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1. Graph and clearly shade the polygonal set that satisfies the following system of linear inequalities.
=
3y
=4 4
−
2y
4x
x+
6
6
2
−6
−4
−2
−2
2
4
6
−4
−6
2. Find the corner point of the above polygonal set.
4 20
,
11 11
3. Find the equation of the line perpendicular to 5x − 2y = 0 and passing through the
point (−4, 1).
3
2
y=− x−
5
5
4. The endpoints of a line segment are (3, −2) and (a, 5). The slope of the line segment
5
is − . Find the value of a.
3
9
a=−
5
5. A company is in the business of producing and selling gambots. The total cost to
produce 20 gambots is $167, and the total cost to produce 80 gambots is $188. Find
a linear function, C(q), that gives the total cost to produce q gambots.
C(q) =
7
q + 160
20
6. Solve the following equations.
For some of them, you may find the quadratic for√
2
−b ± b − 4ac
mula handy: x =
. If the solution is imaginary or there is no solu2a
tion, say so. SIMPLIFY your answers. You are not required to check your solutions
here (though you might want to if you have time).
a)
4
2
−5 =
2−x
3
x=
22
17
b) x2 + 8x = 20
x = −10, 8
c) 2(x − 2)2 + 4 = 13
√
x =2±
d) 2(x2 − 3x) = 5 − x2
e) 8
p
(2t − 1)3 = 16
3
√
2 6
x = 1±
3
√
3
4
1
t= +
2
2
7. Simplify the following as much as possible.
√
√ √
√
a) 3(3 18 − 5 12) − 2 6
√
7 6 − 30
r
72A4 B7
3
b)
27A−3 B11
r
2A2 3 A
B
3B
8. Find the roots of f (x) = 2x3 − x2 − 9x + 6 if (x − 2) is a factor.
√
−3 ± 33
x = 2,
4
9. Solve the following equation by completing the square: 2x2 − 6x − 3.
√
15
3
x= ±
2
2
10. A toy rocket is shot in the air so that its height above the ground in feet after t
seconds is given by h(t) = −16t2 + 256t.
a) When does the rocket attain its maximum height above the ground, and what
is this maximum height?
t = 8sec, height is 1024 feet.
b) When does the rocket hit the ground?
t = 16
c) Draw a sketch of the graph of h(t) for t ≥ 0, showing clearly the points that
correspond to parts a and b. Scale your axes.
(8, 1024)
1100
1000
900
800
700
600
500
400
300
200
100
−2
b
2
4
6
8
10
12
14
16
18
11. I have 24 coins, dimas and quarters only. If their total value is $3.60, how many of
each type of coin do I have? To get any credit, you must set up two equations with
two unknowns and solve the resulting system of equations algebraically.
8 quarters and 16 dimes
EXTRA CREDIT Consider the functions f (x) = x2 − 7x and g(x) = −4x2 + 10. There are
three values of x for which f (x) = g(x). One of them is x = 2. Find the other two. You
must find these algebraically, not by guessing and checking. (Hint: The fact that x = 2 is
a olution should be used at some point in finding the other two.)
x = −5, −1