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To receive grade credit in Prof McFarland's classes, you must submit this quiz before an assigned date.
Enter numbers (such as 7, -11, 2.65, or 0) in each answer box below.
[1](a)
Enter the number or decimal which completes the following square (1 pt):
x2 + 6x +
(b)
Enter the roots of the following equation (2 pts each):
x2 + 6x = 7 :
x =
or
x =
[2](a)
Enter the number or decimal which completes the following square (1 pt):
x2 - x +
(b)
Enter the roots of the following equation (2 pts each):
x2 - x = 2 :
x = or
x =
[3](a)
Enter numbers so that the following trinomial is factored (2 pts each number):
x2 + 4x - 21 =
(x +
) (x +
)
(b)
Enter the roots of the following equation (one-half pt each):
x2 + 4x - 21 = 0 :
x =
or
x =
[4](a)
Enter numbers so that the following trinomial is factored (2 pts each factor):
6x2 + x - 12 =
(
x +
) (
x +
)
(b)
Enter the roots of the following equation (one-half pt each root):
6x2 + x - 12 = 0 :x =
or
x =
[5](a)
Enter the values of a, b, and c for the following equation (1 pt each):
2x2 - 6x + 1 = 0 :a =
and b =
and c =
(b)
Enter the roots of the following equation (one pt each):
2x2 - 6x + 1 = 0 :
x =
or
x =
[6](a)
Enter the values of a, b, and c for the following equation (3 pts : must get all 3 correct):
5x + 2 = 3x2:a =
and b =
and c =
(b)
Enter the roots of the following equation (one pt each):
5x + 2 = 3x2:
x =
or
x =
[7]
Solve the following equation :
x x - 1
+
x + 1 x
=
7 2
x =
or
x =
Scoring : 5 pts if both roots correct ; 2 pts if only one root correct
[8]
Solve the following equation :
2x + 1 x
-
x 2x + 1
=
5 6
x =
or
x =
Scoring : 5 pts if both roots correct ; 2 pts if only one root correct
The following two word problems translate into equations like those in problems 1 through 8
above, but the scoring is only for the translation into an equation. You need not solve for x.
[9]
Homer and Marge both drive 300 miles at a constant speed from Springfield to
Whitewater. Because he overslept, Homer leaves an hour later than Marge,
and drives 10 mph faster. How many hours did Marge spend driving, if she
and Homer arrived in Whitewater at the same?
(a)
Which of the following is the best definition of x to use in
translating the boxed problem above? (2 pts)
(a) Let x = Marge's travel time
(b) Let x = Homer's travel time
(c) Let x = Marge's speed
(d) Let x = Marge
(e) Let x = the the distance Marge travelled
(f) Let x = Homer's speed
To receive points for [9b] below, you must first answer [9a] above correctly.
(b)
Which of the following equations correctly translates
the boxed problem above? (3 pts)
(a) 300x + 300(x-1) = 10
(d)
300 x
=
300 x+1
+ 10
(b) 300x + 300(x+1) = 10
(e)
x 300
=
x+1 300
+
1 10
(c)
x 300
=
x+1 300
+ 10
(f)
300 x-1
=
300 x
+ 10
[10]
Jenny's back yard is a square 100 feet on each side. Jenny plans a
square garden in the center of this yard, surrounded by a grass border
of uniform width, as shown at the right. If the area of the
garden is half the area of the back yard, what is the width of the
grass border?
garden
100 FT
(a)
Which of the following is the best definition of x to use in
translating the boxed problem above? (2 pts)
(a) Let x = width of Jenny's garden
(b) Let x = grass border
(c) Let x = width of Jenny's back yard
(d) Let x = width of the grass border
(e) Let x = area of Jenny's garden
(f) Let x = area of Jenny's back yard
To receive points for [10b] below, you must first answer [10a] above correctly.
(b)
Which of the following equations correctly translates
the boxed problem above? (3 pts)
(a) 2(100 - x)2 = 1002
(d) 2x2 = 1002
(b) 2(100 - 2x)2 = 1002
(e) (100 - 2x)2 = 502
(c) 2(50 - x)2 = 1002
(f) (100 - 4x)2 = 502
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