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Math 011 – Sample Test 5
Show all work. Simplify all answers. Leave all answers exact (reduced fractions not rounded decimals
– unless otherwise indicated).
1) Find the LCM of: 15x 2 y 3 , 18x 3 y 5 , 30xy 4
2) Find the LCM of z 2 + z ! 6 and z 2 + 8z + 15
3) Add. Simplify if possible.
x+w x!w
+
2xw 2 3xw
4) Add. Simplify if possible.
3x
2v ! 6
+
x + 3 3+ x
5) Subtract. Simplify if possible.
a+5 a!4
!
2x
x
6) Subtract. Simplify if possible.
4
2
! 2
2
x ! 4 x ! 5x + 6
7) Solve.
7 3 2
! =
2x 2 x
8) Solve.
4
6
=
x!5 x+2
9) Sue can mow her lawn in 50 minutes. Tom can do the same job in 40 minutes. How long would it
take Sue and Tom to mow the lawn if they worked together?
10) There are approximately 5 lbs of water for every 7 lbs of body weight in a certain animal. For a 250
lb animal, how much of the weight is water?
11) Simplify
2 1
+
x 2x
9 1
!
2x 2
12) Simplify
2 3
!
t t2
5
4+
t
13) The distance, d, you can travel on a tank of gas is directly proportional to how many gallons, g, are
in the tank. If a car can travel 300 miles on 24 gallons, how far can the same car travel on 15 galons?
14) The amount of time, T, you have for each question on a test varies inversely with the number, N, of
items on the test. For a 20 item test, you have 2.5 minutes per item. How much time per item will you
have on a 15 item test?
15) Solve the system of equations by graphing.
3x ! 4y = 12
2x + y = 6
(Don’t forget to write your solution as an ordered pair.)
16) Solve the system of equations by graphing.
y = 12 x + 2
y = 3x ! 4
(Don’t forget to write your solution as an ordered pair.)
17) Solve by the substitution method.
x = 10 ! 2y
y = 2x + 4
18) Solve by the substitution method.
2x ! 3y = 4
x + 5y = !4
19) Solve by the elimination method.
x+y= 4
2x ! y = 6
20) Solve by the elimination method.
2x ! 3y = 5
4x + 2y = 3