Math 48 Review Practice Problems
The actual Math 48 final may include, but is not limited to, the problems listed in this
handout. Study your notes, past homework assignments, quizzes, and tests. Also, see a tutor
and/or your professor if you need any additional assistance.
NO NOTES OR GRAPHING CALCULATORS ARE ALLOWED ON THE FINAL
EXAM.
_______________________________________________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
1) 6 - 13 · -8 ÷ (-4)
A) -224
B) 224
C) -14
D) 14
E) None of a-d.
2)
1)
2 + (-3)2 + 5 · 2 2
5 2 · (4 - 3)
2)
A) 2
31
B)
25
C)
24
17
D) 0
E) None of a-d.
Simplify the expression by combining like terms, if possible.
3) -7(4x + 3y) + 6(4x + 8y)
A) -4x + 3y + 8
B) -4x + 27y
C) -49xy
D) -3x + 27y
E) None of a-d.
4) 3x - 10(x + 10)
A) -7x - 10
B) 13x + 10
C) -7x - 100
D) -7x + 100
E) None of a-d.
3)
4)
1
Solve the equation.
5) 4(3x - 1) = 16
17
A)
12
5)
B) 1
5
C)
3
D)
5
4
E) None of a-d.
6) 1.2x - 4.6 = 0.4x + 1.64
A) {7.7}
B) {7.8}
C) {7.02}
D) {-0.128}
E) None of a-d.
7)
6)
1
1
(x - 9) + (x + 3) = x - 5
3
3
7)
A) 9
B) 21
C) 3
D) 27
E) None of a-d.
Solve the formula for the stated variable.
8) P = 2L + 2W; solve for L
A) L = P - 2W
B) L = P - W
P - 2W
C) L =
2
D) L =
8)
P-W
2
E) None of a-d.
Translate the phrase to an algebraic expression. Let x represent the unknown number.
9) 8 less than 9 times a number
A) 9 - 8x
B) 9x - 8
C) 8x - 9
D) 8 - 9x
E) None of a-d.
10) The product of -36 and the sum of a number and 6.
A) -36(x + 6)
B) -36x + 6
C) -36 + 6x
D) -216x
E) None of a-d.
9)
10)
2
Translate the statement into an equation. Let x represent the unknown number. DO NOT SOLVE.
11) Twelve more than the product of three and x yields forty-eight.
A) 3x + 12 = 48
B) 48x + 3 = 12
C) 12x + 48 = 3
D) 3x + 48 = 12
E) None of a-d.
Find the unknown in each percent question.
12) 10% of 400 is what number?
A) 400
B) 40
C) 4
D) 0.4
E) None of a-d.
11)
12)
13) 0.06 is what percent of 8?
A) 0.75%
B) 0.0075%
C) 13,333%
D) 0.075%
E) None of a-d.
13)
Solve the problem.
14) Alex has saved $336 at the bank. He wants to accumulate $1750 for a trip to soccer camp. What
percent of his goal has been reached?
A) 50%
B) 5%
C) 19.2%
D) 0.192%
E) None of a-d.
Solve the equation. State whether the equation is a contradiction, an identity, or a conditional equation.
15) -6x + 7 + 4x = -2x + 12
A) all real numbers; identity
B) {5}; conditional equation
C) {-7}; conditional equation
D) ∅ or { }; contradiction
E) None of a-d.
3
14)
15)
Find the equation of the line described. Write the equation in slope-intercept form, if possible.
16) x-intercept: 9; y-intercept: 20
9
A) y = x-9
20
B) y = -
9
x+9
20
C) y = -
20
x + 20
9
D) y = -
20
x - 20
9
16)
E) None of a-d.
Find the missing coefficient so that the lines are perpendicular.
17) x - 4y = 5 and y = Bx + 24 ;
A) B = - 4
1
B) B = 4
17)
C) B = 4
1
D) B =
4
E) None of a-d.
Find the equation of the line that has the given properties. Write the equation in slope-intercept form, if possible.
18) Contains (5, 6); parallel to 2x - 5y = -7
18)
5
A) y = - x + 4
2
B) y =
2
x+4
5
C) y =
5
x+4
2
D) y = -
2
x+8
5
E) None of a-d.
Solve the system of equations using substitution.
1
1
x+ y=0
19) 4
4
19)
x - y = -4
A) (-2, 2)
B) no solution
C) (-3, 3)
D) (2, 3)
E) None of a-d.
4
Solve the system of equations using elimination.
4
4x - y = -20
3
20)
31
5
2x - y = 2
2
20)
A) (-4, 3)
B) (-3, 2)
C) no solution
D) (4, 2)
E) None of a-d.
Solve the system of equations using substitution. State whether the system is inconsistent, or consistent and dependent.
21) -5x - 15y = -8
21)
4x + 12y = 0
A) infinitely many solutions; inconsistent
B) no solution; consistent and dependent
C) no solution; inconsistent
D) infinitely many solutions; consistent and dependent
E) None of a-d.
Solve the problem.
22) During a hurricane evacuation from the east coast of Georgia, a family traveled 200 miles west. For
part of the trip, they averaged 60 mph, but as the congestion got bad, they had to slow to 10 mph. If
the total time of travel was 6 hours, how many miles did they drive at the reduced speed?
A) 37 miles
B) 27 miles
C) 42 miles
D) 32 miles
E) None of a-d.
22)
23) The three angles in a triangle always add up to 180°. If one angle in a triangle is 96° and the second
is 3 times the third, what are the three angles?
A) 96°, 62°, 22°
B) 96°, 63°, 21°
C) 96°, 64°, 20°
D) 96°, 61°, 23°
E) None of a-d.
23)
24) There were 630 people at a play. The admission price was $3 for adults and $1 for children. The
admission receipts were $1230. How many adults and how many children attended?
A) 165 adults and 465 children
B) 307 adults and 323 children
C) 330 adults and 300 children
D) 300 adults and 330 children
E) None of a-d.
24)
5
25) A chemist needs 50 milliliters of a 68% solution but has only 62% and 72% solutions available. Find
how many milliliters of each that should be mixed to get the desired solution.
A) 30 mL of 62%; 20 mL of 72%
B) 20 mL of 62%; 30 mL of 72%
C) 23 mL of 62%; 30 mL of 72%
D) 23 mL of 62%; 27 mL of 72%
E) None of a-d.
Evaluate the expression.
2 2
1
2
2
26) + · -4 ·
+
+
5 5
10 15
5
A)
14
75
B)
8
25
C) D)
25)
26)
54
25
14
15
E) None of a-d.
Simplify the expression by combining like terms, if possible.
2
1
27) - (z - 15) z
5
10
A)
27)
1
z+6
2
B) -
1
z+6
2
C)
3
z + 15
10
D)
1
z-6
2
E) None of a-d.
Evaluate the expression using the given value of the variables.
13x - 15y
28)
for x = 7, y = 3
x+6
A)
22
3
B)
46
9
C)
66
13
D)
46
13
E) None of a-d.
6
28)
Solve the equation. Check your solution.
2
1
3 1
29) (4x - ) - =
3
6
4 4
A)
1
12
B)
9
32
C)
7
16
D)
5
12
29)
E) None of a-d.
Find the unknown in each percent question.
30) 70% of what number is 65? Round to the nearest hundredths place.
A) 9.29
B) 92.86
C) 45.5
D) 928.6
E) None of a-d.
Solve the formula for the stated variable.
9
31) F = C + 32; solve for C
5
A) C =
9
(F - 32)
5
B) C =
5
F - 32
C) C =
F - 32
9
D) C =
5
(F - 32)
9
30)
31)
E) None of a-d.
Solve the problem.
32) When Milo got promoted at work, he received a 25% pay raise. He now earns $82,500 per year.
What was his annual salary before his raise?
A) $82,500
B) $16,500
C) $66,000
D) $20,625
E) None of a-d.
7
32)
Use the slope and y-intercept to graph the equation.
33) 6x + 3y = 18
33)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
E) None of a-d.
8
Find the equation of the line that has the given properties. Write the equation in slope-intercept form, if possible.
34) Contains (-10, 5); parallel to 2x - 5y = -7
34)
5
A) y = - x + 9
2
B) y = -
2
x+1
5
C) y =
5
x+9
2
D) y =
2
x+9
5
E) None of a-d.
Solve the system of equations using substitution.
35) x + 3y = -18
-6x + 2y = 28
A) no solution
B) (6, -3)
C) (-6, -4)
D) (-7, -3)
E) None of a-d.
35)
Find the equation of the line that has the given properties. Write the equation in slope-intercept form, if possible.
3
36) y-intercept = ; perpendicular to the line 2x - y = 3
36)
2
A) y = 1
B) y = -
1
3
x+
2
2
C) y = -
1
x+3
2
D) y =
1
3
x+
2
2
E) None of a-d.
9
Solve the system of equations by graphing.
37) 3x + y = -10
2x + y = -7
37)
y
10
5
-10
-5
5
10
x
-5
-10
A) (-1, -3)
B) (-3, -1)
C) no solution
D) (3, 1)
E) None of a-d.
Solve the system of equations using elimination.
38) 2x + 5y = -3
5x - 4y = -24
A) (-4, 1)
B) (-4, -1)
C) (4, 1)
D) (4, -1)
E) None of a-d.
38)
x y
+ =1
3 6
39)
39)
x y
- =0
2 4
A)
3
,3
2
B) infinitely many solutions
3
C) 3,
2
D) no solution
E) None of a-d.
Decide whether the ordered pair is a solution of the system of equations.
40) 2x = 3 - y ; (-2, -1)
3x = 4 - 2y
A) Yes
B) No
10
40)
Without graphing, determine the number of solutions of the system of equations. State whether the system is consistent
or inconsistent. For a system that is consistent, state whether the equations are dependent or independent.
41) 4x + 2y = 108
41)
x = -5y
A) no solution; inconsistent
B) one solution; consistent; dependent
C) one solution; consistent; independent
D) infinitely many solutions; consistent; dependent
E) None of a-d.
y - 6x = 5
42)
42)
6y = 36x + 30
A) infinitely many solutions; consistent; independent
B) infinitely many solutions; consistent; dependent
C) no solutions; inconsistent
D) one solution; consistent; independent
E) None of a-d.
Find the equation of the line described. Write the equation in slope-intercept form, if possible.
5
9
43) 1,
and 2,
8
8
A) y = 2x -
11
8
B) y = 2x -
1
4
C) y =
1
11
x+
2
16
D) y =
1
1
x+
2
8
43)
E) None of a-d.
Solve the problem.
44) A college student earned $7900 during summer vacation working as a waiter in a popular
restaurant. The student invested part of the money at 10% and the rest at 7%. If the student
received a total of $670 in interest at the end of the year, how much was invested at 10%?
A) $3900
B) $4000
C) $1128
D) $3950
E) None of a-d.
45) Two angles are complementary. Twice one angle plus the other is 109°. Find the measure of each
angle.
A) 26°, 57°
B) 19°, 71°
C) 19°, 161°
D) 24°, 66°
E) None of a-d.
11
44)
45)
46) A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's
performance they have sold a total of 1320 tickets. Also, they have sold 4 times as many adult
tickets as children's tickets. How many adult tickets have they sold?
A) 1049
B) 1062
C) 1056
D) 1053
E) None of a-d.
46)
47) One angle of a triangle is 3 times as large as another. The measure of the third angle is 105° greater
than that of the smallest angle. Find the measure of each angle.
A) 20°, 60°, 100°
B) 15°, 45°, 120°
C) 25°, 75°, 80°
D) 15°, 45°, 105°
E) None of a-d.
47)
48) An airplane flies 440 miles with the wind and 330 against the wind in the same length of time. If the
speed of the wind is 20 mph, what is the speed of the airplane in still air?
A) 140 mph
B) 145 mph
C) 130 mph
D) 60 mph
E) None of a-d.
48)
49) A twin-engined aircraft can fly 1330 miles from city A to city B in 5 hours with the wind and make
the return trip in 7 hours against the wind. What is the speed of the wind?
A) 57 mph
B) 76 mph
C) 38 mph
D) 19 mph
E) None of a-d.
49)
50) The manager of a bulk foods establishment sells a trail mix for $9 per pound and premium cashews
for $15 per pound. The manager wishes to make a 36-pound trail mix-cashew mixture that will sell
for $14 per pound. How many pounds of each should be used?
A) 18 lb of trail mix
18 lb of cashews
B) 6 lb of trail mix
30 lb of cashews
C) 33 lb of trail mix
3 lb of cashews
D) 30 lb of trail mix
6 lb of cashews
E) None of a-d.
50)
12
Add the polynomials. Express your answer in standard form.
51) (10x2 - xy - y2 ) + (x2 + 6xy + 12y2 )
51)
A) 10x2 + 6xy + 12y2
B) 11x2 + 5xy + 11y2
C) 9x2 - 7xy - 13y2
D) 11x2 + 7xy + 13y2
E) None of a - d.
Simplify. Express your answer in standard form.
52) (3x2 - 7x + 4) - (x2 - 5x + 2) + (5x2 + 5)
52)
A) 7x2 - 2x + 7
B) -3x2 - 12x + 11
C) 7x2 + 2x + 7
D) 7x2 - 2x + 11
E) None of a - d.
Simplify the expression.
53) (-7x6 y5 )2
53)
A) 49x36y25
B) -14x12y10
C) -49x12y10
D) 49x12y10
E) None of a - d.
Multiply the monomials.
3
54) (-4x)3 x4
8
54)
A) - 24x12
9
B) - x5
2
C) - 24x7
3
D) - x7
2
E) None of a - d.
55) (3x + 8)(x - 11)
A) x2 - 88x - 25
55)
B) x2 - 25x - 26
C) 3x2 - 25x - 88
D) 3x2 - 26x - 88
E) None of a - d.
13
Find the product.
56) (5p + 9)(5p - 9)
A) 25p2 - 81
56)
B) 25p2 - 90p - 81
C) 25p2 + 90p - 81
D) p2 - 81
E) None of a - d.
57) (6x - 11y)(3x - 6y)
A) 18x2 - 36xy + 66y2
57)
B) 18x2 - 69xy - 69y2
C) 18x2 - 69xy + 66y2
D) 18x2 - 33xy + 66y2
E) None of a - d.
58) (6x - 1)(x2 - 2x + 1)
A) 6x3 - 13x2 + 8x - 1
58)
B) 6x3 - 12x2 + 6x + 1
C) 6x3 - 11x2 + 4x - 1
D) 6x3 + 13x2 - 8x + 1
E) None of a - d.
Simplify. Write the answer with positive exponents. All variables are nonzero.
59) (-5x6 y-7 )(2x-1 y)
A) -10x5 y8
-10x7
B)
y8
C)
-3x5
y6
D)
-10x5
y6
E) None of a - d.
14
59)
60)
-2ym 3 n
-9ym 6 n
A)
-7y2 n 2
m3
B)
-7
m3
C)
D)
60)
1
7m 3
2
9m 3
E) None of a - d.
Divide and simplify.
9x6 - 24x4 + 9x2
61)
3x4
A) 3x - 8 +
3
x
B) 3x2 - 8 +
3
x2
C) 3x2 - 8 +
3
x
D) 3x - 8 +
61)
3
x2
E) None of a - d.
Find the quotient using long division.
x3 + 5x2 - 9x - 8
62)
x-2
A) x2 - 7x + 5 -
2
x-2
B) x2 - x - 10 +
12
x-2
C) x2 - 7x - 5 +
2
x-2
D) x2 + 7x + 5 +
2
x-2
62)
E) None of a - d.
Write the number in decimal notation.
63) 1.783 × 10-3
63)
A) 0.00001783
B) 178,300
C) 0.001783
D) 0.0001783
E) None of a - d.
15
Perform the indicated operation. Express the answer in scientific notation.
12.24 × 10-3
64)
3.4 × 10-6
64)
A) 7.2 × 103
B) 3.6 × 10-9
C) 7.2 × 10-9
D) 3.6 × 103
E) None of a - d.
Factor completely. If the polynomial cannot be factored, say it is prime.
65) 4x2 - 9x + 5
65)
A) (2x - 5)(2x - 1)
B) (4x - 5)(x - 1)
C) (4x - 1)(x - 5)
D) prime
E) None of a - d.
66) 16y2 - 8xy +x2
A) (x - 4y) 2
66)
B) (x - 4y)(x + 4y)
C) prime
D) (x + 4y) 2
E) None of a - d.
67) a 2 - 2ab - 24b2
A) (a - 4b)(a + b)
B) (a - 4b)(a + 6b)
C) prime
D) (a + 4b)(a - 6b)
E) None of a - d.
67)
68) 16x2 - 49y2
68)
A) (4x + 7y) 2
B) prime
C) (4x + 7y)(4x - 7y)
D) (4x - 7y) 2
E) None of a - d.
Factor completely.
69) 2y3 - 6y2 - 20y
69)
A) 2y(y - 2)(y + 5)
B) (2y2 + 4y)(y - 5)
C) 2y(y + 2)(y - 5)
D) (y - 2)(2y2 + 10)
E) None of a - d.
16
70) -6n 3 + 6n 2 + 12n
A) 6n(n + 2)(n - 1)
B) -6n(n - 2)(n + 1)
C) 6n(n - 2)(n + 1)
D) -6n(n + 2)(n - 1)
E) None of a - d.
70)
71) 12x3 + 22x2 - 20x
A) 2(3x2 - 2)(2x + 5)
71)
B) x(3x - 2)(4x + 10)
C) 2x(3x - 2)(2x + 5)
D) x(6x - 4)(2x + 5)
E) None of a - d.
72) 49a 3 - 4a
72)
A) a(49a + 1)(a - 4)
B) (7a 2 + 2)(7a - 2)
C) a(7a - 2)2
D) a(7a + 2)(7a - 2)
E) None of a - d.
73) 25a 3 - 81a
73)
A) a(5a + 9)(5a - 9)
B) a(5a - 9)2
C) a(25a + 1)(a - 81)
D) (5a 2 + 9)(5a - 9)
E) None of a - d.
74) x3 - 9x + 2x2 - 18
A) (x - 3)2 (x + 2)
74)
B) (x + 3)(x - 3)(x + 2)
C) (x2 - 9)(x + 2)
D) prime
E) None of a - d.
17
Solve the equation by factoring.
75) 2x2 - 5x - 7 = 0
A)
2
, -1
7
B)
7
, -1
2
C)
2
,1
7
D)
2
,0
7
75)
E) None of a - d.
76) x2 - 8x = -7
A) {-7, 7}
B) {-1, -7}
C) {7, 1}
D) {-1, 7}
E) None of a - d.
76)
77) (x + 8)(x + 1) = 30
A) {1, 8}
B) {-11, 2}
C) {-2, 11}
D) {-8, -1}
E) None of a - d.
77)
78) x3 + 6x2 - x - 6 = 0
A) {-6, 6}
B) {1, -6, 6}
C) {36}
D) {-1, 1, -6}
E) None of a - d.
78)
Solve the problem.
79) Use the given area to find the missing sides of the rectangle.
A = 12
x
2x + 2
A) 2, 4
B) 6, 4
C) 2, 6
D) -3, -4
E) None of a - d.
18
79)
80) Use the Pythagorean Theorem to find the lengths of the sides of the triangle.
10
2x - 2
2x
A) 12, 16
B) 4, 6
C) 6, 8
D) 6, 12
E) None of a - d.
19
80)
Answer Key
Testname: MATH 48 FINAL EXAM STUDY GUIDE
1) D
2) B
3) B
4) C
5) C
6) B
7) A
8) C
9) B
10) A
11) A
12) B
13) A
14) C
15) D
16) C
17) A
18) B
19) A
20) A
21) C
22) D
23) B
24) D
25) B
26) A
27) B
28) D
29) D
30) B
31) D
32) C
33) D
34) D
35) C
36) B
37) B
38) A
39) A
40) B
41) C
42) B
43) D
44) A
45) B
46) C
47) B
48) A
49) C
50) B
51) B
52) A
53) D
54) C
55) C
56) A
57) C
58) A
59) D
60) D
61) B
62) D
63) C
64) D
65) D
66) A
67) D
68) C
69) C
70) B
71) C
72) D
73) A
74) B
75) B
76) C
77) B
78) D
79) C
80) C
20