MTH 112 Practice Test 4
Sections 7.3 - 7.6, 8.1, 8.2, 10.1
Write the partial fraction decomposition of the rational
expression.
x - 2
1)
(x - 4)(x - 3)
Graph the linear inequality.
10) -2x - 3y ≤ -6
y
10
5
Write the form of the partial fraction decomposition of the
rational expression. It is not necessary to solve for the
constants.
5x - 4
2)
2
x + 10x + 21
-10
-5
5
10
x
5
10
x
-5
Write the partial fraction decomposition of the rational
expression.
6x2 + 16x + 23
3)
(x + 5)(x2 + 6)
-10
Graph the inequality.
11) (x + 1)2 + (y + 2)2 > 9
y
Solve the system.
4) y = x - 2
y2 = -8x
10
5
5) x2 + y2 = 85
x + y = -13
-10
-5
-5
6) 5x2 - 5y2 = -35
4x2 + 3y2 = 84
-10
7) 6x2 + y2 = 36
6x2 - y2 = 36
Graph the solution set of the system of inequalities or
indicate that the system has no solution.
12) x2 + y 2 ≤ 49
8) xy = 28
x2 + y2 = 65
x + y > 1
y
10
9) xy = 4
x + y = 4
5
-10
-5
5
-5
-10
1
10
x
Graph the system of inequalities, and find the coordinates
of the vertices.
13) 2x + y ≤ 4
x - 1 ≥ 0
Solve the problem.
16) A steel company produces two types of
machine dies, part A and part B. The company
makes a $3.00 profit on each part A that it
produces and a $5.00 profit on each part B that
it produces. Let x = the number of part A
produced in a week and y = the number of
part B produced in a week. Write the objective
function that describes the total weekly profit.
A) z = 5x + 3y
B) z = 3x + 5y
C) z =3(x - 5) + 5(y - 3)
D) z = 8(x + y)
y
10
5
-10
-5
5
10
x
-5
17) A steel company produces two types of
machine dies, part A and part B and is bound
by the following constraints:
· Part A requires 1 hour of casting time and 10
hours of firing time.
· Part B requires 4 hours of casting time and 3
hours of firing time.
· The maximum number of hours per week
available for casting and firing are 100 and 70,
respectively.
· The cost to the company is $0.75 per part A
and $3.00 per part B. Total weekly costs cannot
exceed $45.00.
Let x = the number of part A produced in a
week and y = the number of part B produced
in a week. Write a system of three inequalities
that describes these constraints.
-10
14) 3x - 2y ≥ -6
x - 1 < 0
y
10
5
-10
-5
5
10
x
-5
-10
18) Mrs. White wants to crochet hats and afghans
for a church fundraising bazaar. She needs 6
hours to make a hat and 2 hours to make an
afghan, and she has no more than 34 hours
available. She has material for no more than 11
items, and she wants to make at least two
afghans. Let x = the number of hats she makes
and y = the number of afghans she makes.
Write a system of inequalities that describes
these constraints.
Graph the solution set of the system of inequalities or
indicate that the system has no solution.
15) y > x2
3x + 6y ≤ 18
y
10
5
-10
-5
5
10
x
-5
-10
2
An objective function and a system of linear inequalities
representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value
of the objective function at each corner of the graphed
region. Use these values to determine the maximum value
of the objective function and the values of x and y for
which the maximum occurs.
21) Objective Function
z = 12x + 5y
Constraints
0 ≤ x ≤ 10
0 ≤ y ≤ 5
3x + 2y ≥ 6
Find the maximum or minimum value of the given
objective function of a linear programming problem. The
figure illustrates the graph of feasible points.
19) Objective Function: z = -x - 8y
Find maximum.
Solve the problem.
20) The Acme Class Ring Company designs and
sells two types of rings: the VIP and the SST.
They can produce up to 24 rings each day
using up to 60 total man-hours of labor. It
takes 3 man-hours to make one VIP ring and 2
man-hours to make one SST ring. How many
of each type of ring should be made daily to
maximize the companyʹs profit, if the profit on
a VIP ring is $60 and on an SST ring is $20?
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Let x = # of VIPs and y = # of SSTs.
y
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 x
a)Write an inequality for man hours.
.Write the augmented matrix for the system.
22) 7x + 3y = 57
7y = 35
b)Write an inequality for # of rings produced.
c)Objective function
23) 2x + 3z = 2
2y + 7z = -4
6x + 7y + 2z = 55
d)Graph
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
y
Write the system of equations that corresponds to the
augmented matrix.
24) 7 -7 5
14 15 -3
25)
6 1 0 2
1 0 5 -2
- 6 7 4 2
Solve the system of equations using your graphing
calculator. If there is no solution or infinitely many
solutions, write that for your answer.
26) x + y + z = 1
x - y + 4z = 17
5x + y + z = -3
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 x
e) Vertices ∣ Profit
27) 5x - y + z = 8
7x + y + z = 6
f) # of VIPs____________________
# of SSTs____________________
3
28) -4x - y - 3z = -22
-4x + 6z = 16
9y + z = 22
29)
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
The nth term of a sequence is given. Find the first 4 terms.
30) a n = 7n - 5
31) a n = 1 n-1
9
32) a n = 2(n + 1)!
Find the indicated term of the sequence.
33) a n = 4n - 1; a15
34) a n = (4n - 5)2 ; a9
Evaluate the sum.
4
1
35) ∑
4k
k=1
5
36)
∑
k=2
1
2k(k + 1)
Find the indicated sum.
4
37) ∑ 2 i
i = 1
4
Answer Key
Testname: 112PRACTICE TEST 4
1)
2
-1
+ x - 4 x - 3
2)
A
B
+ x + 7 x + 3
3)
3
3x + 1
+ x + 5 x2 + 6
4) {(-2, -4)}
5) (-6, -7), (-7, -6)
6) {(3, 4), (-3, 4), (3, -4), (-3, -4)}
7) {( 6, 0), (- 6, 0)}
8) {(7, 4), (-7, -4), (4, 7), (-4, -7)}
9) (2, 2)
10)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
y
10
5
-10
-5
-5
-10
11)
5
Answer Key
Testname: 112PRACTICE TEST 4
y
10
5
-10
-5
5
10
x
-5
-10
12)
13)
y
4
(1, 2)
4x
-4
-4
14)
y
5
(1, 9/2)
5x
-5
-5
15)
y
10
5
-10
-5
5
10
x
-5
-10
16) B
6
Answer Key
Testname: 112PRACTICE TEST 4
17)
x + 4y ≤ 100
10x + 3y ≤ 70
0.75x + 3y ≤ 45
18) 6x + 2y ≤ 34
x + y ≤ 11
y ≥ 2
19) maximum: -20
20) 20 VIP and 0 SST
21) Maximum: 145; at (10, 5)
22) 7 3 57
0 7 35
203 2
23) 0 2 7 -4
6 7 2 55
24) 7x - 7y = 5
14x + 15y = -3
6x + y
= 2
25)
x
+ 5z = -2
-6x + 7y + 4z = 2
26) (-1, -2, 4)
27) infinite solutions
28) {(2, 2, 4)}
29) ∅
30) 2, 9, 16, 23
1
1 1
31) 1, , , 9 81 729
32) 4, 12, 48, 240
33) 59
34) 961
25
35)
48
36)
1
6
37) 30
7