Answers25-26 KCS21 Precalculus ICCumulative Exam

Cumulative Exam — Cumulative exam Answers

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A plane flies 35 km in the direction N 30° W, then flies 60 km in the direction N 60° E. How far is the plane from its original location?

A
29.64 km
B
58.21 km
C
69.46 km
D
93.66 km
2
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The explicit rule for an arithmetic sequence is What is the value of the 47th term? Round to the nearest tenth, if necessary.

Question illustration
A
–55.7
B
–26.4
C
45.6
D
65.8
3

Which graph represents 9x2 – 16y2 – 54x + 64y – 127 = 0?

A
On a coordinate plane, an Ellipse has center (3, 2) and goes through (7, 2), (3, negative 1), (negative 1, 2), and (3, 5).
Option A
B
On a coordinate plane, an Ellipse has center (3, 2) and goes through (6, 2), (3, negative 2), (0, 3), and (3, 6).
Option B
C
Option
Option C
D
On a coordinate plane, one part of a conic graph goes through (negative 1, 6), has a vertex at (0, 2), and goes through (negative 1, negative 1). The second part goes through (7, 6), has a vertex at (6, 2), and goes through (7, negative 1).
Option D
4

Becky is offered the two deals below.Deal 1: She will get a quarter on the first day of the week. Each day thereafter for one week, she will receive double what she received on the previous day.Deal 2: She will get $4 each day for 1 week.Which statement is true in every aspect regarding these two deals?

A
She should go with deal 1 because is greater than by $3.75.
Option A
B
She should go with deal 1 because is greater than by $35.50.
Option B
C
She should go with deal 2 because is greater than by $27.33.
Option C
D
She should go with deal 2 because is greater than by $48.50.
Option D
5

Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.Heron’s formula: Area

Question illustration
A
6 square feet
B
7 square feet
C
19 square feet
D
22 square feet
6

Which conic section is represented by the following equation?–5x2 + 9xy + 5y2 + 6x – 4y + 11 = 0

A
circle
B
ellipse
C
parabola
D
hyperbola
7

Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?

A
30° only
B
90° only
C
30° or 150°
D
30°, 90°, or 150°
8

The graph of an ellipse is shown.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

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

Question illustration
A
0 is less than equal to x and x is less than StartFraction pi over 4 EndFraction
Option A
B
and
Option B
C
x is greater than StartFraction pi over 4 EndFraction but less than StartFraction 5pi over 4 EndFraction
Option C
D
and
Option D
10

Which is the graph of ?

Question illustration
A
A smooth curve resembling an arctangent function. The x-axis ranges from -6 to 6, and the y-axis from -p to p. The curve approaches horizontal asymptotes at y = p/2 and y = -p/2, passing through the origin.
Option A
B
A graph of a function with asymptotic behavior. The x-axis ranges from -5 to 5, and the y-axis ranges from -p to p. The curve is located in the fourth quadrant, approaching the y-axis asymptotically as x approaches zero from both positive and negative directions. The curve also approaches zero asymptotically as x moves away from zero in both directions. The function does not intersect either axis.
Option B
C
A graph of a function with the x-axis ranging from -2.5 to 2.5 and the y-axis ranging from -p to p. The curve passes through the origin (0,0) and changes direction at y=0. It intersects the x-axis at two points, approximately at x=-1 and x=1. The curve is symmetric about the origin.
Option C
D
The image shows a mathematical graph plotted on a Cartesian coordinate system. The x-axis ranges from -2 to 2, and the y-axis ranges from -p to p. A smooth, continuous curve intersects the x-axis at approximately 1. The curve extends into both the positive and negative quadrants. The point p is labeled on the positive y-axis and -p on the negative y-axis.
Option D
11

To solve the trigonometric inequality over the interval radians, Gabby performed the following steps, first simplifying the inequality and then setting both sides equal to y and graphing the equations. Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: In which step did she first make an error, and what was the error?

Question illustration
A
She first made an error in step 3 because she should not have subtracted and added to the right side of the inequality.
Option A
B
She first made an error in step 4 because the simplified form of the inequality should have been instead of .
Option B
C
She first made an error in step 5 because she did not correctly graph .
Option C
D
She first made an error in step 6 because she chose the wrong interval in which the graph of one equation is at or above the graph of the other equation.
12

Which graph represents points on the polar curve r = –4sin(3θ)?

A
On a polar coordinate plane, points are at (4, StartFraction 2 pi Over 4 EndFraction), (4, 0), and (4, StartFraction 4 pi Over 3 EndFraction).
Option A
B
On a polar coordinate plane, points are at (4, pi), (4, StartFraction pi Over 3 EndFraction), and (4, StartFraction 5 pi Over 3 EndFraction).
Option B
C
On a polar coordinate plane, points are at (4, StartFraction pi Over 6 EndFraction), (4, StartFraction 5 pi Over 6 EndFraction), and (4, StartFraction 3 pi Over 2 EndFraction).
Option C
D
On a polar coordinate plane, point are at (4, StartFraction pi Over 2 EndFraction), (4, StartFraction 11 pi Over 6 EndFraction), (4, StartFraction 7 pi Over 6 EndFraction).
Option D
13

Which of the following represents a geometric sequence? I II III IV

Question illustration
A
I
B
II
C
III
D
IV
14

A picture frame has the shape of an ellipse defined by the equation with units in inches. A hook is placed on the back of the picture frame to hang it on the wall. The hook is located at one of the foci of the ellipse. What is the distance from the hook to the top of the picture frame?

Question illustration
A
2 in.
B
4 in.
C
6 in.
D
8 in.
15

What is the area of triangle ABC? Round to the nearest square unit.

Question illustration
A
8 square units
B
15 square units
C
33 square units
D
618 square units
16

Which equation represents a parabola with its vertex at (1, –5) and its focus at (1, 0)?

A
= (x – 1)2
Option A
B
20(y + 5) = (x – 1)2
C
–20(y + 5) = (x – 1)2
D
= (x – 1)2
Option D
17

Review the diagram of the unit circle.

Question illustration
A
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus 1) squared minus (sine (u) minus 0) squared EndRoot
Option A
B
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (negative v) minus 1) squared + (sine (negative v) minus 0) squared EndRoot
Option B
C
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u) minus cosine (negative v) ) squared + (sine (u) minus sine (negative v)) squared
Option C
D
StartRoot (cosine (u + v) minus 1) squared + (sine (u + v) minus 0) squared EndRoot = StartRoot (cosine (u + v) minus cosine (u) ) squared + (sine (u + v) minus sine (u)) squared EndRoot
Option D
18

What is the exact value of sin(105°)?

A
Negative StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option A
B
Negative StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option B
C
StartFraction StartStartRoot 2 minus StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option C
D
StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction
Option D
19

Which summation formula is equivalent to the one below?

Question illustration
A
mc013-2.jpg
Option A
B
mc013-3.jpg
Option B
C
mc013-4.jpg
Option C
D
mc013-5.jpg
Option D
20

The equations and are graphed below. According to the graph, which of the following is part of the solution to the trigonometric inequality over the interval radians?

Question illustration
A
x equal to StartFraction pi over 6 EndFraction
Option A
B
x equal to StartFraction 2pi over 3 EndFraction
Option B
C
x equal to StartFraction 4pi over 3 EndFraction
Option C
D
x equal to StartFraction 3 pi over 2 EndFraction
Option D

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