The figure shows a circle centered at the origin with an angle of measure θ radians in standard position. The terminal ray of the angle intersects the circle at point R, and point S also lies on the circle. The coordinates of R are (-x, y), and the coordinates of S are (x, y). Which of the following is true about the cosine of θ?

cos θ = -x/8, because it is the ratio of the horizontal displacement of R from the y-axis to the distance between the origin and R.

cos θ = x/8, because it is the ratio of the horizontal displacement of S from the y-axis to the distance between the origin and S.

cos θ = -y/8, because it is the ratio of the vertical displacement of R from the x-axis to the distance between the origin and R.

cos θ = y/8, because it is the ratio of the vertical displacement of S from the x-axis to the distance between the origin and S.

The figure shows a circle centered at the origin with an angle of measure θ radians in standard position. The terminal ray of the angle intersects the circle at point S, and point P also lies on the circle. The coordinates of P are (x, y), and the coordinates of S are (x, -y). Which of the following is true about the sine of θ?

sin θ = -y/5, because it is the ratio of the vertical displacement of S from the x-axis to the distance between the origin and S.

sin θ = x/5, because it is the ratio of the horizontal displacement of P from the y-axis to the distance between the origin and P.

sin θ = -x/5, because it is the ratio of the horizontal displacement of S from the y-axis to the distance between the origin and S.

sin θ = y/5, because it is the ratio of the vertical displacement of P from the x-axis to the distance between the origin and P.

The figure shows a circle centered at the origin with an angle of measure θ radians in standard position. The terminal ray of the angle intersects the circle at point P, and point R also lies on the circle. The coordinates of P are (x, y) and the coordinates of R are (x, -y). Which of the following is true about the tangent of θ?

tan θ = y/x, because it is the ratio of the vertical displacement of P to the horizontal displacement of P.

tan θ = x/y, because it is the ratio of the horizontal displacement of P to the vertical displacement of P.

tan θ = -y/x, because it is the ratio of the vertical displacement of R to the horizontal displacement of R.

tan θ = -x/y, because it is the ratio of the horizontal displacement of R to the vertical displacement of R.

The figure shows a circle centered at the origin with an angle of measure θ radians in standard position and a point P on the circle. The terminal ray of the angle intersects the circle at point Q. The length of arc PQ is 15 units. Which of the following gives the distance of point Q from the x-axis?

\( 13\sin \left( \frac{15}{13} \right) \)

\( \cos \left( \frac{15}{13} \right) \)

\( \sin \left( \frac{15}{13} \right) \)

\( 13\cos \left( \frac{15}{13} \right) \)

The figure shows a circle centered at the origin with an angle of measure θ radians in standard position and a point P on the circle. The terminal ray of the angle intersects the circle at point Q. The length of arc PQ is 3 units. Which of the following gives the distance of point Q from the y-axis?

4\cos \left( \frac{3}{4} \right)

3\cos \left( \frac{3}{4} \right)

3\cos \left( \frac{4}{3} \right)

4\cos \left( \frac{4}{3} \right)

The figure shows the graph of a sinusoidal function f. What are the values of the period and amplitude of f?

The period is π/2, and the amplitude is 2.

The period is π, and the amplitude is 1.

The period is π, and the amplitude is 2.

The period is π/2, and the amplitude is 1.

The figure shows the graph of a sinusoidal function g. What are the values of the period and amplitude of g?

The period is 4, and the amplitude is 2.

The period is 2, and the amplitude is 2.

The period is 2, and the amplitude is 4.

The period is 4, and the amplitude is 4.

The sinusoidal function h has a minimum at the point (2π, -1). The first maximum after reaching this minimum value occurs at the point (5π, 7). What are the values of the period and amplitude of h?

The period is 6π, and the amplitude is 4

The period is 6π, and the amplitude is 8

The period is 12π, and the amplitude is 4

The period is 12π, and the amplitude is 8

The sinusoidal function k has a minimum at the point (π/2, -12). The first maximum after reaching this minimum value occurs at the point (π, -2). Which of the following gives the values of the period and the midline of k?

The period is π, and the midline is y = -7

The period is π/2, and the midline is y = -7

The period is π/2, and the midline is y = 5

The period is π, and the midline is y = 5

Which of the following best describes the behavior of g over the interval 0 < θ < π/2?

g is decreasing at an increasing rate.

g is increasing at an increasing rate.

g is increasing at a decreasing rate.

g is decreasing at a decreasing rate.

Which of the following best describes how the rate of change of g is changing over the interval π

The rate of change of g is decreasing because the graph of g is concave down on the interval π

The rate of change of g is increasing because the graph of g is concave up on the interval π

The rate of change of g is decreasing because the graph of g is concave up on the interval π

The rate of change of g is increasing because the graph of g is concave down on the interval π

Which of the following best describes the rate of change of g over the interval 3π/2

The rate of change of g is negative and decreasing.

The rate of change of g is positive and increasing.

The rate of change of g is positive and decreasing.

The rate of change of g is negative and increasing.

Which of the following correctly describes how the rate of change of h is changing on the interval [0, π/2]?

The rate of change of h is decreasing because the graph of h is concave down.

The rate of change of h is increasing because the graph of h is concave up.

The rate of change of h is decreasing because the graph of h is concave up.

The rate of change of h is increasing because the graph of h is concave down.

Which of the following correctly describes how the rate of change of h is changing on the interval [π/2, π]?

The rate of change of h is increasing because the graph of h is concave up.

The rate of change of h is decreasing because the graph of h is concave up.

The rate of change of h is increasing because the graph of h is concave down.

The rate of change of h is decreasing because the graph of h is concave down.

Which of the following correctly describes how the rate of change of h is changing on the interval [π, 3π/2]?

The rate of change of h is increasing because the graph of h is concave up.

The rate of change of h is decreasing because the graph of h is concave up.

The rate of change of h is increasing because the graph of h is concave down.

The rate of change of h is decreasing because the graph of h is concave down.

Which of the following correctly describes how the rate of change of h is changing on the interval [3π/2, 2π]?

The rate of change of h is decreasing because the graph of h is concave down.

The rate of change of h is increasing because the graph of h is concave up.

The rate of change of h is decreasing because the graph of h is concave up.

The rate of change of h is increasing because the graph of h is concave down.

AP Precalculus Unit 3 Part A Passwater's MCQ Exam Review

Authored by Stefanie Frey

Mathematics

12th Grade

CCSS covered

Used 102+ times

AP Precalculus Unit 3 Part A Passwater's MCQ Exam Review

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The figure shows two full periods of the periodic function f. Which of the following statements is true?

The period of f is 5, and f(31) = 1

The period of f is 10, and f(31) = 1

The period of f is 5, and f(31) = 3

The period of f is 10, and f(31) = 3

Tags

CCSS.HSF.TF.A.4

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Using the graph of the periodic function g below, where two full periods of g are shown, what is the period of g?

Tags

CCSS.HSF.TF.A.4

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Using the graph of the periodic function g, what is the value of g(32)?

Tags

CCSS.HSF.TF.A.4

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Using the graph of the periodic function g, on which of the following intervals is g decreasing?

(70, 72)

(72, 74)

(74, 76)

(76, 78)

Tags

CCSS.HSF-IF.C.7B

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the value of ( f(3) )? Use the information provided in the table where the graph of f is periodic with a period of 8. Values of f are shown at selected values of x.

-11

-9

Tags

CCSS.HSF-LE.A.1B

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the value of ( f(-4) )? Refer to the table where the graph of f is periodic with a period of 8, and values of f are shown at selected values of x.

-10

-6

Tags

CCSS.HSF-LE.A.1B

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

For which of the following values of x does f(x) = -4? Consider the table where the graph of f is periodic with a period of 8, and values of f are shown at selected values of x.

x = -12

x = -8

x = 4

x = 9

Tags

CCSS.HSF-LE.A.1B

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AP Precalculus Unit 3 Part A Passwater's MCQ Exam Review

The figure shows two full periods of the periodic function f. Which of the following statements is true?

Using the graph of the periodic function g below, where two full periods of g are shown, what is the period of g?

Using the graph of the periodic function g, what is the value of g(32)?

Using the graph of the periodic function g, on which of the following intervals is g decreasing?

What is the value of ( f(3) )? Use the information provided in the table where the graph of f is periodic with a period of 8. Values of f are shown at selected values of x.

What is the value of ( f(-4) )? Refer to the table where the graph of f is periodic with a period of 8, and values of f are shown at selected values of x.

For which of the following values of x does f(x) = -4? Consider the table where the graph of f is periodic with a period of 8, and values of f are shown at selected values of x.

What is the value of ( h(2) )? Use the information provided in the table where the graph of h is periodic where h(x + 9) = h(x). Values of h are shown at selected values of x.

What is the value of ( h(h(-3)) )? Refer to the table where the graph of h is periodic and h(x + 9) = h(x). Values of h are shown at selected values of x.

What is the value of ( h(9k - 1) ), where k is an integer? Consider the table where the graph of h is periodic and h(x + 9) = h(x). Values of h are shown at selected values of x.

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