Math 73
Final Review
1.- Solve the following equations.
2
1
−2
(a)
−
=
x x−4
2x − 8
(b)
1
2
−2y
−
= 2
y−2 y−3
y − 5y + 6
2.- Solve the following by any method.
(a) (4x + 3)2 = 49
(b) −3x2 + 8x = 1
(c) 2x3 = 50x
3.- Solve the following equations and check the answers.
(a)
√
2x + 3 = 6 − x
(b)
√
x2 + 5x + 4 = x + 3
(c)
√
√
x+3+ x=3
4.- Set up a system of equations to solve the following problems.
(a) Nacho has a collection of pens and key-chains. The number of pens is 5 more than
twice the number of key-chains. If the total amount of items in his collection is 62. How
many of each does he have?
(b) Batman has $8, 000 to invest. He puts his money in two accounts. The first one
pays 5% interest annually and the second one pays 4% interest annually. If the total
interest from both accounts is $370, how much money did he invest in each account?
5.- For
g(x) =
x+2
and f (x) = −x2 + x + 3 find
x+1
(a) g[f (0)]
(b)
f [g(0)]
(d) f [f (0)]
(c)
f [g(−2)]
(e) g ◦ h(x)
(f) f ◦ g(x)
6.- Solve the following by graphing, elimination, and substitution.
(a)
2x + 4y = 6
3x − y = 2
(b) −3x + 2y = 2
2x + y = 8
7.- Graph the following inequalities.
2
(a) y ≥ − x + 2
5
(b)5x + 4y ≤ 20
8.- Graph the following functions, label the vertex and two other points.
(a) f (x) = x2 + 4x − 2
(b) f (x) = −3x2 − 6x + 7
9.- Using the following graph find the following.
f (x)
The Vertex
The y− Intercept
The x− Intercepts
x
The Domain and Range
10.- Graph the following circles. Label the center and the radius.
(a) x2 − 4x + y 2 + 2y = −1
(b) x2 + (y − 3)2 − 4 = 0
11.- Multiply/divide the following fractions
(a)
xy − y + 4x − 4
xy 2 + 2xy + y 2 + 2y
÷ 2
.
xy − 3y + 4x − 12 xy − 3y 2 + 2xy − 6y
(b)
3x4 + 24x
x5 + 4x3
·
.
3x6 − 48x2 4x4 − 8x3 + 16x2
12.- Solve the following inequalities and WSUIN.
7
(b) x − 5 + 22 ≤ 2
8
(a) |7x + 1| − 8 ≥ 3
2
(c) x + 1 ≤ 7
5
13.- Find the equation of the following lines.
y
y
x
y
x
x
14. Simplify the following exponents. Write all the answers with positive exponents
3 2 3
2
4
(a) (−3x y ) (2x y)
(x3 )2 · x6
(b) −4 7 0
x (x )
(c)
3 7 −3
xy
2
4
(4x2 y 3 )2
15.- Expand the following
(c) (3x − 4)(2x2 − 6x − 8)
(d) (x − 3)2 (x + 4)
16.- The path of a missile is given by h(t) = −16t2 + 64t + 80 where h represents the altitude
of the missile after t seconds.
(a) What is the maximum height reached by the missile?
(b) How long does it take to hit the ground?
17.- Graph the following functions and state their domain and range.
(a) y = 3x2 + 6x − 4
(b) y =
√
x+5
18.- Solve the following and WSUIN.
(a) (x2 − x − 12)(x − 5) > 0
(b)
(x + 3)(x − 4)
>0
x+1
19.- Simplify the following roots.
(a)
p
3
16x12 y 19 z 30
(b)
64
x3
2/3
20.- Solve the following absolute value problems.
3
3 (b) |5x − 6| = |8x + 10|
(a) + x = 2
5 10