MTH 112 PRACTICE TEST #3 Sections 2.7, 2.8, 3.1 - 3.4 + study old tests (#1 and #2)
Solve the polynomial inequality. Show your boundary
points and a (+) or (-) for each interval on the number
line. Express the solution set in interval notation.
1) x2 - 5x + 4 > 0
Determine the constant of variation for the stated
condition.
8) g varies directly as f2 , and g = 180 when f = 6.
If y varies directly as x, find the direct variation equation
for the situation.
9) y = 0.4 when x = 0.2
Solve the polynomial inequality and graph the solution
set on a number line. Express the solution set in interval
notation.
2) 9x2 - 2x ≤ 0
Solve the problem.
10) If y varies directly as the cube of x, and y = 12
when x = 36, find y when x = 9.
11) If the resistance in an electrical circuit is held
constant, the amount of current flowing
through the circuit is directly proportional to
the amount of voltage applied to the circuit.
When 3 volts are applied to a circuit,
75 milliamperes of current flow through the
circuit. Find the new current if the voltage is
increased to 11 volts.
3) x < 42 - x2
Write an equation that expresses the relationship. Use k
as the constant of variation.
12) r varies inversely as b.
Solve the rational inequality. Show your boundary
points, zeros and values for which the rational is
undefined, and a (+) or (- ) for each interval on the
number line. Express the solution set in interval
notation.
x - 5
4)
> 0
x + 3
If y varies inversely as x, find the inverse variation
equation for the situation.
1
13) y = when x = 25
5
Solve the problem.
5) 6)
14) x varies inversely as y 2 , and x = 4 when y = 12.
Find x when y = 4.
(x - 1)(3 - x)
≤ 0
(x - 2)2
Solve.
15) The amount of time it takes a swimmer to
swim a race is inversely proportional to the
average speed of the swimmer. A swimmer
finishes a race in 50 seconds with an average
speed of 3 feet per second. Find the average
speed of the swimmer if it takes 30 seconds to
finish the race.
x
≥ 2
x + 4
Write an equation that expresses the relationship. Use k
as the constant of variation.
7) w varies directly as the square of y.
1
21) f(x) = 0.6x
Solve the problem.
16) The volume V of a given mass of gas varies
directly as the temperature T and inversely as
the pressure P. A measuring device is
calibrated to give V = 154 in3 when T = 110°
6
y
4
and P = 10 lb/in2 . What is the volume on this
device when the temperature is 440° and the
pressure is 20 lb/in2 ?
2
-6
-4
-2
2
6 x
4
-2
17) Body-mass index, or BMI, takes both weight
and height into account when assessing
whether an individual is underweight or
overweight. BMI varies directly as oneʹs
weight, in pounds, and inversely as the square
of oneʹs height, in inches. In adults, normal
values for the BMI are between 20 and 25. A
person who weighs 182 pounds and is 71
inches tall has a BMI of 25.38. What is the BMI,
to the nearest tenth, for a person who weighs
120 pounds and who is 65 inches tall?
-4
-6
Graph the function.
22) Graph g(x) = ex - 3.
y
6
4
Write an equation that expresses the relationship. Use k
as the constant of variation.
18) r varies jointly as b and the sum of p and h.
2
-6
-4
-2
2
4
6
x
-2
Approximate the number using a calculator. Round your
answer to three decimal places.
19) 3 2
-4
-6
Graph the function by making a table of coordinates.
20) f(x) = 5 x
6
Approximate the number using a calculator. Round your
answer to three decimal places.
23) e-0.6
y
4
Use the compound interest formulas A = P 1 + 2
-6
-4
-2
2
4
r nt
and A
n
= Pe rt to solve.
24) Find the accumulated value of an investment
of $800 at 10% compounded quarterly for 5
years.
6 x
-2
-4
25) Find the accumulated value of an investment
of $7000 at 7% compounded continuously for
6 years.
-6
Write the equation in its equivalent exponential form.
26) log x = 3
5
2
Write the equation in its equivalent logarithmic form.
27) 6 3 = x
Evaluate the expression without using a calculator.
39) eln 242
40) eln 203
Evaluate the expression without using a calculator.
28) log3 243
29) log
Use properties of logarithms to expand the logarithmic
expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
41) log (125x)
5
1
2 8
30) log 9
9
42) ln 31) log 2 11
2
32) log 1
5
43) log
Graph.
33) g(x) =log3 x
44) log
e5
9
7
5
3
y
x + 2
x5
y
9
6
-6
45) log
6
17
14 n 2 m
1
1
46) 5 log3 2 + log3 (r - 2) - log3 r
5
2
x
47) log t - log s + 6 log u
a
a
a
-6
48) 2ln a - 3 ln b
Use common logarithms or natural logarithms and a
calculator to evaluate to four decimal places
49) log 382
26
Find the domain of the logarithmic function.
34) f(x) = log (x - 5)
5
50) log
Evaluate or simplify the expression without using a
calculator.
1
35) log 100
π
17
Solve the equation by expressing each side as a power of
the same base and then equating exponents.
51) 3 (1 + 2x) = 243
36) 8 log 103.9
52) 16x + 9 = 64x - 5
37) ln e
38) ln 4
Solve the exponential equation. Express the solution set
in terms of natural logarithms.
53) 8 3x = 2.3
e
3
54) 3 x + 8 = 5
68) The population of a certain country is growing
at a rate of 2.6% per year. How long will it take
for this countryʹs population to double? Use
ln 2
the formula t = , which gives the time, t,
k
55) e x + 2 = 4
for a population with growth rate k, to double.
(Round to the nearest whole year.)
Solve the exponential equation. Use a calculator to obtain
a decimal approximation, correct to two decimal places,
for the solution.
56) 2 x + 6 = 3
69) The formula A = 106e0.032t models the
population of a particular city, in thousands, t
years after 1998. When will the population of
the city reach 120 thousand?
57) e2x - 8 - 10 = 1215
70) Find out how long it takes a $3300 investment
to double if it is invested at 7% compounded
semiannually. Round to the nearest tenth of a
r nt
.
year. Use the formula A = P 1 + n
58) 8 x = 14
Solve the logarithmic equation. Be sure to reject any value
that is not in the domain of the original logarithmic
expressions. Give the exact answer.
59) log (x - 2) = 3
2
60) log 3 (x + 6) + log 3 (x - 6) - log 3 x = 2
61) log (x + 2) - log x = 2
7
7
62) 4 ln (7x) = 8
63) log (x + 4) = log (4x - 5)
64) log 4x = log 5 + log (x - 3)
65) log (3x + 5) = log (3x + 8)
6
6
66) 2log x - log 15 = log 60
Solve the problem.
67) The population of a particular country was 23
million in 1984; in 1992, it was 32 million. The
exponential growth function A =23ekt
describes the population of this country t years
after 1984. Use the fact that 8 years after 1984
the population increased by 9 million to find k
to three decimal places.
4
Answer Key
Testname: 112PRACTICETEST3
1) (-∞, 1) ∪ (4, ∞)
2
2) 0, 9
3) (-7, 6)
4) (-∞, -3) or (5, ∞)
5) (-∞, 1] ∪ [3, ∞)
6) [-8, -4)
7) w = ky2
8) k = 5
9) y = 2x
3
10)
16
11) 275 milliamperes
k
12) r = b
13) y = 5
x
14) x = 36
15) 5 feet per second
16) V = 308 in3
17) 20
18) r = kb(p + h)
19) 4.729
20)
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
5
Answer Key
Testname: 112PRACTICETEST3
21)
6
y
4
2
-6
-4
-2
2
6 x
4
-2
-4
-6
22)
y
6
4
2
-6
-4
-2
2
4
6
x
-2
-4
-6
23) 0.549
24) $1310.89
25) $10,653.73
26) 5 3 = x
27) log x = 3
6
28) 5
29) -3
30) 1
31) 11
32) 0
6
Answer Key
Testname: 112PRACTICETEST3
33)
y
6
-6
6
x
-6
34) (5, ∞)
35) -2
36) 31.2
37) 1
1
38)
4
39) 242
40) 203
41) 3 + log x
5
42) 5 - ln 9
1
43) log y
5
7
44) log (x + 2) - 5 log x
3
3
1
45) log 17 - 2 log n - log m
14
14
14
9
46) log3 47) log
48) ln 32
5
r - 2
r
tu6
a s
a2
b3
49) 1.8248
50) 2.4750
51) {2}
52) 33
ln 2.3
53)
3 ln 8
54)
ln 5
- 8
ln 3
55) {ln 4 - 2}
56) -4.42
7
Answer Key
Testname: 112PRACTICETEST3
57) 7.56
58) 1.27
59) {10}
60) {12}
1
61) { }
24
62)
e2
7
63) 3
64) {15}
65) ∅
66) {30}
67) 0.041
68) 27 years
69) 2002
70) 10.1 years
8