Download This is not a practice test and may not cover all topics. You should

Math 1221: Review for Final Exam
Fall 2013
This is not a practice test and may not cover all topics. You should review your tests and quizzes as
well as notes to properly prepare for the final exam.
Find the slope of the line.
1) y = 3x - 4
A) -3
B) 3
C) 0
D) 1
Find the slope of the line passing through the given pair of points.
2) (5, -5) and (-7, -3)
1
A) B) 4
C) - 6
6
Find an equation in slope-intercept form (where possible) for the line.
3) Through (2, -10) and (2, 10)
A) 1x - 10y = 0
B) x = 2
C) 1x + 10y = 0
4) Through (-4, 0) and (6, 3)
4
A) y = - x + 11
3
4
B) y = x + 11
3
3
6
x+
C) y =
10
5
Use the echelon method to solve the system of two equations in two unknowns.
5) -4x - 5y = 15
-2x + 2y = -6
A) (-1, -2)
B) (0, -2)
C) (0, -3)
Perform the indicated operation, where possible.
6) -1 0 - -1 6
62
31
0
-6
A)
B) -2 6
3 1
93
1
D)
6
D) y = -10
3
6
x+
D) y = 10
5
1)
2)
3)
4)
5)
D) No solution
6)
C)
0 6
-3 -1
D) -2
Use the indicated row operation to change the matrix.
1
1
7) Replace R2 by R1 + R2 .
2
2
7)
20 4
-2 2 12
A) 2 0 4
0 2 16
B) 2 0 4
008
C)
204
-1 1 6
D) 2 0 4
018
The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these
products exist.
8) A is 4 × 3, and B is 4 × 3.
8)
A) 3 × 4; 4 × 3
B) 4 × 4; 3 × 3
C) AB does not exist; BA does not exist.
D) 4 × 3; 3 × 4
1
Find the matrix product, if possible.
9) -1 3 -2 0
42
-1 1
A) -1 3
-10 2
9)
B) 3 -1
2 -10
C)
Find the inverse, if it exists, for the matrix.
10) 2 6
-1 -2
A)
B)
1-3
1
1
1
2
-1
2
-1-3
2 -6
-3 -1
D)
20
-4 2
10)
C)
-1-3
1
1
2
D)
-1 3
1
1
2
Graph the linear inequality.
11) 3x + y
11)
-6
A)
B)
C)
D)
2
Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective function.
12) z = 9x - 12y
12)
A) Maximum of 45; minimum of 0
C) Maximum of -48.75; minimum of -72
B) Maximum of -72; minimum of 0
D) Maximum of 45; minimum of -72
Express the given situation as a linear inequality.
13) Marcie Kohl spends 5 hr building a hutch and 7 hr building a display case. She works no more than
42 hr per week. Let x be the number of hutches built and y be the number of display cases.
A) 42(x + y) 12
B) 12(x + y) 42
C) x + y 42
D) 5x + 7y 42
Decide whether the following is a statement or is not a statement.
14) Not all flowers are roses.
A) Statement
B) Not a statement
Write a negation for the statement.
15) Charlie plays football.
A) Charlie plays basketball.
C) Not Charlie plays football.
B) Charlie does not play football.
D) Charlie does not like football.
Translate the symbolic compound statement into words.
16) Let p represent the statement "Students are males" and let q represent the statement "Teachers are
males."
~(p ~q)
A) Students are not males and teachers are not males.
B) It is not the case that students are males and teachers are not males.
C) It is not the case that students are males or teachers are not males.
D) Students are not males or teachers are not males.
13)
14)
15)
16)
Let p represent a true statement, and let q and r represent false statements. Find the truth value of the given compound
statement.
17) ~(q ~r)
17)
A) True
B) False
Determine whether the statement is true or false.
18) If q is true, then (p q) q is true.
A) True
B) False
3
18)
Tell whether the statement is true or false.
19) 8
{16, 24, 32, 40, 48}
A) True
B) False
Insert " " or " " in the blank to make the statement true.
20) {0, 10}
{ 8, 10}
A)
B)
21) {e, d, j, h}
A)
{e, d, j, h, m}
19)
20)
21)
B)
Find the number of subsets of the set.
22) {11, 12, 13}
A) 3
B) 8
C) 6
D) 7
22)
Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of the indicated
set, using set braces.
23) B C
23)
A) {q, s, y, z, v, w, x, y, z}
B) {q, s, v, w, x, y, z}
C) {y, z}
D) {q, s, v, x, y, z}
Shade the Venn diagram to represent the set.
24) C' (A B)
24)
A)
B)
C)
D)
Use the union rule to answer the question.
25) If n(B) = 24, n(A B) = 5, and n(A
A) 18
B) 23
B) = 42; what is n(A)?
C) 25
4
D) 21
25)
Write the sample space for the given experiment.
26) A box contains 10 red cards numbered 1 through 10. One card is drawn at random and its number
is recorded.
A) {10}
B) {1, 10}
C) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
D) {100}
Find the probability of the given event.
27) A single fair die is rolled. The number on the die is greater than 2.
1
2
5
A)
B)
C)
6
3
6
1
D)
3
Find the probability.
28) A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. What is the probability that a
randomly selected marble is not blue?
7
10
3
A)
B)
C) 7
D)
10
7
10
Find the odds.
29) Find the odds in favor of drawing an even number when a card is drawn at random from the cards
shown below.
A) 2 to 5
B) 5 to 2
C) 3 to 2
D) 504
Solve the problem.
32) How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not
allowed?
A) 2520 five-digit numbers
B) 120 five-digit numbers
C) 119 five-digit numbers
D) 16,807 five-digit numbers
Evaluate the combination.
33) C(9, 3)
A) 84
B) 252
C) 1440
Decide whether the situation involves permutations or combinations.
34) An arrangement of 9 people for a picture.
A) Permutation
B) Combination
35) A blend of 2 spices taken from 8 spices on a spice rack.
A) Permutation
B) Combination
5
27)
28)
29)
D) 2 to 3
Solve the problem.
30) If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a double.
1
1
1
1
A)
B)
C)
D)
3
5
6
4
Evaluate the permutation. Round to three decimal places when appropriate.
31) P(9, 2)
A) 9
B) 72
C) 1
26)
D) 60,480
30)
31)
32)
33)
34)
35)
Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of the indicated
set, using set braces.
36) A B'
36)
A) {q, s, t, u, v, w, x, y}
B) {u, w}
C) {r, s, t, u, v, w, x, z}
D) {t, v, x}
37) (A B)'
A) {s, u, w}
C) {r, s, t, u, v, w, x, z}
37)
B) {r, t, v, x}
D) {t, v, x}
Find the mean for the list of numbers.
38) 73, 50, 73, 97, 50 (Round to the nearest tenth, if necessary.)
A) 85.8
B) 68.6
C) 69.1
D) 68.1
Find the median for the list of numbers.
39) 2, 9, 21, 26, 36, 50
A) 26
B) 23.5
C) 24.5
D) 21
Find the mode or modes.
40) 5, 9, 55, 3, 2, 8, 86, 1, 4, 16
A) 18.3
B) 9
C) 8
D) No mode
B) 35
C) 49
D) No mode
41) 20, 27, 46, 27, 49, 27, 49
A) 27
42) 87, 72, 32, 72, 29, 87
A) 87
B) 87, 72
Find the median for the list of numbers.
43) 9, 4, 27, 16, 21, 49, 36, 31
A) 27
B) 24
6
C) 63.2
D) No mode
C) 21
D) 24.5
38)
39)
40)
41)
42)
43)
Answer Key
Testname: 1221FEREVIEWS14
1) B
2) A
3) B
4) C
5) C
6) A
7) D
8) C
9) A
10) C
11) D
12) D
13) D
14) A
15) B
16) C
17) B
18) A
19) A
20) A
21) A
22) B
23) B
24) D
25) B
26) C
27) B
28) A
29) D
30) C
31) B
32) A
33) A
34) A
35) B
36) B
37) B
38) B
39) B
40) D
41) A
42) B
43) B
7