Download Algebra 1 Mid-Term Exam (January, 2012) -

Name:____________________
Daily Algebra Midterm Exam Review
Due: January 20
Date:_____________________
Block:_______________________
___
Section 1-- Solve each problem and circle your answer! Show all work!
1) Does 12 x  3  4 y represent direct variation?
2) What is the solution of 4k 1  4  12 ?
3) What is the slope of the line perpendicular to the line y 
4
x 1 ?
5
4) At a donut shop, there are 2 burned donuts for every 120 donuts cooked. At this rate, how
many burned donuts will there be if 600 donuts are cooked?
5) Simplify
1
(4 y  8)  6 y
2
6) Solve the equation: 3 x  1  24 .
7) What is the solution to the inequality 12x  36 ?
8) Is ( 2, 0) a solution to 2 x  3 y  8 ?
9) Write the equation 2 x  4 y  14 in slope-intercept form.
10) You have $15 to spend on gifts for your 4 friends. N represents how much money you spend
on each friend. Write an inequality to represent how much money you can spend on each
friend.
11) Write the equation of the line, in standard form, that passes through (1, 5) and (0,1)
12) Which inequality is represented by the graph?
a) x  9  24
b) 3x  45
c) x  5  10
d) x  7  8
13) Is the ordered pair ( 2, 7) a solution of 5 x  4 y  18 ?
14) Find the slope of the line that passes through (1, 3) and ( 2, 0) .
15) Solve for x : 8x  4x 14  8
16) Simplify the expression
14  21 y
7
17) Write an equation of the horizontal line through the point (2,3) .
18) What is the solution of the equation
x
 10  6 ?
2
19) Write an equation in point-slope form equation passes through the points (4, 6) and (3, 0) ?
20) Solve for m :
1
3
(24m  32) 
(12m  8)
4
4
21) Given that y varies directly with x, write a direct variation equation that relates x and y when
x  3 and y  12 .
22) What is the x-intercept of the equation 3x  2 y  12 ?
23) If
2
x  7 , what is the value of x?
3
24) What is the slope of the line parallel to the 3 y  7 x  2 ?
25) Write an expression to represent the area of the rectangle.
2x
2x  4
26) Solve for x : 3(4 x  1)  6(2 x  3)
27) Near Frederick, Maryland, you can rent a kayak for $10 per hour. You also pay a $25 fee for
equipment (life jacket and paddle). If your bill comes to $75, how many hours do you kayak?
28) What is the value of f ( 1) if f ( x) 
3
x 5?
2
29) What is the solution of the equation 30 
2
n?
5
30) Write an equation of the line, in slope-intercept form, through the point (4, 6) that is parallel to
y  2 x  4 .
31) The perimeter of a triangle is 28 meters. If the lengths of the sides are x , x  3 , and 3x , find
the value of x
32) Write an equation in point-slope form that goes through the points (4, 2) and (0, 2) .
33) Does the equation 3(6  n)  3(n  8) have a solution?
34) What is the value of x 3 if x  6 ?
35) What is the y-intercept of the line 5 x  4 y  12 ?
36) Find the value of x so the function has the given value: f ( x)  5 x  6 ; 8
37) What is the constant of variation in the equation 3x  7 y  0 ?
38) Let w represent the number of words you typed and let m represent the number of minutes
you typed. Write an expression to represent the words per minute that you typed.
39) Write a direct variation equation that goes through the point (4, 2) . (Hint: What is the other
point it MUST go through?)
40) What is the slope of the line with the equation 2 x  4 y  12 ?
41)Solve the inequality and graph your solution. 4x  2  6 or x  3  2
42) Determine which of the following lines, if any, are parallel, perpendicular, or neither.
_____________________________________________________________________
Line a: 2 x  2 y  3
43) Solve for x :
4
2

x6 5 x
Line b: y 
1
x4
2
Line c: y  x  6
44) Solve the inequality 5  2x 1  45 and graph your solution on the number line.
45) Write an equation in slope-intercept form if the line is through the points (2,3) and (0, 4) .
46) What is the equation of the line shown?
47) What is the equation in slope-intercept form of the line shown?
Section 2—Graphing: Use the coordinate planes provided to graph each equation or inequality.
You may NOT extend the graph or change the scale! If you are graphing an inequality, you must
show your test point!
48) Graph the inequality:
1
x  y  2 .
2
50) Graph the equation: y 
1
x3
4
52) Graph the equation: 3x  2 y  6
49) Graph the inequality 2 y  2 x  4 .
51) Graph the equation: x  5 .
Section 3—Application
53) You are going skiing with a friend. The lift pass costs you $75 and you have to rent skis and
poles for $5 per hour. Before you leave, you are trying to figure out what is the total cost to ski.
a. Define your variables.
i.
x = _______________________
ii.
y = _______________________
b. Write an equation to model this situation.
i.
__________________________
c. If the total cost is $125, how many hours did you ski? _______________________
54) A student is selling wrapping paper and candy to raise money for their school. Candy bars are
$2 each and wrapping paper is $4 per roll. A student sells $48 worth of candy and wrapping
paper.
a. Define your variables.
i.
x = _______________________
ii.
y = _______________________
b. Write an equation to model this situation.
iii.
__________________________
c. Find the intercepts in this situation and describe, in detail, what each tells you about
what the student sold.