Question 1

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for
the graph.
- 
$[ - 5,5 ]$ by $[ - 5,5 ]$

Accepted Answer

A)  $r = 2 + 2 \cos \theta$ 
B)  $r = 3 + 2 \cos \theta$ 
C)  $r = 4 + \cos \theta$ 
D)  $r = 2 + 3 \cos \theta$ 
A)  $r = 2 + 2 \cos \theta$ 
B)  $r = 3 + 2 \cos \theta$ 
C)  $r = 4 + \cos \theta$ 
D)  $r = 2 + 3 \cos \theta$

Question 2

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for
the graph.
- 
$[ - 5,5 ]$ by $[ - 5,5 ]$

Accepted Answer

A)  $r = 1 + 3 \cos \theta$ 
B)  $r = 2 + 2 \sin \theta$ 
C)  $r = 1 + 3 \sin \theta$ 
D)  $r = 3 + \sin \theta$ 
A)  $r = 1 + 3 \cos \theta$ 
B)  $r = 2 + 2 \sin \theta$ 
C)  $r = 1 + 3 \sin \theta$ 
D)  $r = 3 + \sin \theta$

Question 3

Use the given graph to find the values of t that produce the graph in the given quadrant.
-$x=3-|t|, y=t+4,-6 \leq t \leq 6$
 
Quadrant I

Accepted Answer

A)  $3 \leq t \leq 6$ 
B)  $- 3 \leq t \leq 3$ 
C)  $- 6 \leq t \leq - 4$ 
D)  $- 4 \leq t \leq - 3$ 
A)  $3 \leq t \leq 6$ 
B)  $- 3 \leq t \leq 3$ 
C)  $- 6 \leq t \leq - 4$ 
D)  $- 4 \leq t \leq - 3$

Question 4

Determine whether the vectors u and v are parallel, orthogonal, or neither.
-$$\mathbf { u } = \langle 1 , - 4 \rangle , \mathbf { v } = \langle - 3,12 \rangle$$

Accepted Answer

A)  Orthogonal 
B)  Parallel 
C)  Neither 
A)  Orthogonal 
B)  Parallel 
C)  Neither

Question 5

Find a· b.
-$$a = \langle 5 , - 8 \rangle , \quad b = \langle 3,1 \rangle$$

Accepted Answer

A)  $\langle 8 , - 7 \rangle$ 
B)  7 
C)  23 
D)  $\langle 15 , - 8 \rangle$ 
A)  $\langle 8 , - 7 \rangle$ 
B)  7 
C)  23 
D)  $\langle 15 , - 8 \rangle$

Question 6

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle 5,3 \rangle$. Find $- 8 \mathbf { u }$.

Accepted Answer

A)  $\langle - 40,24 \rangle$ 
B)  $( 40,24 )$ 
C)  $( - 40 , - 24 \rangle$ 
D)  $\langle 40 , - 24 \rangle$ 
A)  $\langle - 40,24 \rangle$ 
B)  $( 40,24 )$ 
C)  $( - 40 , - 24 \rangle$ 
D)  $\langle 40 , - 24 \rangle$

Question 7

Solve the problem.
-A force of $629 \mathrm { lb }$ is required to pull a boat up a ramp inclined at $21.0 ^ { \circ }$ with the horizontal. How much does the boat weigh?

Accepted Answer

A)  $2350 \mathrm { lb }$ 
B)  $587 \mathrm { lb }$ 
C)  $608 \mathrm { lb }$ 
D)  $1760 \mathrm { lb }$ 
A)  $2350 \mathrm { lb }$ 
B)  $587 \mathrm { lb }$ 
C)  $608 \mathrm { lb }$ 
D)  $1760 \mathrm { lb }$

Question 8

Find the angle between the given vectors to the nearest tenth of a degree.
-$$\mathbf { u } = \langle 4 , - 8 \rangle , \mathbf { v } = \langle - 6 , - 3 \rangle$$

Accepted Answer

A)  $180 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $0 ^ { \circ }$ 
D)  $45 ^ { \circ }$ 
A)  $180 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $0 ^ { \circ }$ 
D)  $45 ^ { \circ }$

Question 9

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for
the graph.
- 
$[ - 5,5 ]$ by $[ - 5,5 ]$

Accepted Answer

A)  $r = 2 - 2 \sin \theta$ 
B)  $r = 4 - \sin \theta$ 
C)  $r = 3 - 2 \sin \theta$ 
D)  $r = 2 - 3 \sin \theta$ 
A)  $r = 2 - 2 \sin \theta$ 
B)  $r = 4 - \sin \theta$ 
C)  $r = 3 - 2 \sin \theta$ 
D)  $r = 2 - 3 \sin \theta$

Question 10

Find the indicated roots. Write the answer in a + bi form.
-Cube roots of 8

Accepted Answer

A)  $2,1 + \sqrt { 3 } i , 1 - \sqrt { 3 } i$ 
B)  $2 , - 1 + \sqrt { 3 } i , - 1 - \sqrt { 3 } i$ 
C)  $2,1 + \sqrt { 3 } i , - 1 - \sqrt { 3 } i$ 
D)  $2 , - 1 - \sqrt { 3 } i , 1 - \sqrt { 3 } i$ 
A)  $2,1 + \sqrt { 3 } i , 1 - \sqrt { 3 } i$ 
B)  $2 , - 1 + \sqrt { 3 } i , - 1 - \sqrt { 3 } i$ 
C)  $2,1 + \sqrt { 3 } i , - 1 - \sqrt { 3 } i$ 
D)  $2 , - 1 - \sqrt { 3 } i , 1 - \sqrt { 3 } i$

Question 11

Plot the point with the given polar coordinates.
-$\left(-2, \frac{\pi}{4}\right)$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 12

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
-$$r = 3 \cos 5 \theta$$

Accepted Answer

A)  $\mathrm { y }$-axis only 
B)  $x$-axis, $y$-axis, origin 
C)  $x$-axis, $y$-axis 
D)  $x$-axis only 
A)  $\mathrm { y }$-axis only 
B)  $x$-axis, $y$-axis, origin 
C)  $x$-axis, $y$-axis 
D)  $x$-axis only

Question 13

Solve the problem.
-A basketball player shoots the ball with a velocity of $21.5 \mathrm { ft } / \mathrm { s }$ at an angle of $32.4 ^ { \circ }$ with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.

Accepted Answer

A)  $9.1 \mathrm { ft } / \mathrm { s }$ 
B)  $5.8 \mathrm { ft } / \mathrm { s }$ 
C)  $18.2 \mathrm { ft } / \mathrm { s }$ 
D)  $11.5 \mathrm { ft } / \mathrm { s }$ 
A)  $9.1 \mathrm { ft } / \mathrm { s }$ 
B)  $5.8 \mathrm { ft } / \mathrm { s }$ 
C)  $18.2 \mathrm { ft } / \mathrm { s }$ 
D)  $11.5 \mathrm { ft } / \mathrm { s }$

Question 14

Write the complex number in the form a + bi.
-$$\frac { 5 } { 2 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$$

Accepted Answer

A)  $- \frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 2 } \mathrm { i }$ 
B)  $- \frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } \mathrm { i }$ 
C)  $- \frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 4 } i$ 
D)  $- \frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 2 } i$ 
A)  $- \frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 2 } \mathrm { i }$ 
B)  $- \frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } \mathrm { i }$ 
C)  $- \frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 4 } i$ 
D)  $- \frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 2 } i$

Question 15

Find the parametrization for the curve.
-The line segment starting at $( - 3,2 )$ with $t = 0$ and ending at $( 9,22 )$ with $t = 4$

Accepted Answer

A)  $x = 3 t - 3 , y = 5 t + 2$, for $0 \leq t \leq 4$ 
B)  $x = 2 t + 5 , y = - 3 t + 3$, for $0 \leq t \leq 4$ 
C)  $x = - 3 t + 3 , y = 2 t + 5$, for $0 \leq t \leq 4$ 
D)  $x = 5 t + 2 , y = 3 t - 3$, for $0 \leq t \leq 4$ 
A)  $x = 3 t - 3 , y = 5 t + 2$, for $0 \leq t \leq 4$ 
B)  $x = 2 t + 5 , y = - 3 t + 3$, for $0 \leq t \leq 4$ 
C)  $x = - 3 t + 3 , y = 2 t + 5$, for $0 \leq t \leq 4$ 
D)  $x = 5 t + 2 , y = 3 t - 3$, for $0 \leq t \leq 4$

Question 16

Use your grapher to determine which of the graphs matches the given polar equation.
-$r = 4 \cos 3 \theta$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 17

Find the product or quotient. Write the answer in standard form.
-$\frac { 5 - 9 i } { 5 - 6 i }$

Accepted Answer

A)  $\frac { 79 } { 61 } - \frac { 15 } { 61 } \mathrm { i }$ 
B)  $- \frac { 79 } { 11 } - \frac { 15 } { 11 } i$ 
C)  $\frac { 29 } { 11 } - \frac { 15 } { 11 } \mathrm { i }$ 
D)  $- \frac { 29 } { 61 } + \frac { 75 } { 61 } \mathrm { i }$ 
A)  $\frac { 79 } { 61 } - \frac { 15 } { 61 } \mathrm { i }$ 
B)  $- \frac { 79 } { 11 } - \frac { 15 } { 11 } i$ 
C)  $\frac { 29 } { 11 } - \frac { 15 } { 11 } \mathrm { i }$ 
D)  $- \frac { 29 } { 61 } + \frac { 75 } { 61 } \mathrm { i }$

Question 18

Solve the problem.
-Find the length of each petal of the polar curve $r = 4 + 6 \cos 3 \theta$. Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Accepted Answer

A)  4 
B)  22 
C)  6 
D)  10 
A)  4 
B)  22 
C)  6 
D)  10

Question 19

Solve the problem.
-What is the maximum $\mathrm { r }$-value for the polar equation $r = - 1 + 6 \sin \theta$ ? Note that a maximum $r$-value is a maximum value of $| \mathrm { r } |$, the maximum distance from the pole.

Accepted Answer

A)  5 
B)  6 
C)  7 
D)  1 
A)  5 
B)  6 
C)  7 
D)  1

Question 20

Find a· b.
-$a = 10 i + 7 j , \quad b = - 4 i + 3 j$

Accepted Answer

A)  $\langle - 40,21 \rangle$ 
B)  61 
C)  $- 19$ 
D)  $\langle 6,10 \rangle$ 
A)  $\langle - 40,21 \rangle$ 
B)  61 
C)  $- 19$ 
D)  $\langle 6,10 \rangle$

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

Use the given graph to find the values of t that produce the graph in the given quadrant. - $x=3-|t|, y=t+4,-6 \leq t \leq 6$ $Use the given graph to find the values of t that produce the graph in the given quadrant. - x=3-|t|, y=t+4,-6 \leq t \leq 6 Quadrant I$ Quadrant I

Determine whether the vectors u and v are parallel, orthogonal, or neither. - $\mathbf { u } = \langle 1 , - 4 \rangle , \mathbf { v } = \langle - 3,12 \rangle$

Find a· b. - $a = \langle 5 , - 8 \rangle , \quad b = \langle 3,1 \rangle$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 5,3 \rangle$ . Find $- 8 \mathbf { u }$ .

Solve the problem. -A force of $629 \mathrm { lb }$ is required to pull a boat up a ramp inclined at $21.0 ^ { \circ }$ with the horizontal. How much does the boat weigh?

Find the angle between the given vectors to the nearest tenth of a degree. - $\mathbf { u } = \langle 4 , - 8 \rangle , \mathbf { v } = \langle - 6 , - 3 \rangle$

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

Find the indicated roots. Write the answer in a + bi form. -Cube roots of 8

Plot the point with the given polar coordinates. - $\left(-2, \frac{\pi}{4}\right)$ $Plot the point with the given polar coordinates. - \left(-2, \frac{\pi}{4}\right)$

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. - $r = 3 \cos 5 \theta$

Solve the problem. -A basketball player shoots the ball with a velocity of $21.5 \mathrm { ft } / \mathrm { s }$ at an angle of $32.4 ^ { \circ }$ with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.

Write the complex number in the form a + bi. - $\frac { 5 } { 2 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$

Find the parametrization for the curve. -The line segment starting at $( - 3,2 )$ with $t = 0$ and ending at $( 9,22 )$ with $t = 4$

Use your grapher to determine which of the graphs matches the given polar equation. - $r = 4 \cos 3 \theta$

Find the product or quotient. Write the answer in standard form. - $\frac { 5 - 9 i } { 5 - 6 i }$

Solve the problem. -Find the length of each petal of the polar curve $r = 4 + 6 \cos 3 \theta$ . Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Solve the problem. -What is the maximum $\mathrm { r }$ -value for the polar equation $r = - 1 + 6 \sin \theta$ ? Note that a maximum $r$ -value is a maximum value of $| \mathrm { r } |$ , the maximum distance from the pole.

Find a· b. - $a = 10 i + 7 j , \quad b = - 4 i + 3 j$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 6: Applications of Trigonometry

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - [−5,5][ - 5,5 ][−5,5] by [−5,5][ - 5,5 ][−5,5]

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - [−5,5][ - 5,5 ][−5,5] by [−5,5][ - 5,5 ][−5,5]

Use the given graph to find the values of t that produce the graph in the given quadrant. - x=3−∣t∣,y=t+4,−6≤t≤6x=3-|t|, y=t+4,-6 \leq t \leq 6x=3−∣t∣,y=t+4,−6≤t≤6 Quadrant I

Determine whether the vectors u and v are parallel, orthogonal, or neither. - u=⟨1,−4⟩,v=⟨−3,12⟩\mathbf { u } = \langle 1 , - 4 \rangle , \mathbf { v } = \langle - 3,12 \rangleu=⟨1,−4⟩,v=⟨−3,12⟩

Find a· b. - a=⟨5,−8⟩,b=⟨3,1⟩a = \langle 5 , - 8 \rangle , \quad b = \langle 3,1 \ranglea=⟨5,−8⟩,b=⟨3,1⟩

Find the component form of the indicated vector. -Let u=⟨5,3⟩\mathbf { u } = \langle 5,3 \rangleu=⟨5,3⟩ . Find −8u- 8 \mathbf { u }−8u .

Solve the problem. -A force of 629lb629 \mathrm { lb }629lb is required to pull a boat up a ramp inclined at 21.0∘21.0 ^ { \circ }21.0∘ with the horizontal. How much does the boat weigh?

Find the angle between the given vectors to the nearest tenth of a degree. - u=⟨4,−8⟩,v=⟨−6,−3⟩\mathbf { u } = \langle 4 , - 8 \rangle , \mathbf { v } = \langle - 6 , - 3 \rangleu=⟨4,−8⟩,v=⟨−6,−3⟩

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - [−5,5][ - 5,5 ][−5,5] by [−5,5][ - 5,5 ][−5,5]

Find the indicated roots. Write the answer in a + bi form. -Cube roots of 8

Plot the point with the given polar coordinates. - (−2,π4)\left(-2, \frac{\pi}{4}\right)(−2,4π​)

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. - r=3cos⁡5θr = 3 \cos 5 \thetar=3cos5θ

Solve the problem. -A basketball player shoots the ball with a velocity of 21.5ft/s21.5 \mathrm { ft } / \mathrm { s }21.5ft/s at an angle of 32.4∘32.4 ^ { \circ }32.4∘ with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.

Write the complex number in the form a + bi. - 52(cos⁡150∘+isin⁡150∘)\frac { 5 } { 2 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)25​(cos150∘+isin150∘)

Find the parametrization for the curve. -The line segment starting at (−3,2)( - 3,2 )(−3,2) with t=0t = 0t=0 and ending at (9,22)( 9,22 )(9,22) with t=4t = 4t=4

Use your grapher to determine which of the graphs matches the given polar equation. - r=4cos⁡3θr = 4 \cos 3 \thetar=4cos3θ

Find the product or quotient. Write the answer in standard form. - 5−9i5−6i\frac { 5 - 9 i } { 5 - 6 i }5−6i5−9i​

Solve the problem. -Find the length of each petal of the polar curve r=4+6cos⁡3θr = 4 + 6 \cos 3 \thetar=4+6cos3θ . Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Solve the problem. -What is the maximum r\mathrm { r }r -value for the polar equation r=−1+6sin⁡θr = - 1 + 6 \sin \thetar=−1+6sinθ ? Note that a maximum rrr -value is a maximum value of ∣r∣| \mathrm { r } |∣r∣ , the maximum distance from the pole.

Find a· b. - a=10i+7j,b=−4i+3ja = 10 i + 7 j , \quad b = - 4 i + 3 ja=10i+7j,b=−4i+3j

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

Use the given graph to find the values of t that produce the graph in the given quadrant. - $x=3-|t|, y=t+4,-6 \leq t \leq 6$ $Use the given graph to find the values of t that produce the graph in the given quadrant. - x=3-|t|, y=t+4,-6 \leq t \leq 6 Quadrant I$ Quadrant I

Determine whether the vectors u and v are parallel, orthogonal, or neither. - $\mathbf { u } = \langle 1 , - 4 \rangle , \mathbf { v } = \langle - 3,12 \rangle$

Find a· b. - $a = \langle 5 , - 8 \rangle , \quad b = \langle 3,1 \rangle$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 5,3 \rangle$ . Find $- 8 \mathbf { u }$ .

Solve the problem. -A force of $629 \mathrm { lb }$ is required to pull a boat up a ramp inclined at $21.0 ^ { \circ }$ with the horizontal. How much does the boat weigh?

Find the angle between the given vectors to the nearest tenth of a degree. - $\mathbf { u } = \langle 4 , - 8 \rangle , \mathbf { v } = \langle - 6 , - 3 \rangle$

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

Plot the point with the given polar coordinates. - $\left(-2, \frac{\pi}{4}\right)$ $Plot the point with the given polar coordinates. - \left(-2, \frac{\pi}{4}\right)$

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. - $r = 3 \cos 5 \theta$

Solve the problem. -A basketball player shoots the ball with a velocity of $21.5 \mathrm { ft } / \mathrm { s }$ at an angle of $32.4 ^ { \circ }$ with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.

Write the complex number in the form a + bi. - $\frac { 5 } { 2 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$

Find the parametrization for the curve. -The line segment starting at $( - 3,2 )$ with $t = 0$ and ending at $( 9,22 )$ with $t = 4$

Use your grapher to determine which of the graphs matches the given polar equation. - $r = 4 \cos 3 \theta$

Find the product or quotient. Write the answer in standard form. - $\frac { 5 - 9 i } { 5 - 6 i }$

Solve the problem. -Find the length of each petal of the polar curve $r = 4 + 6 \cos 3 \theta$ . Note that this means the distance from the pole to the farthest point on the petal, not the arc length.

Solve the problem. -What is the maximum $\mathrm { r }$ -value for the polar equation $r = - 1 + 6 \sin \theta$ ? Note that a maximum $r$ -value is a maximum value of $| \mathrm { r } |$ , the maximum distance from the pole.

Find a· b. - $a = 10 i + 7 j , \quad b = - 4 i + 3 j$