1
Math 098 - Final Exam Review
Factor completely. Represent each given condition using a single variable, x.
1) 42x3y + 30xy5 20) The base and height of a triangle whose
height is seven less than six times its base.
2) 20x4y + 36xy3
Solve.
21) Find the length of the shorter leg of a right
3) 2a(a - b) + (a - b) triangle if the longer leg is 24 meters and the
hypotenuse is 6 more than twice the shorter
leg.
4) - 27y3 + 12y
22) A triangular piece of glass is being cut so that
5) 30x2 - 25xy + 12xy - 10y2 the height of the triangle is 4 inches shorter
than twice the base. If the area of the triangle
is 120 square inches, how long is the height of
6) u2 - 4uv - 45v2
the triangle?
7) 6y2 + 27y - 15 23) If the cost, C(x), for manufacturing x units of
a certain product is given by
C(x) = x2 - 10x + 1200, find the number of
8) 18x2 - 63x - 36
units manufactured at a cost of $10,200.
9) 25x2 - 40xy + 16y2
24) A window washer accidentally drops a
bucket from the top of a 256-foot building.
10) z2 - 100 The height h of the bucket after t seconds is
given by h = -16t2 + 256. When will the
bucket hit the ground?
11) 81x2 - 49
Find the domain of the rational expression.
12) x3 - 27 1 - 3x
25) f(x) =
x3 - 20x2 + 91x
Solve the equation.
Simplify the expression.
13) x(5x + 8) = 4 14
26) 2m - 6
14) x2 - 36 = 35x
20x2 + 12x
27) 20x
15) y3 = 64y
9x2 + 27x3
28)
10x + 30x2
16) (x + 6)(x + 1) = 24
7x - 28
17) (2x + 1)(5x - 3) = 0 29) 12 - 3x
18) 5x(8x - 5) = 0
19) 15x3 + 90x2 + 120x = 0
1
, 2
4 - x2 42)
5 -a 3 7
30) a + =
4 a
x2 - 11x + 18
3 1
Solve the problem. 43) = 2 -
x x
x3 + 4
31) If f(x) = , find f(-4).
x2 - 4
6 8
44) = 1 +
x-6 x+6
32) If the average cost per unit C(x) to produce x
1200
units of plywood is given by C(x) = ,
x + 40 Solve the equation.
2 t
what is the cost per unit if 50 units of 45) =
t 5t - 12
plywood are produced?
1
Find the product and simplify. 46) 4 -2
+ =
x+7 x+5 2
x + 12x + 35
r2 - t 2 r
33) ·
r + t r2 - r t
Solve the formula for the specified letter.
z3 5 1 1 1 for c
47) + =
34) · a b c
20z 2z2
h(a + b)
48) A = for a
9x4 - 72x x2 + x - 2 2
35)
3x2 - 12 ·
4x3 + 8x2 +16x
Solve.
Find the quotient and simplify. 49) Chuck and Dana agree to meet in Chicago for
the weekend. Chuck travels 78 miles in the
2x13 4x same time that Dana travels 72 miles. If
36) ÷
7x6 14x3 Chuck's rate of travel is 3 mph more than
Dana's, and they travel the same length of
(y - 4)2 2y - 8 time, at what speed does Chuck travel?
37) ÷
2 4
50) Dr. Wong can see 9 patients in 3 hours. At
this rate, how long would it take her to see 72
x2 - 49 7-x patients?
38) 7y ÷
14xy
51) Frank can type a report in 4 hours and James
takes 6 hours. How long will it take the two
p2 - 8p + pq - 8q p-8
39) ÷ of them typing together?
2
10p - 10q 2 6p - 6q
Perform the indicated operation. Simplify if possible.
3x + 12 2x + 5
40) 2 -
x + 6x - 7 2
x + 6x - 7
Solve the equation.
x 8x x
41) + =
6 9 54
2
Math 098 - Final Exam Review
Factor completely. Represent each given condition using a single variable, x.
1) 42x3y + 30xy5 20) The base and height of a triangle whose
height is seven less than six times its base.
2) 20x4y + 36xy3
Solve.
21) Find the length of the shorter leg of a right
3) 2a(a - b) + (a - b) triangle if the longer leg is 24 meters and the
hypotenuse is 6 more than twice the shorter
leg.
4) - 27y3 + 12y
22) A triangular piece of glass is being cut so that
5) 30x2 - 25xy + 12xy - 10y2 the height of the triangle is 4 inches shorter
than twice the base. If the area of the triangle
is 120 square inches, how long is the height of
6) u2 - 4uv - 45v2
the triangle?
7) 6y2 + 27y - 15 23) If the cost, C(x), for manufacturing x units of
a certain product is given by
C(x) = x2 - 10x + 1200, find the number of
8) 18x2 - 63x - 36
units manufactured at a cost of $10,200.
9) 25x2 - 40xy + 16y2
24) A window washer accidentally drops a
bucket from the top of a 256-foot building.
10) z2 - 100 The height h of the bucket after t seconds is
given by h = -16t2 + 256. When will the
bucket hit the ground?
11) 81x2 - 49
Find the domain of the rational expression.
12) x3 - 27 1 - 3x
25) f(x) =
x3 - 20x2 + 91x
Solve the equation.
Simplify the expression.
13) x(5x + 8) = 4 14
26) 2m - 6
14) x2 - 36 = 35x
20x2 + 12x
27) 20x
15) y3 = 64y
9x2 + 27x3
28)
10x + 30x2
16) (x + 6)(x + 1) = 24
7x - 28
17) (2x + 1)(5x - 3) = 0 29) 12 - 3x
18) 5x(8x - 5) = 0
19) 15x3 + 90x2 + 120x = 0
1
, 2
4 - x2 42)
5 -a 3 7
30) a + =
4 a
x2 - 11x + 18
3 1
Solve the problem. 43) = 2 -
x x
x3 + 4
31) If f(x) = , find f(-4).
x2 - 4
6 8
44) = 1 +
x-6 x+6
32) If the average cost per unit C(x) to produce x
1200
units of plywood is given by C(x) = ,
x + 40 Solve the equation.
2 t
what is the cost per unit if 50 units of 45) =
t 5t - 12
plywood are produced?
1
Find the product and simplify. 46) 4 -2
+ =
x+7 x+5 2
x + 12x + 35
r2 - t 2 r
33) ·
r + t r2 - r t
Solve the formula for the specified letter.
z3 5 1 1 1 for c
47) + =
34) · a b c
20z 2z2
h(a + b)
48) A = for a
9x4 - 72x x2 + x - 2 2
35)
3x2 - 12 ·
4x3 + 8x2 +16x
Solve.
Find the quotient and simplify. 49) Chuck and Dana agree to meet in Chicago for
the weekend. Chuck travels 78 miles in the
2x13 4x same time that Dana travels 72 miles. If
36) ÷
7x6 14x3 Chuck's rate of travel is 3 mph more than
Dana's, and they travel the same length of
(y - 4)2 2y - 8 time, at what speed does Chuck travel?
37) ÷
2 4
50) Dr. Wong can see 9 patients in 3 hours. At
this rate, how long would it take her to see 72
x2 - 49 7-x patients?
38) 7y ÷
14xy
51) Frank can type a report in 4 hours and James
takes 6 hours. How long will it take the two
p2 - 8p + pq - 8q p-8
39) ÷ of them typing together?
2
10p - 10q 2 6p - 6q
Perform the indicated operation. Simplify if possible.
3x + 12 2x + 5
40) 2 -
x + 6x - 7 2
x + 6x - 7
Solve the equation.
x 8x x
41) + =
6 9 54
2
