FTCE MATHEMATICS 6-12 Practice Test Version 1 Test (Day 3)

​FTCE Mathematics 6-12 Practice Test Version (Day 3)

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Multiple Choice

Find the answer to the given: #30

• Undefined

• 2

• -1.7

• 1.4

Multiple Choice

Find the Limit. #32

• 0

• -1/4

• -5/4

• 1

• DNE

Multiple Choice

Find the limit. #33

• 0

• 8

• 16

• Does Not Exist (DNE)

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Multiple Choice

Find the derivative of the function y = ln x. #43

• $$\frac{1}{e^x}$$

• $$\frac{1}{x}$$

• $$x$$

• $$e^x$$

Multiple Choice

Find the equation of the tangent line at the given point. #66

• y+1=3(x+1)

• y+1=⅓(x+1)

• y-1=3(x+1)

• y=3x-1

Multiple Choice

Where is

$$f\left(x\right)=5x^3-5x^2$$  increasing? #65

• $$\left(-\infty,0\right)$$  

• $$\left(-\infty,0\right)U\left(\frac{2}{3},\infty\right)$$  

• $$\left(\frac{2}{3},\infty\right)$$  

• $$\left(0,\frac{2}{3}\right)$$  

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Multiple Choice

Find the derivative. f(t) = (t² + 2t)⁵

^#63

• f'(t) = 5(2t+2)⁴

• f'(t) = 5(t² + 2t)⁴

•  f'(t) = 5(t² + 2t)⁴(2t)

• f'(t) = 5(t² + 2t)⁴(2t + 2)

Multiple Choice

Find the derivative of  f(x) = (x⁶ + 4)⁵

#61

• f '(x) = 5x⁵(x⁴ + 4)⁴

• f '(x) = 6x⁵(x⁶ + 4)⁴

• f '(x) = 30x⁵(x⁶ + 4)⁴

• f '(x) = 30x⁶(x⁶ + 4)⁴

Multiple Choice

Find the derivative of y = 2x² (3x - 4). #62

• 6x³ - 8x²

• 18x² - 16x

• 15x² - 6x

• 6x - 4

Multiple Choice

Find the derivative f(x) = xe^x

^#79

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Multiple Choice

Find y' if y = tan(3x²+2). #67

• sec²(3x²+2)

• 6xsec²(3x²+2)

• 6xsec²x(3x²+2)

• sec²(6x)

Multiple Choice

Find dy/dx if y = sec(8x²). #68

• sec(16x)tan(16x)

• 16xcos(8x²)

• 16xsecxtanx(8x²)

• 16xsec(8x²)tan(8x²)

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Multiple Choice

If  $$f'\left(a\right)=0$$  and  $$f'\left(x\right)$$  changes from negative to positive at $$x=a$$  , then  $$f\left(x\right)$$  has. #64

• a relative maximum at x=a

• a relative minimum at x=a

• no relative extrema at x=a

• a vertical tangent line at x=a

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Multiple Choice

s(t) = t² - 20 Find the average velocity from t = 3 to t = 5. #78

• 2

• 4

• 6

• 8

Multiple Choice

Evaluate $$\int_{-1}^3\left(x^3+1\right)dx.$$ #40

• 20

• 22.5

• 23.25

• 24

Multiple Choice

#41

• a. 24

• b. -8

• c. -10

• d. 22

Multiple Choice

Practice 1: Evaluate $$\int_1^4\left(3x^2\ -\ 4x\right)\ dx$$  . #42

• 33

• 32

• -1

• 16

Multiple Choice

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? #73

• v(t) = -2

• v(t) -2t - 1 

• v(t) = t³

• v(t) = -t

Multiple Choice

If the position of a particle is represented by s(t) = -t² + 1, what is its instantaneous velocity at t = 1?  #74

• Velocity = 0

• Velocity = 1

• Velocity = -1

• Velocity = -2

Multiple Choice

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? #75

• v(t) = -2

• v(t) -2t - 1 

• v(t) = t³

• v(t) = -t

Multiple Choice

The position function x(t)=t³+6t²+16t-18 is given on the interval of 0<x<9. What is the velocity at t=6? #76

• 197

• 190

• 18

• 196

Multiple Choice

The velocity of an object is given as v = 2t + 3t³. What is the acceleration of the object at t = 2 secs? #77

• 38 m/s/s

• 27 m/s/s

• 16 m/s/s

• 49 m/s/s

Multiple Choice

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t What is the acceleration of the object at time t = 2 s? #80

• 64 m/s/s

• 60 m/s/s

• 66 m/s/s

• 70 m/s/s

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Multiple Choice

#81

• A

• B

• C

• D

Multiple Choice

Find the area of the region enclosed by the lines and curves.

y = 3x + 4 and y = x² + 4 #83

• 9

• 93/2

• 9/2

• 18

Multiple Choice

Find the area of the region bounded by the equations y = x² + 1 and y = 5. #84

• 32/3

• 64

• 32

• 64/3

• 16

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Multiple Choice

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m? #85

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

Multiple Choice

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in? #86

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

Multiple Choice

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall? #87

• 4/3 ft/sec

• 8/7 ft/sec

• 1 ft/sec

• 8/3 ft/sec

Multiple Choice

Which equation is correct for this situation?

The area of a circle is increasing at a rate of 3 inches squared per second. #88

• $$A=3$$

• $$\frac{dA}{dr}=3$$

• $$\frac{dA}{dt}=3$$

• $$\frac{dA}{dt}=3^2$$