Name_________________________________
Study Guide for Algebra 1 Midterm
Evaluate the expression for the given values of the variables.
when a  3
2.
4[44  (10  8) 2 ]  7
5.
1.
when a = –4
3.
x3  2 y 2 when x  2 , y  3
Evaluate.
4.
6. Is 5 a solution to 10 x  4  20 ?
8.
6.
7.
Is (3, 4) a solution to 3x  y  13
Tell whether each pairing is a function.
Input
5
10
10
20
Translate.
11a.
9.
“Five is less than a number x divided by 7.”
10.
Output
10
15
20
25
“The perimeter P of a square is less than or equal
to four times the difference of a number n and 5.
Graph the function y   x  4 , for domain 2  x  5
b.
State the range in interval notation.
Simplify.
12.
13.
14.
15.
Volume of a Cone:
Solve for h.
16.
Write 2 x  3 y  18 as a function of x
Solve the equation.
17.
18.
19.
20.
21.
22.
23.
1 1
t  t  10
2 3
24.
2
(3x  9)  2( x  4)
3
25.
5
x  15
6
1
2 x  6  (4 x  18)
2
26.
A local gym charges nonmembers $10 per day. Members pay a yearly fee of $80 and $4 per day to use the gym.
Write and solve an equation to find how many days you must use the gym justify becoming a member.
27.
Rewrite the equation so that y is a function of x.
28.
Graph the equation.
29.
3 x  6 y  24
Find the x and y –intercept of
Then graph the equation using the intercepts.
30.
32.
33.
34.
37.
Find the y-intercept.
31.
Find the slope of the line passing through the points.
Find the value of y so that the line passing through the two points has the given slope.
Takeru “The Tsunami” Kobyashi eats 4 Nathan’s hot dogs in 2 minutes and 56 in 12 minutes.
Over the time interval given, calculate the rate of change.
Graph the equation. 6 x  4y  4
35.
Decide whether the graphs of the two functions are parallel lines.
36
Which equation has infinitely many solutions? No solutions?
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.
38.
State the x- and y-intercepts of the line with the
y  3x  3 .
equation
39a.
b.
Write the equation of the line between the two points:
40. (2, 4),(8, 4)
41. (3,6),(3,15)
Determine the slope of the line graphed.
Write the equation.
42.
(1,3),(1,7)
43.
Rewrite the equation 5x  2 y  7  0
in slope-intercept form.
45.
Determine if the line
44.
Find the slope and y-intercept of the line
with the equation 4 x  2 y  32 .
is parallel, perpendicular or neither, to the line
.
Graph.
1
x
5
46.
y
50.
Let
52.
What is the value of the function
when
?.
47.
1
y   x7
3
Find x when
48.
y  2
49.
51.
Compare the graph with the graph of
to the parent function f ( x)  x .
53.
Find the value of x so that g ( x)  14
When g ( x)  2 x  6 .
Solve the inequality and graph the solution. Write each answer in interval notation
54.

2
p  1  3
3
55.
56.
\
57.
x  2 y  4
Write a compound inequality that describes the graph as an inequality and in interval notation.
58.
The triangle has a perimeter = 36. Solve for x.
2x+2
59.
2
( y  1)   ( x  4)
3
Graph the equation
Point:__________
Slope:__________
2x+2
x
60.
61.
Write the equation of a line that passes through the point (4,-2) and has a slope of
Write the equation of the line parallel
to the given line and through point (-4,4).
63.
Find the zero of the function f ( x)  2 x  10
64.
Use the graph to answer the following questions.
a. Function?
YES
NO
a. Domain:________________
c. Range: _________________
d.
f (2) = __________________
e.
What is x if f ( x)  6 ? ______
f.
What is the zero of the function?_______

1
.
2
62. Write the equaltion of the line graphed in slope -intercept
and standard form.
65.
Compare the graph of f ( x)  4 x  2 to the parent function f ( x)  x
Solve and each inequality. Write your answer as an inequality and in interval notation.
66.
2( j  4)  6 or
j  5  2
67.
2 x  16  2( x  7)
68.
9   x  4 x  1  6
Inequality___________________
Inequality__________________
Inequality____________________
Interval Notation_____________
Interval Notation____________
Interval Notation_______________
69.
4
2 1
r 3 r   r
3
3 3
70.
0  5x  6 x
71.
1
(4 x  20)  x  5
4
Inequality___________________
Inequality__________________
Inequality____________________
Interval Notation_____________
Interval Notation____________
Interval Notation_______________
72.
Oberon Cell Phone Company advertises service for 3 cents per minute plus a monthly fee of $29.95.
If Parker’s phone bill for October was $38.95, find the number of minutes he used.
73.
Quin was shopping at a used book sale where all books were selling at the same price. He bought six science fiction
books and eight mysteries. He also decided to buy a poster for $2.40. In total, Quin spent $8.70.
What was the price of a single book?
74.
Ulani has an older sister and a younger sister. Her older sister is one year more than twice Ulani’s age. Ulani’s
younger sister is three years younger than she is. The sum of their three ages is 26. Find Ulani’s age.
75.
The length of a rectangular garden is three feet more than twice its width. If the perimeter of the garden is 114 feet,
then what is the width of the garden?