Download Say Hello to Algebra 1

Summer Mathematics Packet
Say Hello to Algebra
Neelsville Middle School
Summer Math Packet
Student Name: __________________
Say Hello to Algebra 1
For Students Entering Algebra 1
This summer math booklet was developed to provide students in middle school an opportunity
to review grade level math objectives and to improve math performance.
Algebra
-1Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Say Hello to Algebra 1
One goal of Neelsville Middle School is to promote increased math performance at all
grade levels. Completing the summer math booklet allows each student and parent within
the school to work together to achieve this goal. Students who complete the summer math
booklet will be able to:

Increase retention of math concepts,

Work toward closing the gap in student performance.
Student Responsibilities
Students will be able to improve their math performance by:

Completing the summer math booklet,

Reviewing math skills throughout the summer.
_____________________________
Student Signature
________
________
Grade
Date
Parent Responsibilities
Parents will be able to promote student success in math by:

Supporting the math goals of Neelsville Middle School,

Monitoring student completion of the summer math booklet,

Encouraging student use of math concepts in summer activities.
____________________________
Parent Signature
______________
Date
This summer math booklet was adapted by Missy Sigley, Math Resource Teacher at Neelsville Middle School
from the “Sail into Summer with Math!” booklets and from Introductory Algebra 6th Edition by
Keedy/Bittinger, published Addison Wesley, 1991.
Neelsville Middle School
Algebra
-2Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Adding Integers
Hints/Guide:
Rules for Adding Integers:
1. Adding positive numbers – add the numbers and the answer is positive.
2. Adding negative numbers – add the numbers and the answer is negative.
3. Adding a positive and a negative number – subtract the numbers, then

if the greater number is positive, the answer is positive

if the greater number is negative, the answer is negative.
Examples:
1) 3 + 5 = 8
two positive numbers: add the numbers and the answer is positive
2) -12 + (-7) = -19
two negative numbers: add the numbers and the answer is negative
3) -36 + 21 = -15
a negative and a positive: subtract the numbers and keep the sign of the
greater number
Exercises: Follow the rules for adding integers to solve the problems.
1.
-9 + 2
2.
2 + (-5)
3.
-10 + 6
4.
8 + (-3)
5.
-8 + 8
6.
6 + (-6)
7.
-3 + (-5)
8.
-4 + (-6)
9.
17 + (-17)
10.
-15 + 15
11.
-17 + (-25)
12.
-24 + (-17)
13.
8 + (-5)
14.
-7 + 8
15.
-4 + (-5)
Algebra
-3Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Subtracting Integers
Hints/Guide:
Rules for Subtracting Integers:
1. Change the subtraction to addition,
2. Change the sign of the number after the subtraction sign to the opposite:


if it is a positive number, make it negative
if it is a negative number, make it positive
Order of Operations
3. Then follow the rules for addition.
Examples:
1) 2 - 6 = 2 + (-6) = -4
2) 4 – (-9) = 4 + 9 = 13
3) -7 – (-10) = -7 + 10 = 3
change the subtraction to addition, and 6 to (-6)
follow the rules for addition
change the subtraction to addition and (-9) to 9.
follow the rules for addition
change the subtraction to addition and (-7) to 7
follow the rules for addition
Exercises: Follow the rules for subtracting integers to solve the problems.
1.
3–7
2.
4–9
3.
0–7
4.
0 – 10
5.
-8 – (-2)
6.
-6 – (-8)
7.
-10 – (-10)
8.
-6 – (-6)
9.
12 – 16
10.
14 – 19
11.
20 – 27
12.
30 – 4
13.
-9 – (-3)
14.
-7 – (-9)
15.
8 – (-3)
Algebra
-4Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Multiplying Integers
Hints/Guide:
Rules for Multiplying Integers:

a positive number times a positive number equals a positive number
positive • positive = positive

a negative number times a negative number equals a positive number
negative • negative = positive

Order
Operations
a positive number
times aof
negative
number equals a negative number
positive • negative = negative
negative • positive = negative
Examples:
1) 3 • 6 = 18
positive times a positive equals a positive
2) -3 • (-6) = 18
negative times a negative equals a positive
3) 3 • (- 6) = -18
positive times a negative equals a negative
4) -3 • 6 = -18
negative times a positive equals a negative
Exercises: Follow the rules for multiplying integers to solve the problems.
1.
-8 • 2
2.
-2 • 5
3.
-7 • 6
4.
-9 • 2
5.
8 • (-3)
6.
9 • (-5)
7.
-9 • 8
8.
-10 • 3
9.
-8 • (-2)
10.
-2 • (-5)
11.
-7 • (-6)
12.
-9 • (-2)
13.
15 • (-8)
14.
-12 • (-10)
15.
-14 • 17
Algebra
-5Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Dividing Integers
Hints/Guide:
Rules for Dividing Integers (same as multiply):

a positive number divided by a positive number equals a positive number
positive divided by positive = positive

a negative number divided by a negative number equals a positive number
negative divided by negative = positive

Order
a positive number
dividedof
by aOperations
negative number equals a negative number
positive divided by negative = negative
negative divided by positive = negative
Examples: (fraction bar (/) means divide)
1) 6 / -3 = -2
positive divided by a negative equals a negative
2) -15 / -3 = 5
negative divided by a negative equals a positive
3) -24 / 8 = -3
negative divided by positive equals a negative
Exercises: Follow the rules for dividing integers to solve the problems.
1.
36 / (-6)
2.
28 / (-7)
3.
26 / -2
4.
26 / (-13)
5.
-16 / 8
6.
-22 / (-2)
7.
-48 / (-12)
8.
-63 / (-9)
9.
-72 / 9
10.
-50 / 25
11.
-100 / (-50)
12.
-200 / 8
13.
-108 / 9
14.
-64 / (-7)
Algebra
15.
200 / (-25)
-6Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Mixed Integers
Exercises: Simplify the following expressions. Show all work.
1.
4 • (-3) •6
2.
5(-12) • (-4)
3.
-4(-2)(-3)
4.
(-5)(-6)
-2
5.
6(-4)
8
6.
-56
23
7.
6(-5) – (-6)
8.
8(-4 -6)
9.
-6(9 – 11)
10.
45 – 14(5 – (-3))
11.
(-4 + 7)(-16 + 3)
12.
16 – (-13)(-7 + 5)
13.
4 + (-6) – 5 – 3
-6+4
14.
(-2)3(-5- (-6))
15.
13(-9 + 17) + 24
Algebra
-7Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Solving One-Step Equations
Hints/Guide:
The key in solving equations is to get the letter by itself. In one-step equations, we undo the math
operation. Don’t forget to follow all integer rules.
If the math the operation is
addition
subtraction
multiplication
division
then the undo is
subtraction
addition
division
multiplication
Golden RULE of equation solving:
What operation you perform on one side of the equal symbol, you must do the same
operation on the other side of the equal symbol.
Examples:
1) x + 5 = 6
-5 -5
x
=1
3) m – 6 = 7
+6 +6
m
= 13
undo addition with subtraction
Check: 1 + 5 = 6
6=6
2) 4x = 16
4
4
x=4
undo subtraction with addition
Check: 13 – 6 = 7
7=7
4) r/6 = 12
6 • r/6 = 12 • 6 undo division with subtraction
r = 72
undo multiplication with division
Check: 4(4) = 16
16 = 16
Check: 72 ÷ 6 = 12
12 = 12
Exercises: Solve the following equations. Show all work.
1) x + 8 = -13
2) m – (-9) = 4
3) -4b = -12
4) r/4 = 24
5) y – 4 = -3
6) -9 – p = 17
Algebra
-8Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Order of Operations
Hints/Guide:
REMEMBER: Order of Operations
(PEMDAS)
P – parenthesis
E – exponents
M/D – multiply/divide which comes first left to right
A/S – add/subtract which comes first left to right
Remember to simplify the top of the fraction then bottom of the fraction.
Examples:
1) 15 – 2 • 5 + 3 = 15 – 10 +3
= 5+3
= 8
multiply first
subtract
add
2) 5[4 + (8 – 2)] = 5[4 + 6]
= 5(10)
= 50
parenthesis first
add because of parenthesis
multiply
Exercises: Simplify the following expressions. Show all work.
1.
7+2•6
2.
11 + 4 • 4
3.
8•7+6•5
4.
10 • 5 + 1 • 1
5.
19 – 5 • 3 + 3
6.
14 – 2 • 6 + 7
7.
6[9 + 3(3 + 4)]
8.
8[(13 + 6) – 11]
9.
8 + (7 + 9)
10.
(8 + 7) + 9
11.
15(4 + 2)
12.
15 • 4 + 15 • 2
Algebra
-9Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
13.
100 – 15
9+8
14.
3 + 4[ 13 – 2(6 – 3)]
15.
5[2(8 + 5) – 15]
16.
14 + 6 • 2 – 8 ÷ 4
17.
7(14) – 3(6)
2
18.
14 ÷ [3(8 – 2) – 11]
20.
5 + 4 • 3 – 1 = 18
Use parenthesis to make each equation true.
19.
6+8÷4•2=7
Algebra
- 10 Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Evaluating Expressions
Hints/Guide:
REMEMBER: Order of Operations
(PEMDAS)
P – parenthesis
E – exponents
M/D – multiply/divide which comes first left to right
A/S – add/subtract which comes first left to right
Remember to simplify the top of the fraction then bottom of the fraction.
Examples:
1) Evaluate x + y for x = 37 and y = 29
x+y
2) Evaluate 3y for y = 14
6
3y
6
37 + 29
66
=
3(14)
6
=
42
6
= 7
Exercises: Evaluate the following expressions. Show all work.
1.
6x for x = 7
2.
3.
3p for p = 2 and q = 6
4.
5y for y = 15 and z = 25
5.
x + y for x = 10 and y = 20
6.
p + q for p = 2 and q = 16
x – y for x = 20 and y = 4
8
8.
q
5
7.
7y for y = 7
z
2
m – n for m = 16 and n= 6
5
Algebra
- 11 Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Distributive Property
Hints/Guide:

Multiply (distribute) the number in front of the parenthesis with each of the
coefficients (numbers) in the parenthesis.
Examples:
2. 9(x – 5)
=9•x-9•5
= 9x - 45
1. 3(4 + 2)
=3•4+3•2
= 12 + 6
= 18
3. -4(x – 2y + 3z)
= ( -4)(x) + -4(-2y) + (-4)(3z)
= -4x + 8y -12z
Exercises: Solve the following problems. Show all work.
1.
2(b + 5)
2.
4(x + 3)
3.
7(1 + t)
5.
6(5x + 2)
6.
9(6m + 7)
7.
7(x + 4 + 6y)
8.
4(5x + 8 + 3p)
9.
7(4 – 3)
10.
15(8 – 6)
11.
-3(3 – 7)
12.
-7(y – 2)
13.
-9(y – 7)
14.
-9(-5x – 6y + 8)
15.
-2.1(-4.2x – 4.3y – 2.2)
Algebra
4.
- 12 Neelsville Middle School
4(1 + y)
Summer Mathematics Packet
Say Hello to Algebra
Exploring the Graphing Calculator
1.
The key that will turn on the calculator
is__________________________.
2. The two keys that are needed to turn the calculator off are
_____________ and __________.
3. How do you change the lightness/darkness of the viewing screen?
_______________________________________________________________
4. What is the difference between the blue – (subtraction) key and the gray –
(subtraction) key? Do they look different on the home screen? Explain.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
5. The key that will let you type a number as an exponent is ___________________.
6. Explain the function of the ALPHA key:
_______________________________________________________________
_______________________________________________________________
7. The key that will display the variable x without having to use the ALPHA key is
______________________________________________________________.
8. The __________key is used to access the yellow functions that appear above the
gray keys.
9. The __________key is used to enter equations for graphing.
10. The maximum number of equations that can be graphed at one time is __________.
11. The __________key is used to display the graph of any function that you have
entered with an equation.
Algebra
- 13 Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
12. To use the square root function, you must press the _______________and
___________keys.
13. Tell three different ways that you can calculate 782 on the graphing calculator.
__________________________________________________________
14. The Home Screen is where you perform calculations. Find two ways to get back to
the Home Screen. _______________________________________________
15. The ______________key functions as an equal sign.
16. What does the calculator use for Π? ________________________________
17. Carry out the following calculations using your graphing calculator:
a. 3,598 x 45.76 =
b. 68,759,487 ÷ 29 =
c. (3,956 + 5,493 – 3,401) ÷ 32=
d. 8992 + 653 =
e. √2 =
f. (56 + 195)2 =
g. -52 =
h. (-5)2 =
i. │53 - 149│ =
j. │53│ - 149 =
k. 84 =
l. 85
83
m. (56 + 195)2 =
18. Use the ALPHA key to type your name.
Algebra
- 14 Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Parent Packet
Answers to Adding Integers (page 3):
1) -7
2) -3
3) -4
4) 5
5) 0
6) 0
7) -8
8) -10
12) -41
13) 3
14) 1
Answers to Subtracting Integers (page 4):
1) -4
2) -5
3) -7
4) -10
5) -6
6) 2
7) 0
8) 0
11) -7
12) 26
13) -6
14) 2
Answers to Multiplying Integers (page 5):
1) -16
2) -10
3) -42
4) -18
5) -24
6) -45
7) -72
8) -30
12) 18
13) -120
14) 120
Answers to Dividing Integers (page 6):
1) -6
2) -4
3) -13
4) -2
5) -2
6) 11
7) 4
8) 7
12) -25
13) -12
14) 64/7
Answers to Mixed Integers (page 7)
1) -72
2) 240
3) -24
4) -15
5) -3
6) -7
7) -24
8) -80
12) 42
13) 5
14) -8
9) 0
10) 0
11) -42
15) -9
9) -4
10) -5
15) 11
9) 16
10) 10
11) 42
15) -238
9) -8
10) -2
11) 2
15) -8
9) 12
10) -67
11) -39
15) 128
Algebra
- 15 Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Answers to Solving One-Step Equations (page 8)
1) -21
2) -5
3) 3
4) 96
5) 1
6) -26
Answers to Order of Operations (page 9 and 10):
1) 19
2) 27
3) 86
4) 51
5) 7
6) 9
7) 180
8) 64
9) 24
10) 24
11) 90
12) 90
13) 5
14) 31
15) 55
16) 24
17) 40
18) 2
19) 6 + [8 ÷ (4 • 2)] = 7
20) (5 + 4) • (3 – 1) = 18
Answers to Evaluating Expressions (page 11):
1) 42
2) 49
3) 1
4) 3
5) 6
6) 9
7) 2
8) 2
Answers to Distributive Property (page 12):
1) 2b + 10
2) 4x + 12
3) 7 + 7t
6) 54m + 63
7) 7x + 28 + 42y
8) 20x + 32 + 12p
11) 12
12) -7y + 14
13) -9y + 63
4) 4 + 4y
9) 7
5) 30x + 12
10) 30
14) 45x + 54y – 72
15) 8.82x + 9.03y + 4.62
Algebra
- 16 Neelsville Middle School
Summer Mathematics Packet
Say Hello to Algebra
Exploring the TI-83/84 Graphing Calculator (page 13 and 14)
1) ON
2) 2nd and ON
3) 2nd arrow up Δ
4) The blue – minus key is subtraction. The gray – minus key is a negative sign. The gray
key is longer on the home screen.
5) Λ (carrot key)
6) the ALPHA key allows you to type letters.
8) 2nd
10) 10
9) y =
11) GRAPH
13) 78 x 78 or 78x2 or 78Λ2
7) XTθN
12) 2nd and x2
14) CLEAR or 2nd MODE (quit)
15) ENTER
16) pi
17a) 164,644.48
17c) 189
17d) 1,082,826
17e) 1.414213526
17f) 63,001
17g) -25
17h) 25
17j) -96
17l) 64
17i) 96
17b) 2,371,016,793
17k) 4096
17m) 6.208688492 E12
Algebra
- 17 Neelsville Middle School