Math 095 – Review Sheet – Practice Problems for Midterm Exam
1. Solve each equation.
A) 2x +19 = −15
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C) 39 = 6 y − ( y − 9)
B) −7m + 3m = 36
D) −0.3x + 2.1( x − 4) = −6.6
E) 2(3 + 7t ) − (1+15t ) = 2
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1
3
3
F) x − 4 = x + x
G) −6t + 5t − 9 = 3(t − 4) − 5
4
2
4
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H) 7( y − 3) − 4( y +1) = −5( y + 5)
I) 2.3x +13.7 = 1.3x + 2.9
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2
1
4
J) z + 8 = z
K) 5x + 9 = 7x + 21
L) − y = −12
3
4
7
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M) 7 − ( m − 4) = −3m + 2( m +1)
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N) 0.6( x + 20) + 0.8( x −10) = 46
1
1
O) − ( x − 27) + ( x + 3) = x + 67
9
3
P) −8(2x + 4) = −4(4x + 8)
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2. Solve the formula for the specified€variable.
1
A) V = πr 3 h for h
3
B) P = 2L + 2W for W
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1
C) A = h ( b + B) for B
2
3. Solve each proportion.
A)
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x
5
=
24 30
4. Solve each problem.
B)
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x +5 x −3
=
3
4
C)
m 2−m
=
6
2
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A) The land area of Hawaii is 5213 square miles greater than the area of Rhode Island.
Together the areas total 7637 square miles. What is the area of each of the two states?
B) The height of Seven Falls in Colorado is 5/2 the height of Twin Falls in Idaho. The sum of
the heights is 420 feet. Find the height of each.
C) Find the measure of an angle whose supplement measures 14 times its measure.
D) The sum of the measures of the angles of any triangle is 180 degrees. In triangle ABC, the
measure of angle A is 70° more than the measure of angle B. The measure of angle B is twice
the measure of angle C. Find the measure of each angle.
E) The perimeter of a rectangle is 36 yards. The width is 18 yards less than twice the length.
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Find the length and the width of the rectangle.
F) The perimeter of a certain rectangle is 16 times the width. The length is 12 centimeters more
than the width. Find the width of the rectangle.
G) The circumference of a table is 62.5 feet. What is the radius? What is the diameter? What is
the area? Approximate all answers to the nearest hundredth. Use 3.14 as an approximation for
pi.
H) If 2 pounds of fertilizer will cover 120 square feet of lawn, how many pounds would be
needed to cover 600 square feet?
I) The distance between two cities on a road map is 32 cm. The two cities are actually 150 km
apart. The distance on the map between two other cities is 80 cm. How far apart in kilometers
are these cities actually?
5. Solve each absolute value equation.
A) 3x +1 = 4
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B) x + 5 = 12
C) 2 − x − 3 = 4
6. Write the interval notation that corresponds to the following graphs.
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A)
B)
C)
D)
E)
D) 2x − 5 +10 = 3
7. Graph each inequality on the number line.
A) x > −2
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B) x ≤ 8
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E) x > 15
x ≤5
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A) −6x +1 ≤ −17
B) 8( x −1) − (2x + 7) ≤ 9
C) 10 − 4x + 7x < 4x − 3x
D) −3 < 2x +1 ≤ 4
E) −20 ≤ −9z − 2 < 7
F)
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G) x −1 < 7
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D)
8. Solve each€inequality. Express
the solution in interval notation.
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H) 2x − 3 ≥11
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C) −3 < x ≤ 2
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I) 4x + 3 > 27
A) y = −5x −1
(2, ), (0, ), (−1, )
B) 6x − 2 y = 8
(−2, ), (0, ), (3, )
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J) x − 5 < −4
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9. Complete the ordered pairs for each equation.
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C) y = 7
1 2
5
≤ x≤
2 3
4
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(−1, ), (0, ), (1, )
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10. Complete
y = 4x
x
-1
0
1
2
y
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11. Graph each line.
A) with slope 0 and y-intercept (0, −3)
B) with slope -1 and y-intercept (0,4)
C) with slope
6
and €
passing through the point ( −3, −2)
5
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12. Determine
the slope and y-intercept. Then graph the line.
A) y = 2x − 5
B) x + 3y = −3
C) 3x − 4 y = 0
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D) x = −5
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13. Find the slope of each line.
A) through the points ( −1,2) and (4, −5)
D) shown in graph
B) through the points (0, −3) and ( −2, −7)
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C) through the points ( −1, −5) and ( −4, −5)
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14. Find an equation for each line. Write your answer in slope-intercept form.
A) with slope 7 and y-intercept of (0,2)
B) with slope −
3
and passing through the point (2,9)
4
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C) with slope undefined and passing through the point ( −1,3)
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D) passing through the points (2, −5) and (1,4)
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E)
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Solutions to Practice Problems for Exam #1
1. A) x = -17
F) x = -2
G) t = 2
L) y = 21
M) no solution
2. A) h =
C) B =
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3. A)
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B) m = -9
H) y = 0
3V
πr3
2A − hb
h
x=4
C) y = 6
B=
N) x = 30
J) z = -96/5
O) x = -81
P − 2L
2
2A
−b
h
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or
W=
K) x = -6
P) all real numbers
P
−L
2
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B) x = -29
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E) t = 3
I) x = -10.8
B) W =
or
D) x = 1
C) m = 3/2
4. A) Hawaii = 6425 square miles; Rhode Island = 1212 square miles
B) Seven Falls = 300 feet; Twin Falls = 120 feet
C) 12°
D) angle A = 114° ; angle B = 44°; angle C = 22°
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E) width = 6 yards; length = 12 yards
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F) width = 2 cm
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G) radius = 9.95 ft; diameter = 19.90 ft; area = 310.87 ft
H) 10 pounds
I) 375 km
5. A) x = 1 or x = -5/3
B) x = -7 or x = 7
D) x = -5 or x = 9
D) no solution
6. A) ( 2, ∞)
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B)
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[4,7]
C) ( −∞,6)
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D) ( −∞, −5] ∪ [ 3, ∞ )
E) ( −∞, ∞ )
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7. A)
B)
C)
D)
E)
8. A) x ≥ 3 ; [ 3, ∞)
B) x ≤ 4 ; ( −∞, 4]
C) x < −5 ; ( −∞, −5)
E) −1 < z ≤ 2 ; ( −1, 2]
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F)
3 ⎤
3 ⎛
D) −2 < x ≤ ; ⎜ −2, ⎥
2€
2 ⎝
⎦
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G) −6 < x < 8 ; ( −6,8)
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I) x < −6 or x > 6;
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H) x ≤ −4 or x ≥ 7 ; ( −∞, −4] ∪ [7, ∞ )
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(−∞, −6) ∪ (6, ∞)
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9. A) (2, −11), (0, −1), ( −1,4)
€ 10.
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-4
0
4
8
3
15 ⎡ 3 15 ⎤
≤ x ≤ ; ⎢ , ⎥
8 ⎣ 4 8 ⎦
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J) no solution
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B) ( −2, −10), (0, −4), (3,5)
C) ( −1,7), (0,7), (1,7)
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11. A)
B)
C)
12. A) slope = 2, y-intercept = (0, −5)
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B) slope = −
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1
, y-intercept = (0, −1)
3
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12. C) slope =
3
, y-intercept = (0,0)
4
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13. A) m = −
7
5
B) m = 2
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14. A) y = 7x + 2
3
21
B) y = − x +
4
2
1
E) y = − x
3
D) y = −9x +13
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D) slope is undefined, no y-intercept
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C) m = 0
C) x = −1
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D) m = 3