Download Elementary Algebra Review for Exam 4

Elementary Algebra
Review for Exam 4
Factor completely. If the polynomial is prime, state
this.
1) a) 4x2 + 11x - 20
b) 12x2 + 17x + 6
c) 5x2 - 29x - 42
2) a) 25x2 - 60x + 36
b) 9 - 48x + 64x2
c) 2x3 - 4x2 + 2x
3) a) y2 - 36
c) 36x2 + 25
e) 49y4 - 64
b) 81p2 - 4q2
d) x4 - 81
f) 4x2 - 36
Provide an appropriate response.
4) What is the difference between a
trinomial and a quadratic equation?
Solve the equation.
5) (x - 7)(x + 6) = 0
Solve the problem.
16) The length of a rectangular picture
frame is 9 cm more than the width. The
area inside the frame is 90 square cm.
Find the dimensions of the frame.
17) One leg of a right triangle is 6 cm shorter
than the other leg. The length of the
hypotenuse is 30 cm. Find the lengths of
each leg.
18) A 10-ft ladder is leaning against a
building. If the bottom of the ladder is 6
ft from the base of the building, how
high does the ladder reach?
19) In a sports league of n teams in which
each team plays every other team twice,
the total number N of games to be
played is given by N = n2 - n. How
many teams are in a softball league if the
total number of games played is 56?
6) 11 - 0.8x 5 - 0.2x = 0
7) a2 - 12a + 32 = 0
8) x2 + 3x - 88 = 0
9) x2 - x = 72
10) 16k2 - 25 = 0
11) 4x2 = 5x
12) (x - 7)(x + 4) = -24
Provide an appropriate response.
13) Explain the error in the following:
25x2 - 100 = (5x + 10)(5x - 10)
14) Explain the error in the following:
x2 + 16 = (x + 4)(x - 4)
15) Explain the error in the following:
x2 - y2 = (x - y)2
20) If an object is propelled upward from a
height of 96 feet at an initial velocity of
80 feet per second, then its height after t
seconds is given by the equation
h = -16t2 + 80t + 96, where h is in feet.
After how many seconds will the object
reach a height of 196 feet?
List all numbers for which the rational expression
is undefined.
9
21)
a-7
22)
23)
x2 - 25
x2 + 12x + 32
x2 - 49
2
x - 3x - 40
Elementary Algebra Review for Exam 4
Simplify, if possible.
28m6p2
24)
4m9p
Page 2
37)
x2 - 4x - 21
(x + 3)2
(x - 7)2
8x + 24
25)
10x + 30
38)
x2 + 3x - 4 25x3 - 9x
œ
3x - 3
5x3 - 3x2
26)
-4x + 12
-8x
39)
k2 + 8k + 12
k2 + 7k
œ
k2 + 13k + 42 k2 + 6k + 8
27)
b-a
3a - 3b
28)
7t - 14
2-t
29)
30)
31)
3x + 3
2
15x + 21x + 6
y2 - 6y - 16
y2 - 5y - 24
Provide an appropriate response.
32) What is wrong with the following?
4x + 8 4x + 8
=
= 4x
8
8
Multiply and, if possible, simplify.
3x2 28
œ
33)
4
x3
34)
2x2 - 98
7x - 7
œ
2
14x
+ 98
4x - 4
m2 - 16
m2
35)
œ
8m
m2 + 2m - 24
36)
5x + 10 3x2 - 6x + 3
œ
x-1
x2 - 4
œ
Divide and, if possible, simplify.
2x2 x3
40)
d
5
15
41)
4
12x10
d 8x
12y9
12y5
42)
9
3
d
y-x x-y
43)
3p - 3 5p - 5
d
p
2p2
44)
z2 + 15z + 54
z2 + 6z
d
z2 + 16z + 63 z2 + 12z + 35
a2 - 36
a2 + 10a + 24
x-7
45) (y + 5) d
3y2 + 10y - 25
y2 + 8y + 15
Perform the indicated operation. Simplify, if
possible.
4
7
46) a)
+
12x 12x
b)
4m
-12
+
m-3 m-3
c)
m2 - 6m
8
+
m-2
m-2
d)
x2 - 10x
9x - 42
+
2
2
x + 12x + 36 x + 12x + 36
Elementary Algebra Review for Exam 4
47) a)
13
11
q-9 q-9
b)
3a + 15 2a + 7
a-5
a-5
c)
3x + 18
x+6
x2 + 2x - 24 x2 + 2x - 24
Decide whether or not the ordered pair is a
solution of the system.
48) (4, -5)
4x + y = 11
3x + 4y = -8
49) (-3, -4)
4x + y = -16
2x = -22 - 4y
Solve the system of equations by graphing. If there
is no solution or an infinite number of solutions,
state this.
50) x - 3y = 9
x + 2y = -1
51) y = 4x + 16
y = -3x - 5
1
52) y = x + 2
3
x - 3y = 7
53) 3x - y = 5
6x = 2y + 10
Provide an appropriate response.
54) Describe the three possible outcomes
when graphing a system of equations,
and include the number of solutions that
each system has.
55) Explain in your own words what it
means for a system of two linear
equations in two variables to be
dependent.
Page 3
Solve the system using the substitution method. If
there is no solution or an infinite number of
solutions, state this.
56) y = 2x - 8
-3x + y = -2
57) x - 7y = -49
-7x - 6y = -42
58) y - 3x = 8
3y - x = 7
59) x + y = 9
x+y=7
Solve the system using the elimination method. If
there is no solution or an infinite number of
solutions, state this.
60) x - 4y = 9
2x - 4y = 14
61) x - 3y = -7
4y = 7x - 36
62) -2x - 6y = 4
-4x - 12y = 8
63) -4x + 5y = -2
-12x + 15y = 6
Solve the problem.
64) The sum of two angles is 194e. One angle
is 22e less than twice the other. Find the
angles.
65) Two angles are supplementary (they
sum to 180†), and one is 40e more than
three times the other. Find the smaller
angle.
Solve.
66) One rental agency rents a van for $27.00
per day plus $0.16 per mile. A
competitor rents a truck for $18.00 per
day plus $0.18 per mile. For what
mileage is the cost the same for renting
the van one day? Round your answer to
the nearest tenth of a mile.
Elementary Algebra Review for Exam 4
Page 4
Simplify. Do not use negative exponents in your
answer.
67) a) y7œ y-2
b) 3-8 œ 3-6
68) a)
c -5
3
69) a)
p4
p-5
b)
b)
z-8
z-4
3x-4
y-7z-2
c)
7x-6
y-2z3
70) a) (3x-2yz5)-4
b) (x-9y11z2)(x-4y-4z6)
Solve the problem.
71) In a local election, 26,768 people voted.
This was an increase of 12% over the last
election. How many people voted in the
last election?
72) An employee earned $33,956 this year.
This was a raise of 4% over last year.
What was his salary last year?
73) In a local election, 27,896 people voted.
This was a decrease of 12% over the last
election. How many people voted in the
last election?
Solve the equation.
74) 9x - (4x - 1) = 2
75)
2
1
x- x=4
5
3
76)
1
x + 3x = -10
3
77) -4x + 2(-3x - 6) = -15 - 7x
78) -7b + 9 + 5b = -3b + 14
Find the intercepts, then graph the equation.
79) -2x + 5y = 10
Write the slope-intercept equation for the line
with the indicated slope and y-intercept.
3
80) Slope ; y-intercept (0, 2)
4
Write a point-slope equation for the line with the
given slope that contains the given point.
81) m = -2; (5, -3)
Write the slope-intercept equation of the line
containing the given points.
82) ( -2, -6 ) and ( 8, -11)
Answer Key
Testname: EAEXAM4REVIEW_SPRING09
1) a) (x + 4)(4x - 5)
b) (4x + 3)(3x + 2)
c) (5x + 6)(x - 7)
2) a) (5x - 6)2
b) (8x - 3)2
c) 2x (x - 1)2
3) a) (y + 6)(y - 6)
b) (9p + 2q)(9p - 2q)
c) Prime
d) (x2 + 9)(x - 3)(x + 3)
e) (7y2 + 8)(7y2 - 8)
f) 4 x+3 x-3
4) A trinomial is the sum of three monomials. It
is not an equation. A quadratic equation is an
equation of the form ax2 + bx + c = 0, a ≠ 0.
5)
6)
7)
8)
9)
7, -6
13.75, 25
8, 4
-11, 8
-8, 9
5 5
10) , 4 4
11)
5
,0
4
12) -1, 4
13) The largest factor has not been factored out:
25x2 - 100 = 25(x + 2)(x - 2)
14) The polynomial x2 + 16 is not a difference of
squares. Since x2 + 16 is a sum of squares with
no common factor, it cannot be factored.
15) x2 - y2 is a difference of squares, not the
square of a binomial.
x2 - y2 = (x + y)(x - y)
16)
17)
18)
19)
20)
21)
22)
23)
width = 6 cm, length = 15cm
18 cm and 24 cm
8 ft
8
2.5 sec
a=7
x = -8 and -4
x = -5 and 8
7p
24)
m3
25)
4
5
26)
x-3
2x
27) -
1
3
28) -7
29)
1
5x + 2
30)
y+2
y+3
31)
a-6
a+4
32) You can only cancel factors, and 8 is not a
factor of 4x + 8. The 8 has to be divided out of
both terms, not just the last.
21
33)
x
34)
x-7
4(x + 1)
35)
m(m + 4)
8(m + 6)
36)
15(x - 1)
x-2
37)
1
x+3
38)
(x + 4)(5x + 3)
3x
39)
k
k+4
40)
6
x
41)
3x6
2y4
42) -3
6p
43)
5
44)
z+5
z
45)
(y + 5)(y + 3)
3y - 5
Answer Key
Testname: EAEXAM4REVIEW_SPRING09
46) a)
11
12x
53) Infinite number of solutions
b) 4
c) m - 4 d)
x-7
x+6
2
q-9
a+8
a-5
47) a)
b)
c)
2
x-4
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
y
1 2 3 4 5 x
51) (-3, 4)
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
y
1 2 3 4 5 x
52) No solution
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
y
1 2 3 4 5 x
1 2 3 4 5 x
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
48) Yes
49) Yes
50) (3, -2)
5
4
3
2
1
y
5
4
3
2
1
54) (1) The graphs intersect at one point, and the
system has one solution.
(2) The graphs are parallel, and the system has
no solution.
(3) The equations have the same graph, and
the system has an infinite number of solutions.
55) The graph of the system is a single line, and
every point on the line is a solution of the
system. This means that the system has
infinitely many solutions.
56) (-6, -20)
57) (0, 7)
17 13
58) - ,
8 8
59)
60)
61)
62)
63)
64)
65)
66)
No solution
(5, -1)
(8, 5)
Infinite number of solutions
No solution
72e and 122e
35e
450.0
1
67) a) y5
b)
312
68) a)
35
243
or
c5
c5
69) a) p9
70) a)
b)
x8
81y4z20
71) 23,900 people
72) $32,650
73) 31,700 people
b)
3y7z2
x4
1
z4
b)
c)
y7z8
x13
7y2
x6z3
Answer Key
Testname: EAEXAM4REVIEW_SPRING09
74)
1
5
75)
76)
77)
78)
79)
60
-3
1
5
(-5, 0), (0, 2)
3
80) y = x + 2
4
81) y + 3 = -2(x - 5)
1
82) y = - x - 7
2