Quiz about Final review

Question 1

Find the magnitude.

Accepted Answer

5

Answer

3

Answer

25

Answer

-4

Question 2

For vectors $$\overrightarrow{AB}$$ and $$\overrightarrow{CD}$$ , determine if they have the same magnitude, and whether they are parallel.
A(11, -11) and B(8, -4)
C(5, 2) and D(12, -1)
Select all that apply.

Accepted Answer

magnitudes are equal

Accepted Answer

not parallel

Answer

magnitudes are not equal

Answer

parallel

Question 3

A vector is a quantity that has both _______ and _________.

Select all that apply.

Accepted Answer

direction

Accepted Answer

magnitude

Answer

amplitude

Answer

acceleration

Answer

velocity

Question 4

Add

$$<5,\ -2>+<-4,\ 8>$$

Accepted Answer

$$<1,\ 6>$$

Answer

$$<-9,\ 10>$$

Answer

$$<3,\ 4>$$

Question 5

$$a\cdot\overrightarrow{w}\ =\ $$ When multiplying a scalar to a vector, you must multiply the scalar number to BOTH the horizontal component AND the vertical component

Accepted Answer

True

Answer

False

Answer

You cannot multiply scalars and vectors.

Question 6

Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9).

Accepted Answer

10

Answer

6

Answer

8.2

Answer

10.4

Question 7

(-5+i)-(-5-6i)

Accepted Answer

7i

Answer

-5i

Answer

-10+7i

Answer

-7i

Question 8

If w = <2, -5> and y = <2, 0>, find w + y

Accepted Answer

<4, -5>

Answer

<-10, 2>

Answer

<-6, 10>

Answer

<6, -10>

Question 9

Eliminate the parameter. Convert the parametric equation to rectangular. x= 2+4t and y=-1+6t

Accepted Answer

y=(3/2)x - 4

Answer

t=(x-2)/4

Answer

y=x - 4

Answer

y= (2/3)x + 4

Question 10

Sketch the curve of x(t) = 2t + 1 and y(t) = t² + 2.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 11

Which set of parametric equations satisfies the given data table?

Accepted Answer

x(t) = t³ - 1
y(t) = t + 2

Answer

x(t) = t³ - 1
y(t) = 2t

Answer

x(t) = t + 8
y(t) = t + 2

Answer

x(t) = t + 8
y(t) = 2t

Question 12

This particular equation generates what graph

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 13

Which equation below generates this particular graph?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 14

Describe the curve

Accepted Answer

Cardioid

Answer

Rose with 3 leaves

Answer

Circle

Answer

Inner loop limacon

Question 15

The polar coordinate system is based on a point, called the ______ and a ray, called the _______ axis.

Accepted Answer

pole, polar

Answer

radias, x

Answer

pole, x

Answer

radias, polar

Question 16

Convert the polar coordinates to rectangular form $$\left(\sqrt{2},\ -\frac{\pi}{4}\right)$$

Accepted Answer

(1, -1)

Answer

(1, 1)

Answer

(-1, 0)

Answer

(-1, -1)

Question 17

Convert the rectangular equation to polar form.
$$\left(x-3\right)^2+y^2=9$$

Accepted Answer

$$r=6\cos heta$$

Answer

$$r=-2\cos heta+6\sin heta$$

Answer

$$r=6\cos heta+2\sin heta$$

Answer

$$r=-6\sin heta$$

Question 18

Convert the rectangular equation to polar form.
$$x^2+\left(y-2\right)^2=4$$

Accepted Answer

$$r=4\sin heta$$

Answer

$$r=6\sin heta$$

Answer

$$r=-2\cos heta+4\sin heta$$

Answer

$$r=-4\cos heta-2\sin heta$$

Question 19

What is the amplitude of $$f\left(x\right)\ =\ 3\cos\left(x\ +\ \frac{\pi}{2}\right)$$ ?

Accepted Answer

3

Answer

0

Answer

$$-\frac{\pi}{2}$$

Answer

$$\frac{\pi}{2}$$

Question 20

What is the phase shift of $$f\left(x\right)\ =\ \frac{1}{2}\cos\left(x\ -\ 1\right)\ +\ 3$$ ?

Accepted Answer

1

Answer

$$2\pi$$

Answer

$$\frac{1}{2}$$

Answer

3

Question 21

What is the midline of this graph?

Accepted Answer

y = -2

Answer

y = 0

Answer

y = -1

Answer

y = -3

Question 22

Write an equation for the cosine function with the following transformations:

amplitude = 3

period = $$2\pi\ $$

phase shift: $$\pi\ right$$

vertical shift: up 5

Accepted Answer

$$y\ =\ 3\cos\left(x-\pi\right)+5$$

Answer

$$y\ =\ 5\cos\left(x\ -\ \pi\right)\ +\ 3$$

Answer

$$y\ =\ 5\cos\left(x\ +\ \pi\right)\ +\ 3$$

Answer

$$y\ =\ 3\cos\left(x+\pi\right)+5$$

Question 23

What is the phase shift?
$$y\ =\ 4\cos\left(2x\ +\pi\right)-2$$

Accepted Answer

left $$\frac{\pi}{2}$$

Answer

rightundefined

Answer

right $$\pi$$

Answer

left $$\pi$$

Question 24

What is the minimum value of the follow equation:

$$y=-5\sin\left(\frac{1}{2}x+\pi\right)+8$$

Accepted Answer

y = 3

Answer

y = 8

Answer

y = -13

Answer

y = 13

Question 25

What is the minimum value of the follow equation:

$$y=-7\cos\left(2x-\frac{\pi}{2}\right)-4$$

Accepted Answer

y = -11

Answer

y = -4

Answer

y = 3

Answer

y = -3

Question 26

Which graph shows $$y=3\sin\left(2x-\frac{\pi}{4}\right)-1$$

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 27

Which graph shows $$y=4\sin\left(\frac{x}{4}+\frac{3\pi}{4}\right)-1$$

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 28

What is the equation of the graph below:

Accepted Answer

$$y=4\cos\left(2 heta-\frac{\pi}{2} ight)+1$$

Answer

$$y=4\sin\left( heta-\frac{\pi}{2} ight)+1$$

Answer

$$y=-4\cos\left(2 heta+\frac{\pi}{4} ight)+1$$

Answer

$$y=-4\sin\left(2 heta ight)+1$$

Question 29

Which equation is NOT possible for the graph?

Accepted Answer

$$y=-2-3\cos\left(\frac{1}{2}x-\frac{3\pi}{2}\right)$$

Answer

$$y=-2+3\cos\left(\frac{1}{2}x+\frac{\pi}{4}\right)$$

Answer

$$y=3\sin\left(\frac{1}{2}x+\frac{3\pi}{4}\right)-2$$

Answer

$$y=-3\sin\left(\frac{1}{2}x-\frac{\pi}{4}\right)-2$$

Question 30

Which equation below is NOT possible for the graph?

Accepted Answer

$$y=\sin\left(x+270\degree\right)-2$$

Answer

$$y=\cos\left(x\right)-2$$

Answer

$$y=-\cos\left(x+180\degree\right)-2$$

Answer

$$y=-\sin\left(x-90\degree\right)-2$$

Question 31

An NFL punter at the 20 yard line kicks a football downfield with an initial velocity of 75 ft/sec at an angle of 66⁰. The ball leaves his foot at a height of 3 feet.

How high will the ball be when it reaches the crossbar of the goalposts, which are 25 yards (75 feet) away from the kicker?

Accepted Answer

74.734 feet

Answer

-81.516 feet

Answer

28.236 feet

Answer

25 feet

Question 32

An NFL kicker at the 20 yard line kicks a footbal downfield with an initial velocity of 75 ft/sec at an angle of 66 degrees. The ball leaves his foor at a height of 3 feet.

Write a set of parametric equations to model the motion of the ball.

Accepted Answer

$$x\left(t\right)=75\cos\left(66\right)t$$ $$y\left(t\right)=-16t^2+75\sin\left(66\right)t+3$$

Answer

$$x\left(t\right)=20\cos\left(66\right)t\ $$ $$y\left(t\right)=-16t^2+20\sin\left(66\right)t+75$$

Answer

$$x\left(t\right)=75\cos\left(66\right)t$$ $$y\left(t\right)=-16t^2+75\sin\left(66\right)t+20$$

Answer

$$x\left(t\right)=20\cos\left(66\right)t$$ $$y\left(t\right)=-16t^2+20\sin\left(66\right)t+3$$

Question 33

What is the position equation of a point on a Ferris wheel that starts at a low point of 6 feet off the ground, spins counterclockwise to a height of 46 feet off the ground, then goes back down to 6 feet in 60 seconds?

Accepted Answer

$$x\left(t\right)=20\sin\left(\frac{\pi}{30}t\right)$$ $$y\left(t\right)=-20\cos\left(\frac{\pi}{30}t\right)+6$$

Answer

$$x\left(t\right)=-20\sin\left(\frac{\pi}{30}t\right)$$ $$y\left(t\right)=-20\cos\left(\frac{\pi}{30}t\right)+6$$

Answer

$$x\left(t\right)=-20\sin\left(\frac{\pi}{30}t\right)$$ $$y\left(t\right)=20\cos\left(\frac{\pi}{30}t\right)+6$$

Answer

$$x\left(t\right)=-40\sin\left(\frac{\pi}{60}t\right)$$ $$y\left(t\right)=-40\cos\left(\frac{\pi}{60}t\right)+6$$

Question 34

Question 34.

Accepted Answer

1

Answer

0

Answer

DNE

Answer

3

Question 35

Question 35.

Accepted Answer

-1

Answer

-4

Answer

8

Answer

5

Question 36

Question 36.

Accepted Answer

6

Answer

13

Answer

7

Answer

-3

Question 37

Question 37.

Accepted Answer

DNE

Answer

0

Answer

3

Answer

4

Question 38

Question 38.

Accepted Answer

Does not exist

Answer

2

Answer

0

Answer

1

Question 39

Find $$\lim_{x\rightarrow2^+\ }f\left(x\right)$$

Accepted Answer

5

Answer

-1

Answer

0

Answer

DNE

Question 40

What is the limit?

Accepted Answer

12

Answer

DNE

Answer

Infinity

Answer

6

Question 41

Question 41.

Accepted Answer

infinity

Answer

0

Answer

-1

Answer

-infinity

Question 42

Question 42.

Accepted Answer

-1

Answer

Does not exist

Answer

-2

Answer

0

Question 43

Find the vertical asymptote(s) (if any) of the graph of the function.

Accepted Answer

x=-2

Answer

x=2

Answer

None

Answer

X=2, x=-2

Question 44

What is the limit of the function as x approaches -4 from the left?

Accepted Answer

2

Answer

-4

Answer

DNE

Answer

-2

Question 45

Question 45.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 46

What is the limit?

Accepted Answer

1/2

Answer

2

Answer

-2

Answer

-1/2

Question 47

Question 47.

Accepted Answer

-1

Answer

9

Answer

1/4

Answer

0

Question 48

Question 48.

Accepted Answer

-1/4

Answer

-3/10

Answer

-9/5

Answer

-1

Question 49

$$\sin^{-1}\ \frac{1}{2}$$ = _______

Accepted Answer

$$\frac{\pi}{6}$$

Answer

$$-\frac{\pi}{6}$$

Answer

$$\frac{5\pi}{6}$$

Answer

$$-\frac{5\pi}{6}$$

Question 50

$$\sin^{-1}\left(-\frac{1}{2}\right)$$ = _____

Accepted Answer

$$-\frac{\pi}{6}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{5\pi}{6}$$

Answer

$$-\frac{5\pi}{6}$$

Question 51

$$\cos^{-1}\left(-\frac{1}{2}\right)$$ = ______

Accepted Answer

$$\frac{2\pi}{3}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$-\frac{\pi}{3}$$

Answer

$$-\frac{2\pi}{3}$$

Question 52

$$\cos^{-1}\ 1$$ = ______

Accepted Answer

0

Answer

$$\frac{\pi}{2}$$

Answer

$$-\frac{\pi}{2}$$

Answer

$$\pi$$

Question 53

$$ an^{-1}\sqrt{3}$$ = _____

Accepted Answer

$$\frac{\pi}{3}$$

Answer

0

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{\pi}{4}$$

Question 54

$$\sin^{-1}\left(\sin\ \frac{5\pi}{6}\right)$$ = ______

Accepted Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{5\pi}{6}$$

Answer

$$-\frac{\pi}{6}$$

Answer

$$-\frac{5\pi}{6}$$

Question 55

$$\cos^{-1}\left(\cos\ \left(-\frac{\pi}{4}\right)\right)$$ = _____

Accepted Answer

$$\frac{\pi}{4}$$

Answer

$$-\frac{\pi}{4}$$

Answer

$$\frac{3\pi}{4}$$

Answer

$$-\frac{3\pi}{4}$$

Question 56

$$ an\ \left(\sin^{-1}\ \left(\frac{-3}{5} ight) ight)$$ = ________

Accepted Answer

$$-\frac{3}{4}$$

Answer

$$\frac{4}{3}$$

Answer

$$-\frac{4}{3}$$

Answer

$$\frac{3}{4}$$

Question 57

$$\sin\left(\cos^{-1}\ \left(-\frac{4}{5}\right)\right)$$ = _____

Accepted Answer

$$\frac{3}{5}$$

Answer

$$-\frac{3}{5}$$

Answer

$$\frac{4}{5}$$

Answer

$$-\frac{4}{5}$$

Question 58

Find the fully simplified Derivative of y = 4x² + 3x + 6x^-2

Accepted Answer

y' = 8x + 3 -12/x³

Answer

y' = 8x + 3 -12x^-3

Answer

y' = 8x + 3 +12/x³

Answer

y' = 8x + 3 + 12/x

Question 59

Find dy/dx for y = 4x³+ 3x + 1

Accepted Answer

dy/dx = 12x² + 3

Answer

dy/dx = 4x² + 3

Answer

dy/dx = 4x² + 3x

Answer

dy/dx = 12x² + 3x

Question 60

At which point(s) will the slope(s) of the tangent line be POSITIVE?

Accepted Answer

at points A and E only

Answer

at C only

Answer

at points A, C and E only

Answer

at point B and D only

Question 61

Find the derivative of the funtion. (hint: you will need to multiply first!)

Accepted Answer

32x⁷+36x²

Answer

4x⁸+60x⁶+12x³

Answer

12x⁷+36x²

Answer

20x6

Question 62

Where on this graph would you find a HORIZONTAL tangent line?

Accepted Answer

x = 0

Answer

x = -3

Answer

x = 3

Answer

There are no horizontal tangent lines on this graph

Question 63

The derivative of

Accepted Answer

y'=x-2+8x

Answer

y'=2x-x-2

Answer

y'=x-1+8x

Answer

y=8x-x-2

Question 64

Differentiate y = $$\frac{2x^2+x-3}{x}$$

Hint: Simplify first, then take the derivative.

Accepted Answer

y' = 2 + 3x^-2

Answer

y = 2x + 1 - 3x^-1

Answer

y' = 4x + 1 - 1x^-2

Answer

y' = 4x + 1 - 3x^-2

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