Download Review for DSMA 0301 Final Exam

Review for DSMA 0301 Final Exam
Solve the equation.
1) 20x2 + 23x + 6 = 0
1)
Factor completely.
2) ax2 + 2ax - 5a - bx2 - 2bx + 5b
2)
Solve the system by the addition method.
3) 5x + y = 24
5x + y = 34
3)
7x + 4y = -17
-7x - 11y = 59
4)
4) Solve the system by the method of your choice.
5)
1
4x - y = 7
2
5)
28
3
2x - y = 5
5
Determine if the system is dependent, independent, or is inconsistent.
6)
6x - 7y = 8
24x - 28y = 40
Simplify the expression.
7) (-7)0 + (-14)0
7)
Simplify the expression.
13 r3 (r2 )3
8) 14 (r-3 )4
9) 6)
8)
4 -9 x-4 y 2
4 -6 x-7 y 4
9)
Write the following as an algebraic expression.
10) Subtract 4x - 3 from 9x + 10
10)
Find the domain and range.
11) {(2,-3), (-5,9), (3,-2), (-11,-9), (8,-1)}
11)
Simplify the algebraic expression.
12) -[-4x2 + (8x2 - 3)] + [ (-9x2 - (9 + 10x2 )) + 3x2 ]
12)
Factor completely, or state that the trinomial is prime.
13) 5x2 - 9xy - 18y2
13)
1
Simplify the exponential expression.
12x-3 y-2 z 3 -2
14) 3xy-2 z -3
14)
Perform the indicated operation and write the answer in scientific notation.
15) (5 × 10-5 )(1.1 × 10-5 )
16) 6 × 10-7
2 × 10-9
15)
16)
Evaluate the expression for the given values of the variables.
y - 6x
17) ;
x = -3 and y = 4
2x + xy
17)
Factor completely, or state that the trinomial is prime.
18) 7x2 - 26xy - 8y2
18)
Apply the appropriate special product formula(s) to find the product.
19) [7y + (4x + 1)][7y - (4x + 1)]
19)
20) (x - 4)(x + 4)(x2 + 16)
20)
21) (4a n - 7bn )(4a n + 7bn )
21)
Factor completely.
22) 4x3 + 500
22)
Find the solution set.
23) x3 + 5x2 - x - 5 = 0
23)
Find the solution set.
24) -6x - 2 = (3x + 1)2
24)
Find the solution set.
25) 4x3 + 5x2 = 36x + 45
25)
Factor.
26) x2 (x - 9) - (x - 9)
26)
2
Given the graph, determine the x- and y-intercepts.
27)
27)
y
5
-5
5
x
-5
Divide.
28) (-3x5 - x3 - 4x2 + 88x + 20) ÷ (x2 - 5)
28)
Find the product using special product formula(s).
29) (1 + x3 )(1 - x3 )
29)
Factor completely.
30) (x - 10)2 - 36
30)
Divide.
-16y3 - 48y2 + 7y
8y
31)
8y4 + 12y3 - 2y
2y2 + y
32)
33) 3x3 + 20x2 + 12x = 0
33)
31) Divide.
32) Solve.
Factor completely.
34) 8p2 q2 - 12pq3 + 40p4 q5
34)
Solve the equation.
7x2 41x 10
- + = 0
35) 33
33
11
35)
36) 8x + 7(-3x - 5) = -46 - 2x
36)
37) The length of a garden is 6 feet greater than its width. If the area of the garden is 112 square
feet, find its dimensions.
37)
Solve.
3
38) A flagpole is supported by a wire fastened 45 feet from its base. The wire is 15 feet longer than
the height it reaches on the flagpole. Find the length of the wire.
38)
39) An object is dropped from the top of a 144-foot building. The height h of the object after t
seconds is given by h(t) = -16t2 + 144. How long will it take for the object to hit the ground?
39)
40) If an object is propelled upward from a height of 64 feet at an initial velocity of 48 feet per
second, then its height h after t seconds is given by the equation h(t) = -16t2 + 48t + 64. After
40)
how many seconds does the object hit the ground?
Solve.
41) Four times the difference of a number and one is equal to six times the sum of the number and
three. Find the number.
41)
42) A 6-ft. board is cut into 2 pieces so that one piece is 2 feet longer than 3 times the shorter piece.
If the shorter piece is x feet long, find the lengths of both pieces.
42)
43) The code to unlock a safety deposit box is three consecutive odd integers whose sum is 93. Find
the integers.
43)
44) The manager of a coffee shop has one type of coffee that sells for $7 per pound and another type
that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a
mixture that will sell for $12 per pound. How many pounds of the $7 coffee should be used?
44)
Solve.
Solve the formula for the specified variable.
45) S = 2πrh + 2πr2
for h
9
46) F = C + 32
5
45)
for C
46)
Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
47) Ming got a 3% raise in her salary from last year. This year she is earning $ 30,900. How much did 47)
she make last year?
Solve.
48) Dave can hike on level ground 3 miles an hour faster than he can on uphill terrain. Yesterday, he
hiked 28 miles, spending 2 hours on level ground and 5 hours on uphill terrain. Find his average
speed on level ground.
48)
49) A motorcycle traveling at 50 miles per hour overtakes a car traveling at 40 miles per hour that
had a three-hour head start. How far from the starting point are the two vehicles?
49)
Solve the problem.
50) Daniel purchased tickets to an air show for 8 adults and 2 children. The total cost was $190. The
cost of a childʹs ticket was $5 less than the cost of an adultʹs ticket. Find the price of an adultʹs
ticket and a childʹs ticket.
Convert as indicated.
51) 333 oz to lb oz
50)
51)
4
52) 44.6 cg to dekagrams
52)
Convert the measurement as indicated.
53) 70 qt to gallons
53)
Convert as indicated.
54) 710 L to kiloliters
54)
Complete the ordered pair so that it is a solution of the given linear equation.
55) y = -2x - 6;
(-5, ), (-6, ), (0, )
55)
Determine whether the pair of lines is parallel, perpendicular, or neither.
56) y = 3x - 2
y = -3x + 8
56)
57) 3x - 8y = 5
32x + 12y = 1
57)
58) The approach ramp used by a daredevil motorcyclist for flying over a collection of flaming
barrels of oil has a rise of 63 feet for every 90 feet in horizontal distance. Find the grade of the
ramp. Round to the nearest whole percent.
58)
Solve.
Find the standard form of the equation of the line.
6
59) With slope of - , through (4, 3)
7
59)
Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points.
60) (-4, 1) and (-8, 9)
60)
Find the slope-intercept form of the equation of the line.
61) Through (6, -22) and (9, -37)
61)
Find an equation of the line described.
62) Through (-7, 1), parallel to the x-axis.
62)
3
63) With undefined slope, through - , 5 .
8
63)
64) Through (-8, 5), perpendicular to the y-axis.
64)
Convert as indicated.
65) 9.4 ml to deciliters
65)
Solve the system of equations by the substitution method.
66) y = 3x - 7
y = 8x - 8
66)
5
Without graphing, decide:
(a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point?
(b) How many solutions does the system have?
67)
67) y - 4x = 6
5y = 20x + 30
Solve the linear system using substitution.
1
x - 2y = 1
68) 4
68)
x - 8y = 4
Write a system of equations in x and y describing the situation. Do not solve the system.
69) Roger has $14 less in his pocket than Donna has. If Donna had $8 more, she would have 3 times
as much money as Roger.
69)
Solve the system of equations by graphing.
x - 3y = 5
70)
2x + 3y = -8
70)
y
5
-5
5
x
-5
Provide an appropriate response.
71) Determine the slope and the y-intercept of the graph of 5x - 11y = 55.
71)
Divide.
72)
8x3 - 64
2x + 4
72)
Simplify.
73) (3x3 + 9x2 + 3x - 4) - (8x3 - 3x2 - 6x + 7)
73)
Convert the measurement as indicated.
3
74) 12 gal to quarts
4
74)
Perform the indicated operation.
75) 9 gal - 7 gal 3 qt
75)
Solve. Remember to insert units when writing your answer.
76) A case of soft drink holds 12 bottles, each of which contains 16 ounces of soft drink. How many
quarts are there in one case of the soft drink?
6
76)
Solve the system.
77)
x + y + z = 3
x - y + 3z = 7
3x + 3y + 3z = -3
77)
Use intercepts to graph the equation.
78) 2x + 3y = 6
78)
y
5
-5
5
x
-5
Solve the system.
79)
x - y + 4z = 13
5x
+ z = 3
x + 2y + z = 1
79)
80)
80)
x + 7y - z = 2
-4x - 28y + 4z = -8
3x + 21y - 3z = 6
7
Answer Key
Testname: 301 RW FIN
2
3
1) - , - 5
4
2)
3)
4)
5)
6)
7)
8)
9)
37) 8 ft by 14 ft
38) 75 ft
39) 3 sec
40) 4 sec
41) -11
42) shorter piece: 1 ft; longer piece: 5 ft
43) 29, 31, 33
44) 36 pounds
S - 2πr2
45) h = 2πr
(x2 + 2x - 5)(a - b)
∅
{(1, -6)}
{(1, -6)}
inconsistent
2
13 r21
14
5
46) C = (F - 32)
9
x3
64y2
47) $30,000
1
48) 6 mph
7
10) 5x + 13
11) domain = {-11, 2, 3, -5, 8}; range = {-9, -3, -2, 9, -1}
12) -20x2 - 6
49) 600 mi
50) adultʹs ticket: $20; childʹs ticket: $15
51) 20 lb 13 oz
52) 0.0446 dag
1
53) 17 gal
2
13) (5x + 6y)(x - 3y)
x8
14)
16z 12
15) 5.5 × 10-10
16) 3 × 102
17) - 54) 0.71 kl
55) (-5, 4), (-6, 6), (0, -6)
56) neither
57) perpendicular
58) 70%
59) 6x + 7y = 45
1
60) (a) - 2; (b) 2
11
9
18) (7x + 2y)(x - 4y)
19) 49y2 - 16x2 - 8x - 1
20) x4 - 256
21) 16a 2n - 49b2n
22) 4(x + 5)(x2 - 5x + 25)
23) {-1, 1, -5}
24) -1, - 61) y = -5x + 8
62) y = 1
3
63) x = - 8
1
3
5
25) -3, - , 3
4
64) y = 5
65) 0.094 dl
32
1
66) , - 5
5
26) (x - 9)(x - 1)(x +1)
27) x-intercepts: (-2,0), (1,0), (-5,0); y-intercept: (0,-2)
8x
28) -3x3 - 16x - 4 + 2
x - 5
67) identical lines; infinite number of solutions
68) {(x,y)|x - 8y = 4}
69) x = y - 14
y + 8 = 3x
70) {(-1, -2)}
5
71) m = ; (0, -5)
11
29) 1 - x6
30) (x - 4)(x - 16)
7
31) -2y2 - 6y + 8
32) 4y2 + 4y - 2
2
33) -6, - , 0
3
72) 4x2 - 8x + 16 - 34) 4pq2 (2p - 3q + 10p3 q3 )
5 2
35)
, 3 7
128
2x + 4
73) -5x3 + 12x2 + 9x - 11
74) 51 qt
75) 1 gal 1 qt
76) 6 qt
36) {1}
8
Answer Key
Testname: 301 RW FIN
77) ∅
78) intercepts: (0,2), (3,0)
y
10
5
-10
-5
5
10
x
-5
-10
79) (0, -1, 3)
80) {(x, y, z) x + 7y - z = 2}
9