MATD 0390 Intermediate Algegra
Review for Test 2
Test 2 covers all cumulative material, includin new sections 2.4-2.7,3.1,3.2,3.6,4.GR,4.1-4.8
Bring a non-graphing calculator and something to write with and erase with. Be prepared to
show your work on all test problems in order to recieve full or partial credit.
Graph the linear function.
1)
4)
H(x) = -1
Find the zero of the linear function.
2)
h(t) = - 1 t + 9
6
The cost of renting a certain type of
car is $34 per day plus $0.09 per mile.
A linear function that expresses the
cost C of renting a car for one day as a
function of the number of miles
driven x is C(x) = 0.09x + 34. What is
the implied domain of this linear
function?
Solve.
A company has just purchased a new
computer for $9800. The company
chooses to depreciate the computer
using the straight-line method over
10 years. A linear function that
expresses the book value V of the
computer as a function of its age x is
V(x) = -980x + 9800. Graph the linear
function V.
Find the intersection of the sets.
5)
{-5, -2, 3, 6} ∩ {-4, 1, 5, 8}
Solve the compound inequality. Express the solution
using interval notation. Graph the solution set.
V
6)
-6x > -24 and x + 6 > 7
7)
- 1 ≤ 3
7x - 1 1
< 9
3
10000
-2
8000
Book Value ($)
3)
6000
8)
-1
x > 4 or x < 4
4000
2000
Solve the absolute value equation.
2
4
6
8
10
9)
12 x
|4x + 8| + 9 = 11
Time (years)
10) |x -
A‐1
6| = |2 - x|
0
1
2
Solve.
Graph the system of linear inequalities.
11) When the temperature stays the same,
17)
the volume of a gas is inversely
proportional to the pressure of the
gas. If a balloon is filled with 280
cubic inches of a gas at a pressure of
14 pounds per square inch, find the
new pressure of the gas if the volume
is decreased to 70 cubic inches.
y ≤ 4x + 4
y > - 2x
Graph the system of linear inequalities. Tell whether the
graph is bounded or unbounded, and label the corner
points.
18)
2x + 3y ≥ 6
x - y ≤ 3
y ≤ 2
Solve the system of equations by graphing. You must use
this method
2x + y = 2
12) 2x + y = 4
Simplify the expression. All exponents should be positive
integers.
Solve the system of equations using either substitution or
elimination.
13)
19)
x + 4y = 2
-3x + 5y = -6
(3y5z-2)2
-1
(4yz-3)
-1
(6x4y-2)
2xy4 2
20)
· -2
(3x-2y)
3x2y-4
y = 4x + 4
14)
2y + 10x = 26
Solve the problem.
Determine whether the algebraic expression is a
polynomial (Yes or No). If it is a polynomial, determine
the degree and state if it is a monomial, binomial, or
trinomial. If it is a polynomial with more than 3 terms,
identify the expression as polynomial.
15) Jarod is having a problem with
rabbits getting into his vegetable
garden, so he decides to fence it in.
The length of the garden is 12 feet
more than 2 times the width. He
needs 72 feet of fencing to do the job.
Find the length and width of the
garden.
21) -11ab6c5d
Simplify the polynomial by adding or subtracting, as
indicated. Express your answer as a single polynomial in
standard form.
22) (8x6 + 5x4 - 8x) + (3x6 + 8x4 - 8x)
16) Julie and Eric row their boat (at a
constant speed) 24 miles downstream
for 4 hours, helped by the current.
Rowing at the same rate, the trip back
against the current takes 6 hours. Find
the rate of the current.
23) 6x -
A‐2
(15 - 3x)
Solve the problem.
Solve the problem.
24) A projectile is fired upward from the
27) Write a polynomial that represents
ground with an initial velocity of 400
feet per second. Neglecting air
resistance, the height of the projectile
at any time t can be described by the
polynomial function P(t) = -16t2 +
400t. Find the height of the projectile
at t = 5 seconds.
the area of the shaded region.
9x + 12
9x - 12
For the given functions f and g, find the requested
function.
25) f(x) = 2x2 - 2; g(x) = x + 7
Find (f - g)(-3).
The graph of two functions, f and g, is shown below. Use
the graph to find the value.
Find the product of the polynomials.
y
28) (x - 2)(x2 + 2x + 4)
10
f
Find the special product.
5
29)
-5
5
x + 1 x - 1
2
2
10 x
g
30) (9x + 8)2
26) A)(f + g)(8)
Simplify the expression.
B)(f - g)(8)
C)(g - f)(0)
31) (x +
8)(x - 8)(2x + 4)
For the given functions f and g, find (f · g)(x).
32) f(x) = x + 10, g(x) = x2 + 7
Find the requested function.
33) If f(x) = x2 + 1x + 3, find f(x + h) - f(x).
Divide and simplify.
34)
-15x6 + 9x5 - 21x4
-3x5
Divide using long division.
35)
A‐3
15x3 + 11x2 + 13x - 3
5x - 3
Provide an appropriate response.
51) x3 - 125
36) For g(x) = -5x - 4 and f(x) = 2x2 + 2x
+ 3, find f (5).
g
Solve the equation.
37) Factor out the greatest common
Find the domain of the function.
52) q(5q +
factor: 18a8b9 - 63a5b6 - 81a2b4
53) f(x) = Factor completely, or state that the polynomial is prime.
13) = 6
4x - 7
x2 - 64
Find the values of x such that the given function has the
stated value.
38) 12x3 - 768x
54) f(x) = x2 + 7x + 10; f(x) = 10
Factor the polynomial function.
Solve.
39) H(x) = 20x2 + 27x + 9
55) A certain rectangleʹs length is 6
feet
longer than its width. If the area of the
rectangle is 135 square feet, find its
dimensions.
Factor.
40) 10wx - 10wy - 10wz
41) x3 - 2x2 + 9x - 18
42) x2 + 5x - 50
43) 63 - 2x - x2
44) 24z4 + 20z2 - 24
45) 16x4 - 24x3 + 9x2
46) 15x2 - 38xy + 24y2
47) x2 - x - 48
48)
z2 + 12z + 36
49) x2y
2 - 9
50) 25 - (x + 5y)2
A‐4
Answer Key
Testname: 0390REVIEW2SULLIVAN
1)
6
y
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
6 x
5
-2
-3
-4
-5
-6
2) 54
3)
V
10000
Book Value ($)
8000
6000
4000
2000
2
4
6
8
10
12 x
Time (years)
4) [0, ∞)
5) ∅
6) (1, 4)
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
2 4
7) - , 7 7
-2
-1
0
1
2
8) (-∞, 4) ∪ (4, ∞)
-2
0
2
4
6
8
10
12
3
5
9) - , - 2
2
10) 4
11) 56 pounds per square inch
12) ∅
A‐5
Answer Key
Testname: 0390REVIEW2SULLIVAN
13) (2, 0)
14) (1, 8)
15) length: 28 feet; width: 8 feet
16) 1 mph
17)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
-6
-8
-10
18)
19)
20)
The graph is bounded.
36y11
z7
2y20
3x10
21) Yes; degree 13; monomial
22) 11x6 + 13x4 - 16x
23) 9x - 15
24) 1600 ft
25) 12
26) A)6 B)2 C)-4
27) 79x 2 - 144
28) x3 - 8
1
29) x2 - 4
30) 81x2 + 144x + 64
31) 2x3 + 4x2 - 128x - 256
32) x3 + 10x2 + 7x + 70
A‐6
Answer Key
Testname: 0390REVIEW2SULLIVAN
33) 2xh + h 2 + 1h
7
34) 5x - 3 + x
35) 3x2 + 4x + 5 + 36) - 12
5x - 3
63
29
37) 9a 2 b4 (2a 6 b5 - 7a 3 b2 - 9)
38) 12x(x + 8)(x - 8)
39) H(x) = (4x + 3)(5x + 3)
40) 2w(5x - 5y - 5z)
41) (x2 + 9)(x - 2)
42) (x + 10)(x - 5)
43) (-x - 9)(x - 7)
44) 4(3z 2 - 2)(2z 2 + 3)
45) x2 (4x - 3)(4x - 3)
46) (5x - 6y)(3x - 4y)
47) Prime
48) (z + 6)2
49) (xy + 3)(xy - 3)
50) (5 + x + 5y)(5 - x - 5y)
51) (x - 5)(x2 + 5x + 25)
52) -3, 2
5
53) {x|x ≠ 8, -8}
54) {0, -7}
55) 9 ft by 15 ft
A‐7