2) =(2)(2)=
= 4
b)
5 =c)
(10) =
d)
(3) =e)
(5) =f)
8 =
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Solving Equations with One VariableNeed a refresher? Solving Equations with One Variable Video:
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/one-step-equation-
intuition
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same--
thing-to-both-sides--two-step-equations
13. Solve the one-step equations. The first problem has been done for you.
a)
15 = 22
+15 + 15
= 7
b)
21 = 105
c)
12= 11
d) + 9 = 25 e) 7 = 1 f)4
= 5
14. Solve the two-step equations, round your answers to the nearest hundredth if needed. The first problem
has been done for you.
a)
159 = 3
+15 + 15
9 = 18
9 9
= 2
b)6
22 = 16
c)
7 +2
7= 20
d)3
7 17 = 11
e)
5 28 = 11
f)
18 25 + = 6
g)21
28 = 12
h)7 +20
= 24
i)16
18 = 2
Solving Equations with One Variable Extra Practice:
http://cdn.kutasoftware.com/Worksheets/PreAlg/One-Step%20Equations%20With%20Integers.pdf
http://cdn.kutasoftware.com/Worksheets/PreAlg/Two-Step%20Equations%20With%20Integers.pdf
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The Coordinate PlaneNeed a refresher? The Coordinate Plane Video:
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/coordinate-plane/v/the-coordinate-plane
15. Tell what point is located at each ordered pair. The first problem has been done for you.
a) (9, 4)
C
b) (4,7) c) (8, 2) d) (8, 3)
e) (1,3) f) (3, 5) g) (9,3) h) (1,1)
16. Write the ordered pair for each given point. The first problem has been done for you.
a) S
(8, 5)
b) M c) X d) F
e) Y f) Q g) G h) A
17. Plot the following points on the coordinate grid.
a)
(3,5)
b)
(7, 2)
c)
(3,5)
d) (3, 1)e)
(6,8)
f) ((0,7 g) (6, 8) h) (8,3)
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SlopeNeed a refresher? Slope Video:
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/slope-and-intercepts/v/slope-of-a-line
18. Find the slope of each line. The first problem has been done for you.
a)
Slope:
b)
Slope:
c)
Slope:
d)
Slope:
e)
Slope:
f)
Slope:
19. Find the slope from the pair of points. The first problem has been done for you.
a)
(4,4)(0,2)
4 2
4 0=
2
4=
1
2
b)
(3, 4)(4,2)
c)
(5,0) (5,2)
d)
(5, 4)(5,3)
e)
(2, 5) (1,5)
f)
(5, 2)(5,0)
g)
(1,0) (2,5)
h)
(3,0) (0, 3)
Slope Extra Practice:
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/slope-and-intercepts/e/slope_of_a_line
http://cdn.kutasoftware.com/Worksheets/PreAlg/Slope.pdf
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Slope Intercept Form of Linear EquationsNeed a refresher? Slope Intercept Form of Linear Equations Video:
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-slope-intercept/v/graphing-a-line-in-slope-
intercept-form
20. Find the slope and the-intercept of the linear equation. The first problem has been done for you.a)
= 14 2
14
= 2
b)
= 13 1
c)
= 27 + 1
d)
= 34 + 3
21. Write the slope-intercept form of the equation, and plot the equation of each line given the slope and-intercept.
a) b)
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22. Sketch the graph of each line.
a) = 4 b) = + 1 c) = 3
d) = + 3 e) = + 5 f) = 2
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23. Write the equation form each line. The first problem has been done for you.
a)
43
b) c)
d) e) f)
Slope Intercept Form of Linear Equations Extra Practice:
http://cdn.kutasoftware.com/Worksheets/PreAlg/Graphing%20Lines%20in%20Slope-Intercept%20Form.pdf
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-slope-intercept/v/graphing-a-line-in-slope-
intercept-form