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Cumulative Exam — Cumulative exam Answers

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By what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3?M = the magnitude of an earthquakeI = the intensity of an earthquakeI0 = the smallest seismic activity that can be measured, which is 1

Question illustration
A
1.01
B
1.21
C
1.26
D
10.44
2
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The center of an earthquake was detected along the Pacific Rim. Geologists determined that the distance the seismic waves traveled is represented by r = 15sin(θ), where r is in miles. Which graph represents the distance the waves traveled?

A
On a polar coordinate plane, a circle goes through (15, 0) and (15, StartFraction pi Over 2 EndFraction)
Option A
B
On a polar coordinate plane, a circle goes through (30, 0) and (30, StartFraction pi Over 2 EndFraction).
Option B
C
On a polar coordinate plane, a circle goes through (0, 0) and (3, StartFraction pi Over 2 EndFraction).
Option C
D
On a polar coordinate plane, a circle goes through (0, 0) and (25, StartFraction pi Over 2 EndFraction).
Option D
3

Which graph shows the solution set of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

A company’s equipment manager buys $7,000 worth of equipment. This equipment depreciates 19% each year. The manager can replace the equipment after its value falls below $500.After how many years can the manager first replace the equipment?

A
10
B
11
C
12
D
13
5

Which graph includes a function, its inverse, and a dashed line that verifies the relationship?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

What is the solution set to log(x + 7) > log3x?

A
(–∞, 3)
B
(–7, 0)
C
(0, 3)
D
(3, ∞)
7

Given the function g(x) = 41x3 + a for some constant a, which describes the inverse function g–1(x)?

A
no restriction on the domain of g(x); inverse is g–1(x) =
Option A
B
no restriction on the domain of g(x); inverse is g–1(x) =
Option B
C
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) =
Option C
D
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) =
Option D
8

The table shows several points for function j(t).

Question illustration
A
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries negative 1, negative 2, negative 10, negative 250.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 0.5, 0.1, 0.004.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 2, 10, 250. Column 2 is labeled j Superscript negative 1 Baseline (t) with entries 1, 8, 10, 17.
Option D
9

What is the exact value of cos(c + d), given for c in Quadrant II and for d in Quadrant III?

Question illustration
A
Negative StartFraction 47 Over 100 EndFraction
Option A
B
Negative 1 and StartFraction 3 Over 100 EndFraction
Option B
C
StartFraction 21 minus 24 StartRoot 7 EndRoot Over 100 EndFraction
Option C
D
StartFraction 21 + 24 StartRoot 7 EndRoot Over 100 EndFraction
Option D
10

Review the graph of z2.

Question illustration
A
A
B
B
C
C
D
D
11

What is the solution to the trigonometric inequality over the interval radians?

Question illustration
A
x is greater than StartFraction pi over 4 EndFraction but less than StartFraction 7pi over 4 EndFraction
Option A
B
and
Option B
C
x is greater than StartFraction pi over 2 EndFraction but less than StartFraction 3pi over 2 EndFraction
Option C
D
and
Option D
12

Given: < A < and , < B < What is the value of cos(A – B)?

Question illustration
A
Negative StartFraction 2 StartRoot 5 EndRoot Over 25 EndFraction
Option A
B
Negative StartFraction StartRoot 5 EndRoot Over 5 EndFraction
Option B
C
StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction
Option C
D
StartFraction 11 StartRoot 5 EndRoot Over 25 EndFraction
Option D
13

Information about two gears is shown in the table.Which statements compare the angular and linear velocities of the gears? Check all that apply.

Question illustration
A
Gear 1 has a greater angular velocity than Gear 2.
B
Gear 1 has a lesser angular velocity than Gear 2.
C
Gear 1 has a greater linear velocity than Gear 2.
D
Gear 1 has a lesser linear velocity than Gear 2.
14

Which is an x-intercept of the graph of the function ?

Question illustration
A
(StartFraction pi over 6 EndFraction, 0)
Option A
B
(StartFraction pi over 3 EndFraction , 0)
Option B
C
(3pi, 0)
Option C
D
(6pi, 0)
Option D
15

Review the graph.

Question illustration
A
The period of the graph is
Option A
B
The amplitude of the graph is 2 units.
C
The domain of the graph is the set of x-values from –3 to 3, inclusive.
D
The graph represents a reflection over the x-axis of the function y = 3sin(2x).
16

Which expression is equivalent to ?

Question illustration
A
StartFraction negative 1 minus tangent (2 x) Over 1 minus (negative 1) (tangent (2 x) ) EndFraction
Option A
B
StartFraction negative 1 minus tangent (2 x) Over 1 + (negative 1) (tangent (2 x) ) EndFraction
Option B
C
StartFraction 1 minus tangent (2 x) Over 1 + (1) (tangent (2 x) ) EndFraction
Option C
D
StartFraction 1 + tangent (2 x) Over 1 minus (1) (tangent (2 x) ) EndFraction
Option D
17

What is the vertical shift of the graph of the parent cosecant function to the graph of the function below?

Question illustration
A
1 unit down
B
2 units down
C
3 units down
D
4 units down
18

Which trigonometric functions have a domain of [–1, 1]?

A
y = arcsinx and y = arccosx
B
y = arccosx and y = arctanx
C
y = arcsinx and y = arctanx
D
y = arcsecx and y = arccscx
19

Let csc(x) = , where . Which ratio has a value of ?

Question illustration
A
cos(x)
B
sin(x)
C
sec(x)
D
cot(x)
20

For the complex number z = , what is arg(z)?

Question illustration
A
150°
B
210°
C
240°
D
330°

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