2014 – 2015
Bishop Kelley High School
Summer Math Program
Course: Algebra 1 Part 2 Fall 2014
(this is ONLY for FALL 2014 and ONLY for students taking Part 2 in the Fall)
NAME:
DIRECTIONS:
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•
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Show all work neatly in the packet. You may not use a calculator for the math packet but you do need to
purchase a TI-30X IIS calculator for the course. The TI-30X IIS calculator is the ONLY one allowed for the course.
This material will be collected, graded, and points awarded at the discretion of each teacher on the first day of
the math class.
A test on this material will be administered during the first week of the class.
An additional resource for help with this packet is http://www.khanacademy.org. It provides videos of about 10
minutes in length on hundreds of different math topics.
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Math Teachers will be available in C-1 the following dates/times if you need help.
Date
Time
Wednesday, July 30th
8-9:30am
Monday, August 4th
8-9:30am
Tuesday, August 5th
8-9:30am
Name________________________________________________________________________________
SUMMER MATH PACKET
Only for students entering Algebra I Part 2 in Fall 2014
Students entering Algebra 1 Part 1 will be required to have a calculator for some portion of the course. Students are
only allowed to use the Texas Instrument TI-30X IIS calculator for this course—NO OTHER CALCULATOR WILL BE
ALLOWED!!!!! It comes in many colors and you may purchase whatever color you want. Please consider purchasing
the calculator in late July when they are on sale (for about $9 or $10) and in great supply. If you wait until midAugust, they are typically not on sale anymore and very hard to find.
Directions for the Summer Math Packet: Use a pencil and SHOW ALL work in this packet- not on a separate sheet of
paper!! NO calculators are permitted for any section except for the one section that is so marked. This will be turned in
on your first day of math class.
ORDER OF OPERATIONS:
1.
2.
3.
4.
Do operations that occur within grouping symbols (parentheses, brackets, absolute value bars, radicals).
Evaluate powers if there are any.
Then do multiplications and divisions as you see them, in order, from left to right.
Finally, do additions and subtractions as you see them, in order, from left to right.
EXAMPLES:
16 + 4 ÷ 2 − 3 Since there are no grouping symbols or exponents, do the division first
16 + 2 − 3
From left to right, do the addition next
18 − 3
15
2
2
10 − 6 ( 7 − 4 ) + 3 + 2 ( −1)


Since there are grouping symbols, do inside them first.
10 − 6 32 + 3 + 2 ( −1)
Next do the powers
10 − 6 [9 + 3] + 2 (1)
10 − 6 (12 ) + 2 (1)
10 − 72 + 2
2
Now do inside the brackets
Time to multiply
From left to right, do the subtraction
−62 + 2
−60
Simplify each expression. (This will require order of operations)
1. 2 + 3 × 8 ÷ 6
2. 32 ÷ 2 × 8 + 6
3. 5 + (12 × 3)
4. 30 − 42 + (3 + 2)
6. 82 ÷ 8 + 6 × 3
5. (12 − 7) 2 × 3 − 6
Evaluate when x =3, y =1, and z=2
7. 12 − ( z − y ) 2
8. 3 + [(13 − x) × 18]
Write the mixed number as an improper fraction.
10. 7
9.
y
z + 3y
Write each fraction as a mixed number.
2
9
11.
43
9
Evaluate. Express answer in simplest form.
12.
2 4
+
9 9
15.
5 1
−
9 4
18.
8 6
÷
9 36
21.
−48
12
13.
3 1 5
+ +
4 3 6
6 −21

7 11
16.
19. 10 ÷ 3
1
2
−4
−3
22.
1
3
1 1
9 3
14. 1 −
17.
11 −4

20 22
20. 3.2 / 8
Evaluate.
23. 12- 18
26. (-14) + ( -3)
24. (-17) – 12
25. (-8) - ( -6)
27. (-7) + 11
28. 9 + ( -5)
30. 3%
31. 250%
Write each percent as a decimal.
29. 54%
Write each percent as fraction in simplest form.
32. 64%
33. 20%
Write each fraction as a percent.
34.
3
10
35.
17
25
Solve. Set up the equation and then you may use a calculator to solve these 4 equations but do NOT just show an
answer.
36. What number is 5% of 186?
38. What percent of 25 is 20?
37. What number is 75% of 192?
39. 25% of what number is 6?
COMBINING LIKE TERMS:
Like terms have the same variables and the same exponents. You can add and subtract like terms by combining the
coefficients (the numbers in front) and leaving the variables and exponents the same.
EXAMPLES:
2( x + y) − x (4 − y)
= 2 x + 2 y − 4 x + xy
=
−2 x + 2 y + xy
4 x ( x − 5) − 2 x ( 4 − x )
= 4 x 2 − 20 x − 8 x + 2 x 2
= 6 x 2 − 28 x
−3 ( 2a + 4b ) − ( 3a − 2b )
=
−6a − 12b − 3a + 2b
=
−9a − 10b
7 − 3 10 − ( 3 y + 2 ) 
3 x + 2  − ( 5 x − 3) − 2 ( 3 x + 1) 
=7 − 3 [10 − 3 y − 2]
7 − 3 [8 − 3 y ]
=
=7 − 24 + 9 y
= 3 x + 2 [ −5 x + 3 − 6 x − 2]
= 3 x + 2 [ −11x + 1]
=3 x − 22 x + 2
=
−19 x + 2
=
−17 + 9 y
Simplify. Use the distributive property when necessary.
40. 2x + 7 + 8x -12
41. 18a – 12b + a – 15b
42. c – 2d – 10c + 8d
43. 2( 8 – 5g) + 6( 3 + 2g)
44. ( 3r – 2v) – 4( r – 5v)
45. -2( 3x – 9) – ( 3x – 12)
46. 3 ( 2a – 4b ) + ( 4a – 6b) – ( 9a – 3b)
47. 3( 2c + 5d) – 5 ( 8c – 2d)
SOLVING EQUATIONS:
*Distribute and combine like terms as needed.
*Get the variable by itself by moving across the equal sign, again always looking for like terms to
combine.
*If a variable drops out, look at the remaining part of the equation. If you are seeing a “true”
statement, then the solution is all real numbers. If you see a “false” statement, then the solution is the
empty set.
EXAMPLES:
7 ( a − 2 ) − 6 = 2a + 8 + a
7 a − 14 − 6 = 2a + 8 + a
7 a − 20 = 3a + 8
4a = 28
a=7
Solve. ( Make sure you show work and not just an answer!)
48. x – 6 = - 13
51. -7n = 56
54. 3n – 2 = 10
57. 8y – ( 2y – 3) = 9
49. a + 18 = 2
52.
55.
n
= −20
5
a
−4=
8
3
58. 2(x – 4) + 3( 2x – 6) = 8x – 10
50. c – ( -2) = -32
53. 12 – x = 5
56.
n
1
=3
2
4
59. 4x – 3(x + 8) =7x
SOLVING AND GRAPHING LINEAR INEQUALITIES
1. Solve as you would an equation.
2. If multiplying or dividing by a negative, reverse the inequality symbol.
3. On the number line, an open circle is used for the > and < symbols and a closed dot is used
for the ≥ and ≤ symbols. The > and ≥ will have the line pointing to the right and the
< and ≤ will have the line pointing to the left.
EXAMPLES:
12 − 2 x < 10
−2 x < −2
x >1
Solve and graph each inequality (on a number line)
60. 2 x < −14
61. r − 8 ≥ −10
62. −3 x ≥ 12
Using the graph paper below, graph the following points and label them.
63. A ( 2,5)
64. B( -2, 4 )
65. C(3, 0)
66. D ( -3, -2)
67. E ( 0, -2)
68. F ( 1, -4)
FORMULA FOR SLOPE:
(
)
Given two points, x1, y1 and ( x2 , y2 ) , the formula for slope is:
m=
y2 − y1
x2 − x1
Find the slope of each line.
69. ( 5,6) and (3,2)
70. (-4, 2) and (2, -5)
Slope-intercept form of a line is y = mx + b
m- slope which is a ratio of
b- the y-intercept- the y-coordinate of the point
where a line crosses the y-axis.
** The key is putting an equation in slope-intercept form is to isolate the y. Then the number in front of the x is the
slope and the other number is the y-intercept.
Example: 2x + y = 3
-2x
So, first subtract 2x from both sides.
-2x then get
y = -2x + 3 so the slope (or m) = -2 and the y-intercept (or b) = 3
Find the slope and y-intercept given the linear equation.
71. y = ½ x – 5
72. 3x + y = 7
73. 6x + 2y = 10
Graph each equation using the slope and y-intercept.
74. y = 2/3 x -1
74. y = - ½ x + 3
75. y= 3x – 4
WRITING EQUATIONS OF LINES:
POINT-SLOPE FORM:
SLOPE-INTERCEPT:
STANDARD FORM:
y − y1= m ( x − x1 )
=
y mx + b
Ax + By =
C
*Given the slope and y intercept: m =
*Given the slope and a point:
3
, y intercept ( b ) = −7
5
3
x−7
5
Method 1
Method 2
3
m=
− through ( 8, −1)
4
3
m=
− through ( 8, −1)
4
Use the slope and point and
put in the slope intercept form
to find b :
Use the slope and point and
put in the point slope form:
=
y mx + b
y − y1= m ( x − x1 )
3
(8) + b
4
−1 =−6 + b
5=b
y + 1 =−
−1 =−
3
− x+5
Equation: y =
4
*Given two points:
Answer: =
y
Method 1
( 2,1) and ( −3, −9 )
Find slope:
1 − (−9) 10
= = 2
2 − (−3) 5
Use one of the given points (it
does not matter which one)
and the slope and put in the
slope intercept form to find b :
=
y mx + b
=
1 2 ( 2) + b
1= 4 + b
−3 =b
Equation: =
y 2x − 3
Write an equation for the line in slope-intercept form.
76. slope = -3 and y-intercept = 5
78. Passes through ( -6, 10) and ( -4, -2)
3
( x − 8)
4
3
y + 1 =− x + 6
4
3
y=
− x+5
4
Method 2
( 2,1) and ( −3, −9 )
1 − (−9) 10
= = 2
2 − (−3) 5
Use one of the points (it
does not matter which one)
and the slope and put in the
point-slope form:
y − y1= m ( x − x1 )
y −=
1 2 ( x − 2)
y − 1= 2 x − 4
=
y 2x − 3
77. Slope= - 2 and passes through (4, -6)
MIDPOINT
The midpoint of a line segment is the point that occurs halfway between the two endpoints.
If a line segment has endpoints A ( x1 , y1 ) and B( x2 , y2 ) , then the midpoint M is: (
x1 + x2 y1 + y2
,
).
2
2
Example: Find the midpoint of the line segment with endpoints (3,-2) and (7, 6).
 3 + 7 −2 + 6   10 4 
,=
,  (5, 2)
 =
2   2 2
 2
Solution: 
Find the midpoint of the line segment with the following endpoints:
79. (5,2) and (9, 8)
80. (-3, 6) and (7, 12)
81. (-2, 0) and (-8, 9)
SCATTERPLOTS AND CORRELATION
82. Does the scatterplot at right exhibit positive, negative, or no correlation?
83. If the average daily temperature was 90 degrees, how many visitors
would you expect to find at the beach?
84. If there were only 150 visitors, what would you expect the average daily
temperature to be?
85. If the temperature was 100 degrees, how many visitors would you expect to find at the beach?
MEAN, MEDIAN, MODE, and RANGE
10 students in Ms. Schaunaman’s first block Algebra class had the following scores on the first chapter test:
92, 88, 76, 62, 92, 89, 92, 100, 98, 70
86. What is the range of the test scores?
87. What is the mean of the test scores?
88. What is the mode of the test scores?
89. What is the median of the test scores?
PROBABILITY
Johnny spins a spinner like the one to the right.
90. What is the probability that Johnny spins a 4?
91. What is the probability that Johnny spins a 3 or a 4?
92. What is the probability that Johnny spins a 4 or an odd number?
93. If Johnny spins the wheel TWO times, what is the probability he spins a 3 and then a 4?
RATIO AND PROPORTION
Solve the following proportions:
94.
x 3
=
6 15
95.
x+2 6
=
5
7
96.
11 x − 2
=
20
5
97. Ceci is 5 feet tall. At a certain point in the day, she casts a shadow that is 8 feet long. At the exact same time,
Ceci’s favorite tree casts a shadow that is 20 feet long. How tall is her favorite tree?
98. If it takes Ms. Schaunaman 3 cups of flour to make 48 cookies, how many cups of flour will it take her to make
80 cookies?
COMPOUND INEQUALITIES
Graph the following compound inequalities.
99. x < 4 OR x > 8
100. x > 2 AND x < 5
101. x < 3 AND x > 6
Solve and graph the following compound inequalities.
102. 3 x + 1 ≤ −16 OR -2x - 3 ≤ −15
103. −3 < 2 x − 1 ≤ 5
ABSOLUTE VALUE EQUATIONS AND INEQUALITIES
Solve the following absolute value equations.
104. x = 7
105. x + 3 =
6
106. −2 x + 1 =−10
Solve and graph the following absolute value inequalities.
107. x > 5
108. 2 x − 3 ≤ 7
109. x − 6 ≥ 4
RELATIONS AND FUNCTIONS
Remember: A relation is a set of ordered pairs. A function is a special type of relation where each element in the
domain corresponds to exactly one element in the range. In other words, a function is a relation where no elements
in the domain repeat. On a graph, a function will pass the vertical line test (if you pass a vertical line across the graph
of a function, the vertical line will never touch two points on the graph at the same time).
Example:
{ (-3, 2), (5,6), (7, 2) } is a function because no elements in the domain repeat.
{ (-3,2), (-3,6), (5,7) } is NOT a function because the element -3 in the domain repeats.
Determine whether each relation is a function.
110. { (-4,2), (-6, 5), (7,0), (10,3) }
111. { (1,2), (2,2), (3,3), (4,2) }
112. { (5,3), (-4, 9), (5, 10) }
113.
114.
115.
Evaluating a Function:
Example: Given the function f(x) = 2x + 3, find f(-4).
Answer: Replace all the x’s with -4 and evaluate the function.
f(-4) = 2(-4) + 3 = -8 +3 = -5
Given f(x) = -3x +5, evaluate the following:
116. f(0)
117. f(-2)
118. f(-1/2)
DIRECT AND INVERSE VARIATION
119. If y varies directly as x and y is 10 when x is 4, what is the value of y when x = 20?
120. If y varies indirectly as x and y is 10 when x is 4, what is the value of y when x = 20?