Algebra 1 Midterm
2012-2013
Study Guide
Name___________________________
Date:______________ Period:___________
THIS REVIEW WILL BE COLLECTED JANUARY 4th or January 7th . One problem each page will be
graded! You may not turn this exam review in after the due date!
Evaluate the expression for the given values of the variables.
1) 3n when n = 4 _____
3)
2) 8 + 5a2 when a = 7
3a − 7
when a = -4 _____
2
4)
____
n + m 2 when m = -2 and n = -3 ______
Evaluate.
5)
_____
8)
_____ 9)
11)
12)
6)
_____
______
7)
10)
_____
______
_____
Check whether the given number is a solution of the equation or inequality:
; 5 _____
Tell whether the pairing is a function.
13) _________
Input
1
2
3
4
14) __________
Output
20
21
21
22
Input
5
10
10
20
Output
10
15
20
25
15)
Write the verbal sentence as an equation or an inequality: Five is less than a number x divided by 7.
16)
Write an equation or inequality to model the situation:
equal to four times the difference of a number n and 5.
_______________
The perimeter P of a square is less than or
_____________
1 Simplify.
17)
______ 18)
____ 19)
_____ 20)
______
Solve the equation.
21)
_____
24)
_____
27) 4x – 1 = 2(2x + 3)
22)
______
25)
28) −
_____
2
( 6 x − 9 ) = −4 x + 6
3
30) Identify the property being illustrated:
-8 + 8 = 0
23)
26)
_____
_____
29) 4(2- 2y) + 6 = 2(7 = 4y) _____
__________________________
31) Which statement illustrates the Commutative Property of Multiplication?
A) 3i( 4 + 2 ) = 3i 4 + 3i2
C) 3i( 4i2 ) = ( 4i2 )i3
B) 3i( 4i2 ) = ( 3i 4 )i2
D) 3 + ( 4i2 ) = ( 4i2 ) + 3
32) Members of a local gym pay a yearly fee of $150 and $2 per day to use the volleyball courts. Write a
function of the cost in terms of the number of days you use the volleyball courts.
____________________
33) Rewrite the equation so that y is a function of x.
____________________
2 34)
Decide whether the given ordered pair is a solution of the equation.
_______
35)
Find the x-intercept.
_____
36)
Find the y-intercept. ______
37)
Find the slope of the line passing through the points.
38)
Find the value of y so that the line passing through the two points has the given slope.
______
_____________
39) Find the slope and the y-intercept of the graph 4x – 9y + 18 = 0.
40)
_____________
In 1999, a software company had a profit of $30,000,000. In 2005, the company had a profit of
$210,000,000. Find the average rate of change of the company's profit in dollars per year.
___________________________
41)
The variables x and y vary directly. Use the given values to write an equation that relates x and y.
__________________
For questions 42 – 45: State whether the equation is a direct variation. If so, state the constant of variation.
42) y = 4 _____________
43) 3x – 4y = 0
_____________________
44) -x + 2y = 4 ________________
45) 2 + 4y = -4x + 2
______________________
46) Each month, Laura’s cell phone charges c vary directly with the number of minutes m that she talks.
Last month, she talked 450 minutes and was charged $13.50.
a) Write a direct variation equation that relates c and m. _____________________
b) How much would Laura pay if she talked 300 minutes? _____________________
3 Graph the equations.
47) 6 x − 4 y = 8y
48) x – y = 1
x
50)
51) 5(x + 1) = y –y 10
y
2
x +2
3 y
x
x
52) x = 1
y
x
x
x
53) y = −
49) y = −
y
2
x + 3 for the domain x > 3
3
54) x - 2y = 4 for the domain -4 ≤ x ≤ 4
y
y
53) Range:
_______________________
54) Range:
_______________________
x
x
4 55)
Decide whether the graphs of the two functions are parallel lines.
_____________
56)
Write a rule for the function of the values in the table below?
Input, x
Output, y
57)
1
9
2
12
3
15
4
18
____________________
5
21
A music store sells CDs for $12.99 each.
a. Write a rule for the cost of CDs as a function of the number of CDs purchased. _____________
b. Let the domain equal 0, 1, 2, and 3. Make a table and identify the range. ___________________
58)
Mrs. Fox loves basketball and was able to get the season NBA Pass for $140 per year and $3.50 for
each game she watches on tv. Write the function that relates the variables.
_________________
59)
Which equation is an identity? Which has no solutions?
_____________________
____________________
_____________________
60)
Write
as a function of x.
_____________________
___________________
61)
State the x- and y-intercepts of the line with the equation y = -3x + 6.
62)
Determine the slope of the line graphed below.
63)
Find the slope of the line that contains (2, 4) and
64)
Find the slope of the line through the points (–1, –3) and (–1, 7).
________ _______
_______________
___________________
____________________
5 65)
On January 1, Mario had a savings account balance of $2742 and by April 1, his balance had
increased to $3597. Find Mario's average savings rate in dollars per month for that period.
_________________________________
66)
Rewrite the equation
in slope-intercept form.
67)
Find the slope and y-intercept of the line with the equation
68)
Determine if the line
69)
In the equation y =
70)
True or False: The graphs of direct variation equations always contain the point (0, 0). ________
71)
Let
72)
What is the value of the function when
73)
Find the value of x so that
is parallel to the line
_____________
. _________ _________
. _____________
, does y vary directly with x? ________
Find x when
____________
.
?.
___________
________________
Write the equation of the line that passes through the points in slope-intercept form AND standard form.
74) (4, -3) and (2, -2 )
__________________
________________
75) (0, 5) and (-3, -1)
__________________
________________
76) (5, 9) and (6, 4)
__________________
________________
6 77) Write the equation of the line that passes through (7, -8) with a slope of -3. _________________
78) Write the equation of the line that passes through the point (1, 7) and is parallel to the line -6x + y = -1.
____________________
79) Write the equation of the line that passes through the point (-2, -4) and is perpendicular to the line
2
7
y = − x +1
____________________
80)
For the given data set -2, 8, 12, -7, 10, 3 find:
a. the mean ______
Round to 3 significant figures if necessary.
b. the MAD score _____ c. the variance _____
d. standard deviation _____
7 81)
You scored an 82 on your statistics test. The mean for the class was 85 and the standard deviation
was 3.4.
a. Calculate your z-score. ___________
b. Mark where your z-score falls on a bell curve.
c. Within how many deviations of the mean is your score?
__________________
82)
You took a test and earned a z-score of 2.5. The mean for the test was 79 and the standard
deviation was 6. What was your raw score?
_______________________
83) The following numbers represent the number of stories in the world’s 10 tallest buildings:
140, 88, 88, 108, 88, 88, 80, 69, 102 and 78.
a) Find the mean:_______________ b) median: _______________ c) mode: _______________
d)
Make a box-and-whisker plot of the data. Identify any outlier.
8