Math 011 – Sample Test 6
Show all work. Simplify all answers. Leave all answers exact (reduced fractions not rounded decimals
– unless otherwise indicated).
1) You have two colors of paint – Sky Blue, which is 10% blue pigment, and Royal Blue, which is 40%
blue pigment. You wish to make 15 gallons of Deep Sea Blue, which is 25% blue pigment. How much
of each should you use?
2) Simplify
! 121
3) Simplify
16
4) Simplify.
( 10xy )2
5) Simplify by factoring.
108
6) Simplify by factoring.
8x 3 y10
7) Multiply and then simplify by factoring, if possible.
10 30
8) Multiply and then simplify by factoring, if possible.
8x 4 y 2y 6
9) Divide and simplify.
12
27
10) Simplify.
144
25
11) Rationalize the denominator.
8
3
12) Rationalize the denominator.
3
6
13) Rationalize the denominator.
3
15x
14) Add. Simplify by collecting like radical terms, if possible.
5 5!3 5
15) Subtract. Simplify by collecting like radical terms, if possible.
8+4 2
16) Multiply.
2( 50 ! 3)
17) Multiply.
(2 ! 6 )(2 + 6 )
18) Rationalize the denominator.
3
4+ 2
19) Solve
3x ! 4 = 3
20) Solve
3+ 2 n !1 = 9
21) Solve
2x ! 3 = x ! 3
22) Solve for x.
3x 2 ! x + 5 = 0
23) Solve for r.
r2 = 5 ! r
24) Find the vertex then sketch the graph of
y = x 2 ! 4x + 3
(Note: on the test this question is multiple choice for the graph part.)
Vertex:
25) Given the function f (y) = x ! x 2 , find each of the following.
f (8) =
f (!2) =
f ( 12 ) =