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Algebra 1 Midterm Exam Review
>= means greater than or equal to
<= means less than or equal to
^ means the number is squared
Some questions require you to graph equations. No graphs will be given.
Currently a work in progress. I will update answers as the break continues.
Work is shown first. Then the answer is at the bottom.
Evaluate the expression.
11 + 8 x 3^ - 8
11 + 8 x 3^ - 8
11 + 8 x 3^ - 8
11 + 8 x 9 - 8
11 + 72 - 8
83 - 8
75
11 + 8 x 9 - 8
11 + 72 - 8
83 - 8
75
Evaluate the expression.
2/3 ((5 + 2)^ - 13)
2/3 ((5 + 2)^ - 13)
2/3 ((5 + 2)^ - 13)
2/3 (7^ - 13)
2/3 (49 - 13)
2/3 (36)
24
2/3 (7^ - 13)
2/3 (49 - 13)
2/3 (36)
24
Evaluate the expression.
5k^ - 7k when k=3
5k^ - 7k when k=3
5(3^) - 7(3)
5(9) - 7(3)
45 - 21
24
5(9) - 7(3)
45 - 21
24
Check whether the given number is a solution of the equation or inequality.
7x-11=17;4
7x-11=17;4
7(4)-11=17
28-11=17
17=17
yes
28-11=17
17=17
yes
Check whether the given number is a solution of the equation or inequality.
9y + 3 < 13; 2
9y + 3 < 13; 2
9(2) + 3 < 13
18 + 3 < 13
21 < 13
no
18 + 3 < 13
21 < 13
no
Check whether the given number is a solution of the equation or inequality.
5z - 9 >= 7z - 11; -2
5z - 9 >= 7z - 11; -2
5(2) - 9 >= 7(5) - 11
10 - 9 >= 35 - 11
1 >= 24
no
10 - 9 >= 35 - 11
1 >= 24
no
Solve. 5 + (-13)
5 - 13
-8
-8
Solve. -17 + (-21)
-17 - 21
-38
-38
Solve. 15 - (-12)
15 + 12
27
27
-7(-11)
77
-1/2(15)(-8)
-15/2(-8)
60
60
72/-6
-12
Find the square root of 169.
13
Find the negative square root of 9.
-3
Find the positive and negative square roots of 256.
16 and -16
Find the positive and negative square roots of 0.04.
0.2 and -0.2.
Solve, if possible. x + 7 = 19.
x + 7 = 19
- 7 - 7
x = 12
- 7 - 7
x = 12
Solve, if possible. 23 - y = 14
23 - y = 14
-23 -23
-y = -9
y = 9
-23 -23
-y = -9
y = 9
Solve, if possible. 7p - 11 = 10
7p - 11 = 10
+11 +11
7p = 21
p = 3
+11 +11
7p = 21
p = 3
Solve, if possible. q/4 + 8 = 13
q/4 + 8 = 13
-8 -8
q/4(4) = 5(4)
q = 20
-8 -8
q/4(4) = 5(4)
q = 20
Solve, if possible. 15j + 7 j = 11
22j/22 = 11/22
j = 1/2
j = 1/2
Solve, if possible. 14m + 7 - 8m = -17
14m - 8m + 7 = -17
6m +7 = -17
-7 -7
6m/6 = -24/6
m = -4
6m +7 = -17
-7 -7
6m/6 = -24/6
m = -4
Solve, if possible. -3.1t + 4.3 = -1.9t + 3.7
-3.1t + 4.3 = -1.9t + 3.7
-4.3 -4.3
-3.1t = -1.9t - 0.6
+1.9t +1.9t
-1.2t/-1.2 = -0.6/-1.2
t = 1/2
-4.3 -4.3
-3.1t = -1.9t - 0.6
+1.9t +1.9t
-1.2t/-1.2 = -0.6/-1.2
t = 1/2
Solve, if possible. 3(4k - 2) = 16k -32
12k -6 = 16k -32
+6 +6
12k = 16k - 26
-16k -16k
-4k/-4= -26/-4
k = 13/2
+6 +6
12k = 16k - 26
-16k -16k
-4k/-4= -26/-4
k = 13/2
Solve, if possible. 1/3(9g - 6) = 3/5(5g + 15)
3g - 2 = 3g + 9
3g = 3g + 11
no solution/not possible
3g = 3g + 11
no solution/not possible
A student can read 4 pages in 5 minutes. How many pages can the student read in 60 minutes.
4/5 = 60/x CROSS MULTIPLY
300/4 = 4x/4
x = 75
75 pages
300/4 = 4x/4
x = 75
75 pages
What precent of 38 is 15.2?
38p/38 = 15.2/38
p = .4
40%
p = .4
40%
What number is 35% of 150.
150(.35) = n
n = 52.5
52.5
n = 52.5
52.5
At your school, 74% of students bought their lunch at the cafeteria. There are 1250 students in the school. How many students bought their lunch.
1250(.74) = b
b = 925
925 students
b = 925
925 students
Solve ax + by = c for a.
ax+by=c
ax=-by+c
a=(-by+c)/x
ax=-by+c
a=(-by+c)/x
Solve ax - y/b =c for y
ax-y/b=c
-y/b=-ax+c
-y=-abx+bc
y=abx-bc
-y/b=-ax+c
-y=-abx+bc
y=abx-bc
Plot point A(3, 6) on a coordinate plane and describe its location on the graph.
(3, 6) is in Quadrant I.
Plot point B(-2, -4) on a coordinate plane and describe its location on the graph.
(-2, -4) is in Quadrant III.
Plot point C(0, -3) on a coordinate plane and describe its location on the graph.
(0, -3) is on the x-axis.
Find the slope of the line that passes through the points (4, 8) and (5, 13).
(13-8)/(5-4)
5/1
The slope is 5.
5/1
The slope is 5.
Find the slope of the line that passes through the points (-3, 6) and (2, 7).
(7-6)/(2--3)
1/5
The slope is 1/5.
1/5
The slope is 1/5.
Find the slope of the line that passes through the points (-8, -2) and (-5, -2).
(-2--2)/(-5--8)
0/3
The slope is undefined.
0/3
The slope is undefined.
Graph y-2x=-3.
y-2x=-3
y = 2x + 3
Possible points: (0, 3), (1, 5), (2, 7), (-1, 1), (-2, -1)
y = 2x + 3
Possible points: (0, 3), (1, 5), (2, 7), (-1, 1), (-2, -1)
Graph x = -4.
Possible points: (-4, -2), (-4, -1), (-4, 0), (-4, 1), (-4, 2)
Graph y = 3/5x +3.
Possible points: (-10, -6), (-5, 0), (0, 3), (5, 6), (10, 9)
Evaluate f(x) = -1/2x + 3 when x = -2.
f(-2) = -1/2(-2) + 3
f(-2) = 1 + 3
f(-2) = 4
f(-2) = 1 + 3
f(-2) = 4
Evaluate g(x) = 8x - 7 when x = 0.5.
g(0.5) = 8(0.5) - 7
g(0.5) = 4-7
g(0.5) = -3
g(0.5) = 4-7
g(0.5) = -3
The amount of water w (in thousands of gallons) flowing over a dams spillway varies directly with time t (in hours). In four hours, six thousand gallons of water flow over the spillway. Write a direct variation equation that related w and t. How many gallons of water will be released in twelve hours?
w = at
6 = 4a
3/2 = a
w = 3/2(12)
w = 18
w = 3/2t; 18 thousand gallons
6 = 4a
3/2 = a
w = 3/2(12)
w = 18
w = 3/2t; 18 thousand gallons
Write an equation in slope-intercept form that passes through the point (-1, 3) and has a slope of 2.
3 = 2(-1) + b
3 = -2 + b
5 = b
y = 2x + 5
3 = -2 + b
5 = b
y = 2x + 5
Write an equation in slope-intercept form that passes through the point (4, -3) and has a slope of 3/4.
-3 = 3/4(4) +b
-3 = 3 + b
-6 = b
y = 3/4x - 6
-3 = 3 + b
-6 = b
y = 3/4x - 6
Write an equation in slope-intercept form that passes through the point (2, -7) and has a slope of -5.
-7 = -5(2) +b
-7 = -10 + b
3 = b
y = -5x + 3
-7 = -10 + b
3 = b
y = -5x + 3
Write an equation in standard form of the line that passes through the point (3, -7) and has a slope of -7.
y + 7 = -7(x - 3)
y + 7 = -7x + 21
y = -7x + 14
7x + y = 14
y + 7 = -7x + 21
y = -7x + 14
7x + y = 14
Make a scatter plot using the points (0, 7), (2, 16), (4, 25), (6, 38), and (8, 50). Describe the correlation of the data.
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Solve and graph x - 13 < -8
x - 13 < -8
x < 5
x < 5