MATD 0390 Intermediate Algegra
Review for Test 3
Test 3 covers all cumulative material, including new sections 5.1-5.4, 5.6, 6.1-6.8, 7.1, 7.2
Bring a non-graphing calculator and something to write with and erase with. Be prepared to
show your work on all test problems in order to recieve full or partial credit.
State the domain of the rational expression.
1)
Solve the formula for the indicated variable.
4x - 1
8)
x2 - 12x + 20
9)
y2 - 25 y2 + 9y + 18
· y2 - 9 y2 - 8y + 15
Perform the indicated operation and simplify the result.
3)
for t
Solve the proportion problem.
Multiply the rational expression. Express the product as a
rational expression in lowest terms.
2)
P = A
1 + rt
y2 -14y + 49 y2 -14y + 49
+ y2 - 9
9 - y2
On a map of Natureʹs Wonder Hiking
Trails, 1 centimeter corresponds to 5
miles. Find the length of a trail
represented by a line that is 1.50
centimeters long on the map. (Round
your answer to the nearest
hundredth, if necessary.)
Solve the work problem.
10) Mark and Rachel work for Smith
Add or subtract, as indicated, and simplify the result.
4)
Landscaping Company. Mark can
finish a planting job in 3 hours, while
it takes Rachel 5 hours to finish the
same job. If Mark and Rachel work
together on the job and Smith
Landscaping charges $50 per hour for
a two-person crew, then how much
will Smith Landscaping charge for the
job? (Round your answer to the
nearest cent, if necessary.)
y - 4 y - 4
- y + 3 y + 1
Simplify the complex rational expression using Method 2.
5)
1 + 3
x x2
x + 27
x2
Simplify the radical.
Solve the equation.
6)
6 - 1 = 3
5x x + 1 2x2 + 2x
11)
Solve the problem.
7)
Let f(x) = 12)
x - 7
x + 3
and g(x) = . For
x + 5
x - 4
3 - 1
27
8
a8
Evaluate the expression, if possible.
13) 9-1/2
what value(s) of x does f(x) = g(x)?
A‐1
Rewrite the expression with a positive rational exponent.
Simplify, if possible.
14)
3
Rationalize the denominator.
24)
7y
2
7 + 3
Evaluate the radical function at the indicated value.
Evaluate the expression, if possible.
15) 1252/3
25) f(x) = 3
x + 5
f(-13)
Rewrite the expression with a positive rational exponent.
Simplify, if possible.
Solve the equation.
(3x6/7)2
16)
x-2/5
26)
x - 8 + 2 = 5
Add or subtract.
Use the product rule to simplify the expression. Assume
that the variables can be any real number.
17)
3
27) (6 + Multiply. Write the result in the form a + bi.
-8a8b5
28) ( 5 + Use the product rule to multiply. Assume all variables
represent positive real numbers.
18)
3
-7) + (8 - -63)
3 i )( 5 - 3 i )
Divide.
3
3 · 9
29)
Use the quotient rule to divide and simplify.
1 - 16i
-4i
Simplify.
6 s5
19)
4096
30) i16
Use the square root property to solve the equation.
Simplify the radical expression. Assume that all variables
represent positive real numbers.
20)
3
31) x2 - 14 = 0
Solve the equation by completing the square.
64x4y5
32) x2 + 10x = -6
Add or subtract. Assume all variables represent positive
real numbers.
Solve.
33) A rectangular park is 30 km long and
2 + 2 18 + 2 128
21)
8 km wide. How long is a pedestrian
route that runs diagonally across the
park?
Multiply, and then simplify if possible. Assume all
variables represent positive real numbers.
22) (
w - b)( w + b)
Use the quadratic formula to solve the equation.
34) x2 - 6x + 45 = 0
Rationalize the denominator. Assume that all variables
represent positive real numbers.
23)
3 -10
9
A‐2
Determine the discriminant of the quadratic equation.
Use the value of the discriminant to determine whether
the quadratic equation has two rational solutions, two
irrational solutions, one repeated real solution, or two
complex solutions that are not real.
35) x2 + 3x + 7 = 0
36) -8 - 6x2 = 5x - 13
Solve the problem.
37) The area of a rectangular wall in a
classroom is 171 square feet. Its length
is 8 feet shorter than three times its
width. Find the length and width of
the wall of the classroom.
Graph the system of linear inequalities.
38)
2x - y ≤ 2
x + 2y ≥ -2
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
-6
-8
-10
A‐3
Answer Key
Testname: 0390REVIEW3SULLIVAN
1) {x|x ≠ 10, x ≠ 2}
(y + 5)(y + 6)
2)
(y - 3)2
3) 0
4)
5)
6)
-2(y - 4)
(y + 3)(y + 1)
1
x2 - 3x + 9
3
2
7) x = 8) t = 13
19
A - P
Pr
9) 7.5 mi
10) $93.75
1
11) - 3
12) |a|
1
13)
3
14) (7y) 1/3
15) 25
16) 9x74/35
3
17) - 2a 2 b a 2 b2
18) 3
6
s5
19)
4
3
20) 4xy xy2
21) 23 2
22) w - b2
3
23)
-30
3
24)
14 - 3 2
-2
25) -2
26) {17}
27) 14 - 2 7i
28) 28
1
29) 4 + i
4
30) 1
31) {- 14, 14}
A‐4
Answer Key
Testname: 0390REVIEW3SULLIVAN
32) {-5 - 19, -5 + 19}
33) 2 241 km
34) {3 - 6i, 3 + 6i}
35) Two complex solutions that are not real
36) Two irrational solutions
37) width = 9 ft; length = 19 ft
38)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
-6
-8
-10
A‐5