Precalculus - Dalton State College
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Transcript Precalculus - Dalton State College
Precalculus
Final Exam Review Questions
Determine the interval on which the
function is increasing.
a. (0, 1)
b. (4, 3)
c. (3, 0)
d. (1, 2)
Which of the following is symmetric
with respect to the origin?
a. y (x 4)
2
b. x y
2
c. y x 2
d. y x x
3
Write an equation for a function that has the
shape of y x, but is shifted left 3 units
and down 5 units.
a. f (x) x 3 5
b. f (x) x 5 3
c. f (x) x 3 5
d. f (x) x 5 3
The graph of f is given.
Which graph below
represents the graph of
g(x) = 2f(x) + 1?
a.
b.
c.
d.
Find the zeros of the polynomial function
and state the multiplicity of each.
f(x) = (x + 3)2(x + 1)
a. –3, multiplicity 2, 1 multiplicity 1
b. 3, multiplicity 2, 1 multiplicity 1
c. –3, multiplicity 2, 1 multiplicity 2
d. 3, multiplicity 3, 1 multiplicity 1
For f(x) = 2x4 + 3, use the intermediate
value theorem to determine which interval
contains a zero of f.
a. between 1 and 0
b. between 0 and 1
c. between 1 and 2
d. between 2 and 3
Find the quotient and remainder when
x4 + 5x2 – 3x + 2 is divided by x – 2.
a.
x3 2 x2 9 x 15, R 32
b.
x 2 x 9 x 21, R 44
c.
x3 2 x 2 9 x 21, R 44
d.
x3 7 x2 14 x 25, R 52
3
2
Find a polynomial function of lowest degree
with rational coefficients and 3 and 4i as
some of its zeros.
a.
f ( x) x 3x 4xi 12i
b.
f ( x) x3 3x2 16 x 48
c.
f ( x) x 3x 16 x 48
d.
f ( x) x3 3x2 16 x 48
2
3
2
Use the rational zeros theorem to determine
which number cannot be a zero of
P(x) = 10x4 + 6x2 – 5x + 2.
a.
1
5
b. 2
c. 5
d.
2
5
Which graph represents the polynomial
x3
.
function f (x) 2
x 3x 4
a.
b.
c.
d.
Solve 3x2 > x + 10.
5
a. , (2, )
3
5
b. 2,
3
3
c. , 2 ,
5
5
d. , 2 ,
3
Convert to a logarithmic equation:
2x = 20.
a. x = log220
b. x = log10
c. 2 = logx20
d. x = log202
Find log 0.001. Do not use a calculator.
a. –4
b. –3
c. 3
d. 1000
Express in terms of sums and
differences of
a.
x2
logarithms: log 3 .
y
1
1
log x log y
9
3
b. 6log x 3log y
c.
d.
2
1
log x log y
3
3
2
log x log y
3
Solve: log3(3x + 6) – log3(x – 6) = 2.
a. 14
b. 10
c.
3
2
d. Does not exist
Solve: 25+x = 32x-4.
a.
b.
c.
d.
9
4
15
4
69
15
25
4
Find log58 using the change-of-base
formula.
a. 0.2041
b. 0.7740
c. 1.2920
d. 1.6
Suppose $2000 is invested at interest rate, k,
compounded continuously, and grows to
$2,473.53 in 5 years. Find the approximate
interest rate.
a. 3.83%
b. 4.25%
c. 4.75%
d. 7.89%
Given the triangle, find cos.
a.
3 109
109
10
c.
3
10 109
b.
109
d.
109
3
Find the exact function value, if it exists, of
7
sin
.
6
a.
c.
1
2
3
2
3
b.
2
1
d.
2
Given right triangle ABC with a = 16.5
and A = 23.5º, find c. Standard lettering
has been used.
a. 18.0
b. 41.4
c. 15.1
d. 6.6
Convert 220º to radian measure in terms of
π.
11
a.
9
c.
9
11
11
b.
18
11
d.
9
8
Given that cos
and that the
89
terminal side is in quadrant III, find sin.
a.
5
89
5
c.
89
b.
8
5
5
d.
8
3
Find cos
exactly in degrees.
2
1
a. 120º
b. –60º
c. 150º
d. 30º
For the function y 2 cos x 4,
4
find the period.
2
a.
3
b. π
c. 2π
d. 4π
Simplify
a.
b.
sec x cot x cos x .
1 sin x
sin x
cos x 2
sin x
c.
1 csc x
d.
cot x 1
x
Simplify 2 sin 1.
2
2
a.
cos2x
b.
cos x
c.
sin x
d.
cos x
Use a sum or a difference identity to
7
find sin
exactly.
12
a.
2 6
4
c.
2 6
4
2 6
b.
4
d.
2 6
4
Use a half-angle identity to evaluate
5
exactly.
cos
8
2 2
a.
2
2 2
b.
2
2 3
c.
2
2 3
d.
2
Find all the solutions of
3 4 sin x 0 in 0, 2 .
2
a.
c.
2
b.
,
3 3
5 7 11
,
6 6
,
6
,
6
d.
2 5
, , ,
6 3 3 6
2 4 5
,
3 3
,
3
,
3
Find all the solutions of
2sin x cos x 2 sin x in 0, 2 .
a.
c.
3
,
4 4
3
,
2 2
b.
3 3
, , ,
4 2 4 2
3
d. 0, , ,
4 4
Solve triangle ABC to find b.
a = 10 m, B = 14º, C = 28º
a. 3.6 m
b. 13.1 m
c. 5.2 m
d. No solution
Solve triangle ABC to find A.
a = 12.5 in., b = 10.5 in., c = 8.5 in.
a. 8.5º
b. 87.9º
c. 81.5º
d. No solution