MATH 1810-001 TestI (Study Guide)
Find the slope of the line passing through the given pair of points.
1) (9, 5) and (9, -8)
13
1
A) Not defined
B)
C) 18
6
Find the slope of the line.
2) A line parallel to 4y - 5x = 8
5
4
A)
B)
4
5
1)
D) 0
2)
C) -
3) A line perpendicular to 7x = 4y - 5
4
7
A)
B) 7
4
8
5
D) -
5
4
3)
4
C) 7
Find an equation in slope-intercept form (where possible) for the line.
4) Through (-4, 4), with undefined slope
A) 1x + 4y = 0
B) y = 4
C) 1x - 4y = 0
5
D) 4
4)
D) x = -4
5) y-intercept -2, x-intercept 10
1
A) y = - x - 2
B) y = 5x + 10
5
5)
1
C) y = x - 2
5
D) y = - 5x + 10
6) Through (-1, -4), perpendicular to 7x - 2y = -15
1
15
2
30
A) y = x B) y = - x 2
2
7
7
7
7
C) y = - x 2
2
2
30
D) y = x 7
7
7) Through (5, -3), parallel to -7x + 9y = -44
7
62
7
62
A) y = x B) y = - x +
9
9
9
9
5
44
C) y = - x 9
9
9
3
D) y = x +
7
7
6)
7)
1
Find the slope of the line.
8)
8)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
B)
3
2
x
-4
-6
-8
-10
A) -
2
3
C)
2
3
D) -
3
2
Solve the problem.
9) After two years on the job, an engineer's salary was $60,000. After seven years on the job, her
salary was $66,000. Let y represent her salary after x years on the job. Assuming that the
change in her salary over time can be approximated by a straight line, give an equation for this
line in the form y = mx + b.
A) y = 1200x + 60,000
B) y = 1200x + 57,600
C) y = 6000x + 60,000
D) y = 6000x + 48,000
Evaluate the function as indicated.
10) Find g(k2 ) when g(x) = -3 - 5x.
A) -3 + 5k2
9)
10)
B) -3 + -5k2
C) -3 - 5x2
D) -3 + k2
Write a cost function for the problem. Assume that the relationship is linear.
11) A cab company charges a base rate of $1.00 plus 10 cents per minute. Let C(x) be the cost in
dollars of using the cab for x minutes.
A) C(x) = 1.00x - 0.10
B) C(x) = 1.00x + 0.10
C) C(x) = 0.10x + 1.00
D) C(x) = 0.10x - 1.00
Solve the problem.
12) Let the demand and supply functions be represented by D(p) and S(p), where p is the price in
dollars. Find the equilibrium price and equilibrium quantity for the given functions.
D(p) = 175,500 - 270p
S(p) = 900p
A) $630; 5400
B) $630; 135,000
C) $150; 135,000
D) $195; 122,850
13) Given the supply and demand functions below, find the demand when p = $12.
S(p) = 5p
D(p) = 120 - 4p
A) 72
B) 60
C) 48
D) 132
2
11)
12)
13)
14) A shoe company will make a new type of shoe. The fixed cost for the production will be
$24,000. The variable cost will be $36 per pair of shoes. The shoes will sell for $103 for each
pair. What is the profit if 600 pairs are sold?
A) $59,400
B) $64,200
C) $16,200
D) $40,200
14)
15) Midtown Delivery Service delivers packages which cost $1.50 per package to deliver. The
fixed cost to run the delivery truck is $92 per day. If the company charges $5.50 per package,
how many packages must be delivered daily to break even?
A) 15 packages
B) 13 packages
C) 61 packages
D) 23 packages
15)
Determine whether the rule defines y as a function of x.
16)
x y
-1 3
1 1
5 2
9 9
12 -9
A) Function
16)
B) Not a function
17)
17)
X
Y
6
93
16
16
71
35
37
2
103
A) Function
B) Not a function
Give the domain of the function.
18) f(x) = 16 - x
A) (-∞, 16]
C) [0, 16]
18)
B) (-∞, ∞)
D) (-∞, 16) ∪ (16, ∞)
3
Give the domain and range of the function.
19)
19)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4
-6
-8
-10
A) Domain {-6, 4, 6} ; Range {-8, -4, -1, 1, 4, 8}
B) Domain [-8, 8] ; Range [-6, 6]
C) Domain [-6, 6] ; Range [-8, 8]
D) Domain {-8, -4, -1, 1, 4, 8} ; Range {-6, 4, 6}
Use the graph to evaluate the function f(x) at the indicated value of x.
20) Find f(1.5).
20)
f (x)
2
1
-2
-1
1
2
x
-1
-2
A) -2
C) 0
B) 1
D) None of these are correct.
Evaluate the function.
21) f(x) = -3x2 + 2x - 2; Find f(r + h).
A) -3r2 - 3rh - 3h2 + 2r + 2h - 2
21)
B) -3r2 - 6rh - 3h2 + 2r + 2h - 2
C) -3r2 - 3h2 - 4r - 4h - 2
D) -3r2 - 3h2 + 2r + 2h - 2
4
Evaluate the function for the given value.
x-5
1
if x ≠ 2x + 1
2
22) f(x) =
1 ; f(5)
12
if x = 2
A) 0
Find
B)
22)
1
11
C) 12
D) 60
f(x + h) - f(x)
.
h
23) f(x) =
4
x + 21
23)
A)
4
(x + h + 21)(x + 21)
B)
-84
(x + h + 21)(x + 21)
C)
-4
(x + 4)2
D)
-4
(x + h + 21)(x + 21)
Decide whether the graph represents a function.
24)
24)
y
x
A) Function
B) Not a function
Classify the function as even, odd, or neither.
25) f(x) = -2x3 + 4x
A) Even
25)
B) Odd
C) Neither
Solve the equation.
26) 2 (5 + 3x) =
A) 8
1
16
26)
B) 3
C) -3
D)
Classify the function as even, odd, or neither.
27) f(x) = 7x3 - 4
A) Even
1
8
27)
B) Odd
C) Neither
5
Solve the problem.
28) Assume the cost of a car is $15,000. With continuous compounding in effect,find the number of
years it would take to double the cost of the car at an annual inflation rate of 5%. Round to the
nearest hundredth.
A) 192.32 yr
B) 13.86 yr
C) 1.92 yr
D) 206.18 yr
29) Find the interest earned on $8000 invested for 6 years at 7.2% interest compounded quarterly.
Round to the nearest cent.
A) $12,275.43
B) $4275.43
C) $1909.76
D) $1.53
Evaluate the logarithm without using a calculator.
30) log8 32
3
5
A)
B)
2
4
C)
4
3
D)
5
3
31)
D) 8
Write the exponential equation in logarithmic form.
1
32) 2 -3 =
8
1
=2
8
32)
B) log1/8 2 = -3
C) log2 -3 =
1
8
D) log2
1
= -3
8
Use the properties of logarithms to find the value of the expression.
A
33) Let logb A = 3.508 and logb B = 0.259. Find logb .
B
A) 0.909
B) 3.767
C) 3.249
B) 1
6
C) 5
33)
D) 3.508
Solve the equation.
34) log (x + 4) = log (2x + 5)
A) -1
29)
30)
Use the properties of logarithms to find the value of the expression.
31) Let logb A = 3 and logb B = -5. Find logb AB.
A) -15
B) 15
C) -2
A) log-3
28)
34)
D) 9
Solve the problem.
35) Assume the cost of a car is $21,000. With continuous compounding in effect, find the number
of years it would take to double the cost of the car at an annual inflation rate of 4%. Round to
the nearest hundredth.
A) 2.49 yr
B) 17.33 yr
C) 266.14 yr
D) 248.81 yr
36) A college student invests $11,000 in an account paying 5% per year compounded annually. In
how many years will the amount at least triple? Round to the nearest tenth when necessary.
A) 30.8 yr
B) 22.5 yr
C) 25.7 yr
D) 28.4 yr
6
35)
36)
37) A certain noise has intensity 3.55 × 108 I0 . What is the decibel rating of this sound? Use the
37)
formula D = 10 log I0 , where I0 is a faint threshold sound, and I is the intensity of the sound.”
A) 76 decibels
B) 9 decibels
C) 197 decibels
D) 86 decibels
38) Find the effective rate corresponding to the nominal rate. 6% compounded monthly. Round to
the nearest hundredth.
A) 6.17%
B) 6.23%
C) 6.26%
D) 6.12%
38)
39) The number of books in a small library increases according to the function B = 3100e0.03t,
where t is measured in years. How many books will the library have after 7 years? Round to
the nearest book.
A) 3824 books
B) 5028 books
C) 4838 books
D) 2101 books
39)
40) In the formula N = Iekt, N is the number of items in terms of an initial population I at a given
time t and k is a growth constant equal to the percent of growth per unit time. How long will it
take for the population of a certain country to double if its annual growth rate is 3.4%? Round
to the nearest year.
A) 20 yr
B) 1 yr
C) 9 yr
D) 59 yr
40)
Decide whether the limit exists. If it exists, find its value.
41) lim f(x) and lim f(x)
x→0 x→0 +
8
41)
f(x)
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
A) -1, 4
B) 4, -1
C) -4, -1
D) 4, 1
Solve the problem.
42) In the formula A(t) = A0 ekt, A(t) is the amount of radioactive material remaining from an
initial amount A0 at a given time t and k is a negative constant determined by the nature of the
material. A certain radioactive isotope has a half -life of approximately 900 years. How many
years would be required for a given amount of this isotope to decay to 30% of that amount?
A) 1533 yr
B) 1563 yr
C) 463 yr
D) 630 yr
7
42)
Give an appropriate answer.
43) Let lim f(x) = 2 and lim g(x) = -4. Find lim [f(x) - g(x)].
x→3
x→3
x→3
A) 3
B) -2
C) 2
43)
D) 6
Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.
x2 + 8x + 12
44) lim
x+2
x→-2
A) 8
45) lim
x→∞
B) Does not exist
D) 32
-5x2 + 7x - 4
3x2 + 6
A) 0
46) lim
x→∞
A)
C) 4
45)
B) -
3
2
C) ∞
D) -
5
3
4x2 + 2x - 7x4
6x2 - 4x + 5
2
3
44)
46)
B) -∞
C) ∞
D) Does not exist
Use the properties of limits to help decide whether each limit exits. If a limit exists, find its value.
-3x + 9
47) Let f(x) = 1
3x - 10
A) 0
if x < 1
if x = 1 . Find lim f(x).
x→1
if x > 1
B) -7
47)
C) 6
D) Does not exist
2
48) Let f(x) = x - 5 if x < 0 . Find lim f(x).
2
if x ≥ 0
x→-2
A) -1
48)
B) Does not exist
C) 2
D) -5
Solve the problem.
49) Find the present value of the deposit. $13,000 at 8% compounded continuously for 10 years.
Round to the nearest dollar.
A) $73,022
B) $235,522
C) $5841
D) $199,120
50) The population of a particular city is increasing at a rate proportional to its size. It follows the
function P(t) = 1 + ke0.1t where k is a constant and t is the time in years. If the current
population is 49,000, in how many years is the population expected to be 122,500?
A) 70 yr
B) 9 yr
C) 5 yr
D) 4 yr
8
49)
50)
Answer Key
Testname: STUDYGUIDE TESTI_14
1) A
2) A
3) C
4) D
5) C
6) B
7) A
8) D
9) B
10) B
11) C
12) C
13) A
14) C
15) D
16) A
17) A
18) A
19) B
20) C
21) B
22) A
23) D
24) B
25) B
26) C
27) C
28) B
29) B
30) D
31) C
32) D
33) C
34) A
35) B
36) B
37) D
38) A
39) A
40) A
41) B
42) B
43) D
44) C
45) D
46) B
47) D
48) A
9
Answer Key
Testname: STUDYGUIDE TESTI_14
49) C
50) B
10