Download Algebra 1 Summer Packet

2014-2015 (entering) Grade 8/Algebra Summer Math Packet
Dear Students and Parents:
The purpose of this packet is to review pre-algebra concepts as you look forward to Algebra 1
next year. All concepts in this packet have been previously covered in 7th grade. Please use
this summer to assure all pre-requisite concepts have been understood. This packet will be
checked for completion by the end of the first week back in September (9/12). Show all your
work for each problem.
Have a wonderful summer!
Operations with Integers
Evaluate each expression.
Remember that - (-) = +. There must be no number between the two negatives.
1. 14 – (-5) =
2. –15 – (-7) =
3. 3x + 9x – (-4x) =
4. –(-7) + 18 =
5. 12x – (-4x) =
6. -8x – (-3x) –(-2x) =
For #7-9, Substitute the given value for the variable and evaluate. x = - 4, y = -7, m = 3
7. x + y + 5 =
8. m – ( x) =
9. – (-y) + x =
10. 8 – (-20) =
11. -45 ÷ 5 =
12.
14. 5 – 3 + 12 – (-9) =
15.
13.
 16
=
 16
 48
=
12
4
=
3
 
4
1
16. |(−2)(4)| − |(−5)(−1)|=
17. 2
2  5
18.    1  =
3  9
1 7
=

3 9
Order of Operations
19.
52 – (12  2 x 3)  9 + 15
20. 5 – 52 + 12 ÷ -3
21. [-5 × -4 – (-10)]2
Solving Equations: Here is an example: The check is a required step!
3b + 2 = 6(3 – b)
3b + 2 = 18 – 6b
-2 -2
3b = 16 – 6b
+6b
+ 6b
9b = 16
9
9
16
b=
9
Check:
16
16
) + 2 = 6(3 – ( ))?
9
9
16
11
+ 2 = 6( )
3
9
16
6 22
+ =
3
3
3
22
22
=
✓
3
3
Does 3(
Solve the equation & inequalities. Include a check.
1
d 23
22.
23. 2(11- 3x) £ -63- x
4
24.
3
1- (v + 2) = -5
4
2
2a 2

7 3
25.
29.
26. 7x + 28 ≤ 14(x – 4)
3.2x  2.6  23
30.
x
27.
3 1

5 2
31.
y
 5  11
12
3b  12
3
2
Properties of Exponents
Rule #1: Multiplying Powers with the Same Base
Rule #2: Dividing Powers with the Same Base
When multiplying powers with the same base
you ADD the exponents.
When dividing powers with the same base you
SUBTRACT the exponents.
Example: a3 x a2 = a3 + 2 = a5
Example: a5  a3 = a5 – 3 = a2
Rule #3: When Raising Powers to Another Power
Rule #4: Powers with a Negative Exponent
When raising a power to another power you
MULTIPLY the exponents.
Powers with a negative exponent can be written
as a FRACTION with a POSITIVE exponent.
Example: (a4)2 = a4 x 2 = a8
Example: a-5 =
1
a5
Rule #5: A Power with an Exponent of One
Rule #6: A Power with an Exponent of Zero
When evaluating a power with an exponent of
one, the answer will be the base.
When evaluating a power with an exponent of
zero, the answer will be one.
Example: a1 = a
32. 4  4
2
36.
4
 9   9 
33.
3
Example: a0 = 1
(a )
2
3
37. a 6  a 3
52
34. 5
5
3
35.  
7
38. 50
39.
3
( )
4a -2
2
3
Shapes and Designs
40. What is the sum of the interior angles of a hexagon?
41. What is the measure of one angle of a regular hexagon?
42. If you know the sum of the angles of a regular polygon, how can you find the measure of
one of the congruent angles?
43. Three angles of a quadrilateral measure 98 o, 75 o, 108 o. Find the measure of the fourth
angle.
2x
x
44) Find the length of each side of the triangle if the perimeter is 43 cm.
16
Finding Slope
45) Find the slope of the line through the given points.
a) (-1, 2) and (-5,10)
b) (-7, 10 ) and (1, 10)
46. Find the slope of the line, given the following graph.
a) b
b)
47. Find the slope of the line, give the following table.
a)
x
5
10
15
y
23
43
63
b)
x
y
-2
-8
-1
-5
0
-2
4
Translating Expressions and Equations
Set up an algebraic expression or equation to represent each verbal expression. DO NOT
SOLVE.
Example: 18 less than the quotient of a number and 3.
let n = a number ;
n
 18
3
48.
The sum of six times a number and 25
49.
7 less than fifteen times a number
50.
Four times a number increased by
five times the same number
51.
The sum of a number and 23 is 78.
52.
The sides of a rectangle are a
number and 4 less than that same
numbers. The perimeter is 56 meters.
53.
If a number is decreased by 6, and
the result is multiplied by 3, then the
answer is 15.
Percent Problems and Percent Word Problems
54. Our meal was $40 but we got 20% off because it came late. What did our meal end up
costing us?
55. My new jersey was $60 but I got 30% off. What did I pay?
56. $50.00 spring jackets were on sale for 30% off, how much are they now?
57. My cell phone was supposed to cost me $150 to fix. I only paid $112. What percent
of the original price did I pay?
5
58. What number is 70% of 45?
59. 23% of 75 is what number?
Mean Absolute Deviation (MAD)
Follow these steps to find the mean absolute deviation
1) Find the mean of the data
2) Find the distance each number is from the mean
3) Take the average mean of the absolute value of the distances
60. The following are scores on a Math test:
80, 82, 81, 0, 85, 90, 87, 92
Find the mean absolute deviation. (MAD)
61. Use the table to the left to determine the following information:
Hourly Tips
a. Greg’s mean tip money. ____________
Greg
Trent
$15
$20
$24
$22
b. Trent’s mean tip money. ____________
$26
$18
$18
$18
$17
$17
c. Combined mean tip money. ____________
d. Mean absolute deviation of combined tip money. _____________
e. Mean absolute deviation of Trent’s tip money. _______________
f. Mean absolute deviation of Greg’s tip money. _____________
g. Who’s mean absolute deviation is closer to the deviation of the combined tip money? ______
h. Is a mean more relevant if the mean absolute deviation is smaller or larger? _______
My child completed this packet over the summer and will be ready to submit it by the end
of the first week back to school in September. (9/12)
Parent Signature
_______________________________
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