Tennessee State University
College of Engineering
Department of Mathematical Sciences
Pre Calculus I
Final Exam Review Package
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Final Exam Review Package
1.
If f (x) = −x2 − x − 6, find f (−3).
(d) f (−3) = −12
(b) f (−3) = 8
4.
Let a and h be two real numbers such that
h 6= 0. If f (x) = 7x−8, find the difference quotient
f (a + h) − f (a)
.
h
f (a + h) − f (a)
h
f (a + h) − f (a)
(b)
h
f (a + h) − f (a)
(c)
h
f (a + h) − f (a)
(d)
h
(a)
3.
(d) f (a) + f (h) = a2 + h2 − a − h
(c) f (−3) = −18
(a) f (−3) = 10
2.
(c) f (a) + f (h) = a2 + h2 + a + h + 4
4x
and a is a non-negative real
√+ 5
number, find g( a).
√
5.
(b) [−3, ∞)
=7
(a) f (a) + f (h) =
a2
(b) f (a) + f (h) =
a2
+
h2
+
h2
6.
−a−h+4
(a) [25, ∞)
Page 1 of 15
√
6x + 18
(c) (3, ∞)
(d) (−∞, 6)
Find the domain of f (x) =
(b) (−5, 5)
+a+h
√
4 a
(c) g( a) =
a+5
√
Find the domain of f (x) =
(a) [3, ∞)
= 7x
Let a and h be two real numbers. If f (x) =
2
x − x + 2, find f (a) + f (h).
x2
4a
(a) g( a) =
a+5
√
4a
(b) g( a) = 2
a +5
=8
= −7x
If g(x) =
√
x2 − 25
(c) [5, ∞)
(d) (−∞, −5] ∪ [5, ∞)
Review Package · Pre Calculus I
7.
Department of Mathematical Sciences
(a) V = x(3 − x)(7 − x)
9
Find the domain of f (x) = 2
9x + 9x − 180
(b) V = x(3 − 2x)(7 − 2x)
(a) (−∞, −2) ∪ (2, −6) ∪ (6, ∞)
(c) V = (3 − 2x)(7 − 2x)
(b) (−∞, −2) ∪ (6, ∞)
(d) V = 2x(3 − x)(7 − x)
(c) (−∞, −5) ∪ (−5, 4) ∪ (4, ∞)
12.
(d) (−∞, −5) ∪ (4, ∞)
8.
Find the range of f (x) = 2 − x2
(c) (2, ∞)
(a) (−∞, 2]
(b) (−∞, 2)
9.
Find the intervals in which f (x) = x2 − 5 is
decreasing
(a) (−∞, 0]
(b) (−∞, 5]
10.
(c) (−∞, −5]
(d) [0, ∞)
Let x and h be two real numbers with h 6= 0.
If f (x) = x2 + 4, find the difference quotient
f (x + h) − f (x)
h
f (x + h) − f (x)
h
f (x + h) − f (x)
(b)
h
f (x + h) − f (x)
(c)
h
f (x + h) − f (x)
(d)
h
(a)
11.
A hot-air balloon is released at 1:00 PM and
rises vertically at a rate of 2 m/sec. An observation point is situated a meters from a point on
the ground directly below the balloon (see the
figure). If t denotes the time (in seconds) after
1:00 PM, express the distance d between the balloon and the observation point as a function of t.
(a) d =
= 2x + h
(b) d =
= 2x + h + 8
13.
=x+h
√
√
125 + 2t
(c) d =
15625 − 2t2
(d) d =
√
15625 + 4t2
15625 + 2t2
Determine whether f (x) = x3 +4x is odd, even,
or neither odd nor even
(a) f is odd
(b) f is even
= 2x
From a rectangular piece of cardboard having
dimensions a = 3 inches b = 7 inches, an open box
is to be made by cutting out an identical squares
of area from each corner and turning up the sides
(See figure below). If each side of the squares taken
off the cardboard is x, express the volume V of the
box as a function of x.
√
14.
Graph the function f (x) = |x| + 8
(a)
Page 2 of 15
(c) f is neither odd
nor even
Review Package · Pre Calculus I
15.
Department of Mathematical Sciences
(b)
(b)
(c)
(c)
Graph the function f (x) =
√
3x − 1
16.
The graph of the function f with domain [0, 4] is shown in the figure below
(a)
Then the graph of f (x + 3) is given by
Page 3 of 15
Review Package · Pre Calculus I
Department of Mathematical Sciences
Use properties of symmetry, shifts, and reflecting
to find equations for graphs (a) and (b) in terms
of the function f .
(a) The graph of (a) is y = f (x + 7) + 1 and the
graph of (b) is y = f (x + 6) − 1
(a)
(b) The graph of (a) is y = f (x + 7) + 1 and the
graph of (b) is y = −f (x + 6) − 1
(c) The graph of (a) is y = f (x − 6) + 1 and the
graph of (b) is y = −f (x − 7) − 1
18.
Sketch the graph of

 x+6
x3
f (x) =

−x + 3
(b)
(a)
(c)
17.
The graph of a function f is shown in the figure
below together with graphs of two other functions
(a) and (b).
(b)
(c)
Page 4 of 15
if x ≤ −1
if − 1 < x < 1
if x ≥ 1
Review Package · Pre Calculus I
19.
Find the standard equation of any parabola that
has vertex V (−6, 7).
(a) y = (x + 6)2 − 7
(b) y = a(x + 6)2 + 7
20.
Department of Mathematical Sciences
(c) (g ◦ f )(x) = 4x2 − 4
(d) (g ◦ f )(x) = −16x2 + 32x − 16
(e) (g ◦ f )(x) = −4x2 + 32x − 16
(c) y = (ax − 12)2 + 7
(d) y = a(x − 7)2 + 6
26.
Express the function f (x) = x2 − 10x + 35 in
the form a(x − h)2 + k
Let f (x) = 2x − 9 and g(x) = 6x2 − x + 3. Find
(g ◦ f )(x)
(a) (g ◦ f )(x) = 31x2 − 436x + 498
(b) (g ◦ f )(x) = −24x2 + 218x − 514
(a) f (x) = (x − 5)2 + 10
(c) (g ◦ f )(x) = 24x2 − 218x + 498
(b) f (x) = (x − 8)2 − 3
(d) (g ◦ f )(x) = −24x2 + 218x − 498
(c) f (x) = −5(x − 1)2 + 10
(d) f (x) = (x + 5)2 + 8
21.
22.
Find the minimum value of the function f (x) =
x2 + 6x + 16
(a) f (−3) = 7
(c) f (2) = 6
(b) f (7) = 3
(d) f (0) = 16
A piece of wire 44 inches long is bent into the
shape of a rectangle having width x and length y.
Express the area A of the rectangle as a function
of x.
Let f (x) = 5x + 2 and g(x) = x2 .
(f + g)(6).
(a) (f + g)(6) = 73
(b) (f + g)(6) = 68
(c) (f + g)(6) = 136
24.
Let f (x) =
domain of f · g.
6x
x−9
Find the solutions of the equation (f ◦g)(x) = 0
for f (x) = x2 − 36 and g(x) = x + 4.
(b) (−∞, 1] ∪ [−9, ∞)
(a) x = 2 and x = −10
(b) x = 5 and x = −15
(c) x = 2 and x = 10
Find
29.
x−2
7
x
+
2
(b) f −1 (x) =
7
(a) f −1 (x) =
(e) (f + g)(6) = 65
x
x+1 .
Find the
(c) (−∞, 1) ∪ (−9, ∞)
(d) (−∞, −1] ∪ [9, ∞)
(e) (−1, 9)
Let f (x) = 4x − 4 and g(x) = −x2 . Find
(g ◦ f )(x)
(a) (g ◦ f )(x) = −4x2 − 4
(b) (g ◦ f )(x) = 16x2 − 32x + 16
30.
(d) x = 5 and x = −10
(e) x = 2 and x = −15
Find the inverse of the function f (x) = 2x + 7
(d) (f + g)(6) = 67
and g(x) =
(a) (−∞, −1)
∪
(−1, 9) ∪ (9, ∞)
25.
28.
(c) A = x2 + 44x
(a) A = −x2 + 22x
(b) A = (x − 22)2
23.
(e) (g ◦ f )(x) = −31x2 + 436x − 514
√
Let f (x) = x2 − 9x and g(x) = x + 5. Find
27.
(f ◦ g)(x)
√
(a) (f ◦ g)(x) = x2 − 9x + 5
√
(b) (f ◦ g)(x) = x + 5 − 9 x + 5
√
(c) (f ◦ g)(x) = x2 − 9x
√
(d) (f ◦ g)(x) = x2 − 9x + 5
x−7
2
1
(d) f −1 (x) =
2x + 7
(c) f −1 (x) =
Find the inverse of the function f (x) = 3 − 7x2
when x ≥ 0.
r
3−x
−1
(a) f (x) = −
7
r
3−x
(b) f −1 (x) =
7
r
3−x
(c) f −1 (x) = −
5
r
5−x
(d) f −1 (x) = −
7
Page 5 of 15
Review Package · Pre Calculus I
31.
Find the inverse of the function f (x) = 3x3 − 5
=
r
(b) f −1 (x) =
r
(a)
32.
f −1 (x)
3
3
5+x
3
3+x
5
=
r
3
(d) r
f −1 (x)
3 11 + x
3
Find the inverse of the function f (x) =
(a) f −1 (x) = (x − 2)3
(b) f −1 (x) = (x − 5)3
33.
(c)
f −1 (x)
5+x
11
=
(c)
√
3
x+5
(c) f −1 (x) = (x − 3)3
(d) f −1 (x) = (5 − x)3
Sketch the graph of f (x) = 7x3 − 2
Department of Mathematical Sciences
The solution of the inequality 36x − x3 < 0 is
34.
(a) (−9, 0] ∪ [9, ∞)
(b) (−∞, −6) ∪ (6, ∞)
35.
Find all the values x such that f (x) < 0 if
f (x) = x3 + 8x3 − 25x − 200.
(a) (−∞, ∞)
(b) (−∞, −8) ∪ (−5, 5)
36.
(a)
(c) x = 5 and x = −25
If one zero of f (x) = x3 − 12x2 − kx + 96 is −2.
Find the two other zeros.
(a) x = −8 and x = 6
(b) x = 12 and x = 96
(b)
39.
(c) (−6, 6)
If one zero of f (x) = x3 − 4x2 − 25x + 100k is
x = 4. Find the other zeros
(a) x = ±7
(b) x = ±5
38.
(c) (−∞, −8]∪[−5, ∞)
Find all the values of x such that f (x) > 0 if
f (x) = x2 (x + 6)(x − 3)2 (x − 6).
(a) (−∞, −3) ∪ (3, ∞)
(b) (−∞, −6) ∪ (6, ∞)
37.
(c) (−6, 0) ∪ (6, ∞)
(c) x = 8 and x = 6
Use synthetic division to find f (c) if f (x) =
5x3 + 9x2 − 6x + 3 and c = 2.
Page 6 of 15
(a) f (2) = 76
(c) f (2) = 3
(b) f (2) = 64
(d) f (2) = 67
Review Package · Pre Calculus I
40.
Use synthetic division to decide if c = −4 is a
zero of f (x) = 5x4 + 22x3 − 9x2 − 65x + 12
(a) c is not a zero of
f (x)
41.
(a)
(b)
(b) c is a zero of f (x)
(c)
Find a polynomial p(x) of degree 3 that has 4,
−1, and 3 as zeros and such that p(0) = 36.
(d)
(a) p(x) = 4x3 − 21x2 + 15x + 36
(e)
(c) p(x) = 3x3 − 18x2 + 15x + 36
(g) x = 0 with multiplicity 3
(f) x = 0 with multiplicity 1
(b) p(x) = 10x3 − 7x2 + 36x + 15
(d) p(x) = 36x3 − 15x2 + 18x + 3
42.
46.
Show that the number 1 is a zero of f (x) =
− 10x5 + 35x4 − 60x3 + 55x2 − 26x + 5 with
multiplicity 5 by factoring f (x)
x6
Find a polynomial p(x) of degree 3 that has −4,
3i, and −3i as zeros and such that p(2) = 156.
(a) f (x) = (x − 5)5 (x − 1)
(a) p(x) = 2x3 + 8x2 + 18x + 72
(b) p(x) = 3x3 + 11x2 + 18x + 72
(b) f (x) = (x − 6)5 (x − 3)
(c) p(x) = 9x3 + 6x2 + 72x + 18
(c) f (x) = (x − 1)5 (x − 5)
(d) p(x) = 72x3 + 18x2 + 8x + 2
43.
(d) f (x) = x(x − 5)5
Find a polynomial p(x) of degree 4 with leading
coefficient 1 such that both 3 and −1 are zeros of
multiplicity 2
47.
(a) p(x) = x4 − 4x3 − 2x2 + 12x + 9
Use Descartes’ rule of signs to determine the
number of possible positive, negative, and non-real
complex solutions of the equation 4x3 − 7x2 + x −
6=0
(b) p(x) = x4 − 5x3 − 2x2 + 12x + 8
(a) 1 positive roots, 2 negative roots, 0 nonreal
roots
(c) p(x) = x4 − 4x3 + 10x2 + 12x + 9
(d) p(x) = x4 − 12x3 − 9x2 + 4x + 2
44.
(b) 1 positive roots, 0 negative roots, 2 nonreal
roots
Find the zeros of f (x) = x(x − 3)2 (3x − 2)4 and
state the multiplicity of each zero.
(c) 0 positive roots, 3 negative roots, 0 nonreal
roots
2
with multiplicity 4
3
3
x = with multiplicity 4
2
x = 3 with multiplicity 2
2
x = with multiplicity 2
3
x = 0 with multiplicity 1
(a) x =
(b)
(c)
(d)
(e)
(d) 0 positive roots, 0 negative roots, 0 nonreal
roots
(e) 3 positive roots, 0 negative roots, 0 nonreal
roots
(f) 2 positive roots, 1 negative roots, 0 nonreal
roots
(f) x = 3 with multiplicity 4
48.
(g) x = 0 with multiplicity 2
45.
Department of Mathematical Sciences
2
x = − with multiplicity 2
7
7
x = with multiplicity 2
2
2
x = − with multiplicity 1
7
2
x = with multiplicity 2
7
x = 0 with multiplicity 2
Use Descartes’ rule of signs to determine the
number of possible positive, negative, and non real
complex solutions of the equation
Find the zeros of f (x) = 49x5 + 28x4 + 4x3 and
state the multiplicity of each zero
Page 7 of 15
3x4 + 4x3 − 3x + 6 = 0
Review Package · Pre Calculus
(a) 2 positive roots, 2
negative roots, 0
(d)
nonreal roots
(b) 3 positive roots, 1
negative roots, 0
nonreal roots
(e)
(c) 0 positive roots, 0
negative roots, 4
49.
55.
0 positive roots, 2
negative roots, 2
nonreal roots
(b) x2 + 12x + 52
Department of Mathematical Sciences
7
Find the graph of f (x) =
.
x−3
0 positive roots, 3
negative roots, 1
nonreal roots
Which of the following polynomials has leading
coefficient 1 and has a zero at 6 + 4i with multiplicity 2.
(a) x2 − 12x + 36
50.
I
nonreal roots
(a)
(c) x2 − 36x + 52
(d) x2 − 12x + 52
Which one of the following polynomials has
leading coefficient 1, has roots 5 and −4 − 3i, and
has degree 3.
(a) (x − 5)(x2 + 8x + 25)
(b) (x − 5)(x2 + 16x + 25)
(c) (x − 3)(x2 + 8x + 25)
(d) (x − 4)(x2 + 8x + 25)
51.
(b)
Which of the following polynomials has leading
coefficient 1, has roots 6 + i and −5 + i, and has
degree 4.
(a) (x2 − 12x + 37)(x2 + 10x + 26)
(b) (x2 − 12x + 37)(x2 + 10x + 25)
(c) (x2 − 12x + 36)(x2 + 10x + 25)
(d) (x2 − 12x + 36)(x2 + 10x + 26)
52.
Determine whether the equation x5 −8x3 +9x2 +
4x − 2 = 0 has rational roots.
(a) Has no
roots
53.
rational
(c)
Does there exist a polynomial of degree 3 with
real coefficients and roots at 8, −8, and i?
(a) Yes
54.
(b) has rational roots
(b) No
8
.
x
(c) (−∞, 8) ∪ (8, ∞).
Find the domain of f (x) =
(a) (−∞, ∞).
(b) (−∞, 0) ∪ (0, ∞).
56.
Page 8 of 15
Find the graph of f (x) =
−2x2
x2 + 1
Review Package · Pre Calculus I
Department of Mathematical Sciences
3 − x2
(c) f (x) = 2
x + 4x − 7
58.
Which of the following rational functions has
vertical asymptotes at x = −1 and x = 4?
2x3 + 6x2 − 8x
x3 − 3x2 − 4x
4x3 + x2 − 8x
(b) f (x) = 3
x − 6x2 − 4x
8x2 − 4x − 4
(c) f (x) = 3
x −x+6
(a) f (x) =
(a)
59.
Determine the domain of f −1 (x) if
f (x) =
(a) (−∞, 3) ∪ (3, ∞)
(b) (−∞, ∞)
60.
(b)
(a) (−∞, 3) ∪ (3, ∞)
11
(b) (− 11
3 , 3 )
62.
57.
Which of the following rational functions has
vertical asymptotes at x = −7 and x = 3?
105x2 − 210x − 840
x3 − 37x + 84
10x2 − 210x − 10
(b) f (x) = 3
x − 105x + 84
(a) f (x) =
Page 9 of 15
11x + 3
3x − 9
11
(c) (−∞, 11
3 ) ∪ ( 3 , ∞)
Solve the equation 7x+6 = 73x−4 .
(a) x = 8
(b) x = 71
(c) x = −5
(c)
(c) (−∞, 0) ∪ (0, ∞)
Determine the domain of f −1 (x) if
f (x) =
61.
3
x+1
(d) x = 5
(e) x = 7
Which of the following is the graph of f (x) = 2x
(a)
Review Package · Pre Calculus I
Department of Mathematical Sciences
(b)
(b)
(c)
(c)
64.
63.
Which of the following is the graph of f (x) =
An investment of $827 increased to $5529 in
19 years. If the interest was compounded continuously, find the interest rate.
ex+2
(a) 20%
(c) 12%
(b) 7%
(d) 10%
2
Solve the equation ex = e12x−35
65.
(a) x = 5
(b) x = −5 and x =
−7
(a)
(c) x = 5 amd x = 7
(d) x = 7
Solve the equation e4x = e3x−2
66.
(a) x = 2
(c) x = 4
(b) x = 3
(d) x = −2
Page 10 of 15
Review Package · Pre Calculus I
67.
When writing the equation
1
= −3
log8
512
Department of Mathematical Sciences
74.
Write the expression as one logarithm. 6 ln(x)−
8 ln( y1 ) − 2 ln(xy)
(a) ln(x6 y 4 )
(b)
in exponential form, we obtain
(a) 512 = 33
(b) 512 = 38
(c) 512 = 88
68.
69.
70.
1
512
= 8−3
75.
(e) 512 = 83
Solve the equation log2 x = log2 (14 − x)
(a) 2
(c) 7
(b) 14
(d) 4
(a) 12
(c) 10
(b) 18
(d) 7
(d) ln(x) + ln(y)
x w
y2 z4
(c) 5 log9 (x) + log9 (w) − 2 log9 (y) − 4 log9 (z)
Express in terms of logarithms of x, y, z.
q
7
ln 4 yx5 x9
(d)
73.
log 11
log 8
log 8
log 11
81.
≈ 0.85
(c)
log 8
log 11
≈ 1.13
(d)
log 11
log 8
− 2 ≈ −1.41
≈ 1.15
log7 512
log7 8
(c) 3
(b) 2
(d) 4
Find the solution of the equation 4−x = 64
(b) x = −3
Write the expression as one logarithm.
log3 (7z) − log3 (x)
(d) x = −6
(a) 1
(a) x = −4
ln(x) + 45 ln(y) + 94 ln(z)
(c) x = 9
Evaluate the expression:
80.
ln(x) − 45 ln(y) − 94 ln(z)
(d) x1 = 3, x2 = −242
Find the exact solution using common logarithms, and a two-seminal-place approximation of
the solution of the equation. 82−x = 11
79.
(a) 7 ln(x) + 5 ln(y) + 9 ln(z)
√
√
√
(b) 4 7 ln(x) − 4 5 ln(y) − 4 9 ln(z)
(c) x = 5
Solve the equation. log5 (x+7)+log5 (x+11) = 1
(b) 2 −
(d) 5 log9 (x) + log9 (w) − 4 log9 (y) − 2 log9 (Z)
7
4
7
4
Solve the equation. log3 (x + 78) + log3 x = 5
(a) 2 −
(b) 5 log9 (x) + log9 (w) + 2 log9 (y) + 4 log9 (z)
(c)
(d) x = 8
(b) x = 6
(a) log9 (x) + log9 (w) − log9 (y) + log9 (z)
72.
(b) x = 10
(a) x = −9
78.
(d) ln(x4 y 6 )
(c) x = 13
77.
(c) log6 (x) + log6 (y)
(c) ln(6x − 8y − 2xy)
(a) x = 5
(b) x = 3
Express
5 in terms of logarithms of x, y, z, w.
log9
− (xy)2 )
(a) x = −242
Express in terms of logarithms of x, y. log7 (xy)
(b) log7 (x) + log7 (y)
− y8
Solve the equation. log6 (3x − 17) = log6 (28) −
log6 (4)
76.
Solve the equation log2 (x − 4) = 3
(a) log7 (x) − log7 (y)
71.
(d)
ln(x6
(c) x = 4
(d) x = 7
Find a two-decimal-place approximation of the
solution of the equation log(x2 + 9) − log(x + 3) =
1 + log(x + 3)
x
)
(a) log3 ( 7z
(c) log3 ( 7z
x)
(a) x = 2.81
(b) log3 (7zx)
(d) log3 (7z − x)
(b) x = 4.34
Page 11 of 15
(c) x = −3.83
(d) x = 3.32
Review Package · Pre Calculus I
82.
Solve the equation log(x7 ) = (log x)2
83.
84.
85.
86.
88.
(a) 100000000
(c) 2 and 1000000
(b) 1 and 10000000
(d) 1 and 10
Use common logarithms to solve for x in terms
x
−x
of y. y = 10 +10
12
p
(a) x = log(6y + 12y 2 − 1)
p
(b) x = log(12y ± 36y 2 + 1)
p
(c) x = log(36y − y 2 − 6)
p
(d) x = log(6y ± 36y 2 − 1)
89.
(c) (6, 0)
(b) (-19, 5)
(d) no solution
(c) (11, 3)
(b) (3, 11)
(d) (0,0)
The price of admission to a high school play
was $3 for students ant $6 for non-students. If 250
tickets were sold for a total of $981, how many of
each kind of ticket purchased?
(a) (14, -7)
(c) (5, 2), (14, -7)
(b) no solution
(d) (5, 2)
Use the method of substitution to solve the system.

 x + 5y − z = −23
9x − y + z = 27

x + 3y + 3z = 5
(a)
9
x−8
(b)
10
x−5
(c)
10
x−8
92.
−
−
−
10
x+5
9
x+8
9
x+5
Find the partial fraction decomposition.
(a)
1
x
+
4
x−3
(b)
4
x
+
3
x−1
(c)
4
x
+
1
x−3
Find the partial fraction decomposition.
3
x−1
+
4
x+3
(c) The system is inconsistent.
(b)
3
x−1
+
4
x+3
(d) (5, 4, 2)
(c)
4
x−1
+
4
x+3
93.
(a)
(b)
(c) (−1,
(d) (−5,
5
2)
3
2)
5x−12
x2 −3x
6x2 −25x−17
(x−4)(x+3)(x−1)
(a)
(5, − 12 )
(3, − 52 )
(e) 178 students
Find the partial fraction decomposition.
91.
(b) (2, -4, 5)
Solve the system.
3r + 4s = 7
r − 8s = −21
(d) 188 students
x+122
x2 −3x−40
(a) The system is dependent.
87.
(a) no solution
90.
Use the method of substitution to solve the system
(x − 7)2 + (y + 5)2 = 53
x+y =7
(e) (2, 4, 5)
3y − 11x = 0
6y + 7x = 0
(a) 62 non-students
(b) 173 students
(c) 77 non-students
Use the method of substitution to solve the system
2
y =6−x
x + 5y = 6
(a) (6, 0), (-19, 5)
Department of Mathematical Sciences
Solve the system:
−
−
−
1
x−3
1
x−4
1
x−4
Find the partial fraction decomposition.
2x2 −49
x2 (x+7)
(a)
1
x
(b)
1
x
(c)
1
x
Page 12 of 15
−
−
−
7
x2
7
x2
1
x2
−
1
x+1
+
1
x+7
+
7
x+7
Review Package · Pre Calculus I
94.
Find the partial fraction decomposition.
x2 +x−20
(x2 +1)(x−1)
9
(a) − x−1
+
9
+
(b) − x−1
(c)
11
x−1
+
Department of Mathematical Sciences
101.
Find the specified term of the arithmetic sequence that has the two given terms. a1 : a8 = 44,
a9 = 50
10x+11
x2 +1
10x−9
x2 +1
10x+9
x2 +1
102.
95.
Find the third term of the sequence {17 − 6n}
(c) a3 = −7
(a) a3 = 17
(b) a3 = 23
96.
(b) a7 =
97.
98.
18
7
39
7
(c) a7 =
(d) a7 =
Find the third term of the recursively defined
infinite sequence a1 = 3, ak+1 = (ak )k
(c) a3 = 729
(b) a3 = 726
(d) a3 = 9
k=1
(3k − 2)
(a) S = 35
(c) S = 37
(b) S = 39
(d) S = 22
Find the sum of the arithmetic sequence S0
that satisfies the stated conditions. a7 = − 10
3 ,d =
− 32 , n = 18
103.
104.
(c) S = −86
(d) S = −90
Insert five arithmetic means between 9 and 33.
(a) 13, 17, 21, 25, 29
(c) 13, 19, 26, 25, 29
(b) 13, 21, 26, 25, 29
(d) 13, 19, 24, 25, 29
Find the total length of the red-line curve in
the figure if the width of the maze formed by the
curve is 16 inches and all halls in the maze have
width of 1 inch.
(1)
Find the n-th term of the arithmetic sequence:
23, 20, 17, 14, . . .
(a) an = 23 · 3n
(b) an = 3n + 26
100.
(d) a1 = 2
Find the sum
5
X
99.
(b) a1 = 8
(b) S = −88
25
7
32
7
(a) a3 = 735
(c) a1 = 1
(a) S = −80
(d) a3 = −1
Find the seventh term of the sequence {3 + n4 }.
(a) a7 =
(a) a1 = 14
a = 1in., b = 16in.
(c) an = 3n + 23
(a) 271 inches
(c) 272 inches
(d) an = 3n + 20
(b) 275 inches
(d) 270 inches
Find the common difference for the arithmetic
sequence with the specified terms. a4 = 26,
a11 = 82
(a) d = 5
(c) d = 7
(b) d = 15
(d) d = 8
105.
Find the sixth term of the geometric sequence:
4, 16, 64, 256 ...
(a) 4096
(b) 5460
(c) 4132
Page 13 of 15
(d) 16420
(e) 16384
Review Package · Pre Calculus I
9
X
3k
106.
Find the sum
Department of Mathematical Sciences
114.
The ratio of women to men in a mathematics
class is 5 to 8. How many women are in the class
if there are 48 men?
k=1
107.
(a) 29520
(c) 29523
(b) 9840
(d) 19682
Find the rational number represented by the
repeating decimal: 0.61
(a)
(b)
(c)
108.
109.
64
99
61
99
58
9
111.
(c) 102
(b) 204
(d) 48
116.
Insert two geometric means between 9 and 576.
(c) 48
(b) 8
(d) 5
The ratio of lime to sand in a mortar is 7 to
4. How much lime must be mixed with 32 bags of
sand to make a mortar?
(a) 4 bags
(c) 56 bags
(b) 32 bags
(d) 7 bags
Find the constant of proportionality for the
stated conditions: z is directly proportional to the
sum of x and y, and when z = 45, x = 6, and
y = 9.
(d) 148
(e) 36
If a deposit of $400 is made on the first day of
each month into an account that pays 9% interest per year compounded monthly, determine the
amount in the account after 12 years.
117.
(a) k = 45
(c) k = 3
(b) k = 6
(d) k = −3
Given that P varies jointly with r and s and
P = 7 when r = 3 and s = 6, find P when r = 9
and s = 24.
(a) $103857.76
(c) $103867.81
(a) P = 84
(c) P = 3
(b) $103861.81
(d) $103084.63
(b) P = 9
(d) P = 24
After being discounted 30%, a radio sells for
$67.90. Find the original price.
Solve the proportion
(e) $97.00
18
x
(a) x1 = −7, x2 = 6
(b) x1 = 7, x2 = 6
=
119.
(d) no solution
x
21
=
Given that m varies jointly with the square of
n and the square root of q and m = 30 when n = 3
and q = 8, find m when n = 15 and q = 32
(a) m = 30
(c) m = 3
(b) m = 1500
(d) m = 8
2
3
(c) x = −27
(b) x = 27
Solve the proportion
118.
(d) $98.00
(a) x = 18
113.
62
999
(a) 144
(a) $102.00
(b) $99.00
(c) $89.00
112.
(e)
115.
Find the geometric mean of 12 and 192.
(a) 144
(b) 38
(c) 324
110.
(d)
58
99
(a) 30
2
x+1
(c) x1 = 7, x2 = −6
(d) no solutions
The distance that an object will fall in t seconds
varies directly with the square of t. An object falls
7 feet in 1 second. How long will it take to fall 112
feet?
(a) t = −4sec
(b) t = 16sec
Page 14 of 15
(c) t = 4sec
(d) t = 112sec
Review Package · Pre Calculus I
Department of Mathematical Sciences
Answer Key
Problem
Answer
Problem
Answer
Problem
Answer
Problem
Answer
Problem
Answer
1
D
25
D
49
D
73
C
97
D
2
D
26
C
50
A
74
D
98
A
3
A
27
B
51
A
75
D
99
D
4
C
28
A
52
B
76
B
100
D
5
B
29
C
53
A
77
D
101
D
6
D
30
A
54
B
78
A
102
D
7
C
31
A
55
C
79
C
103
A
8
A
32
B
56
B
80
B
104
C
9
A
33
C
57
A
81
D
105
A
10
A
34
C
58
A
82
B
106
C
11
B
35
B
59
C
83
D
107
B
12
C
36
B
60
C
84
A
108
D
13
B
37
B
61
D
85
C
109
D,A
14
C
38
C
62
C
86
B
110
D
15
C
39
D
63
A
87
C
111
E
16
C
40
B
64
D
88
D
112
B
17
B
41
C
65
C
89
C
113
A
18
A
42
A
66
D
90
C
114
A
19
B
43
C
67
D
91
C
115
C
20
A
44
A,C,E
68
C
92
B
116
C
21
A
45
A,G
69
A
93
B
117
A
22
A
46
C
70
B
94
A
118
B
23
B
47
B
71
C
95
D
119
C
24
A
48
D
72
C
96
C
Last Review: November 19, 2013
Page 15 of 15