Free Printable PreCalc Final Review (F21)

1.

Factor Completely:

2n³ + 7n² - 2n - 7

a)

cannot be factored

b)

(n - 1)²(2n + 7)

c)

(n² - 1)(2n + 7)

d)

(n + 1)(n - 1)(2n + 7)

2.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

(x - 2)(x + 2)(2x + 5)

3.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

4.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

5.

Factor Completely:

k⁴ - 10k² - 39

a)

(k² - 13)(k² + 3)

b)

(k - 13)(k + 3)

c)

(k² + 15)(k² - 3)

d)

(k + 13)(k - 3)

6.

Factor Completely:

256x⁴ - 81

a)

(16x²+ 9)(16x²- 9)

b)

(16x²+ 9)(4x + 3)(4x - 3)

c)

(4x²+ 9)(4x²- 9)

d)

(16x²+ 9)(2x + 6)(2x -6)

7.

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

8.

a)

2

b)

1

c)

4

d)

cannot be determined

9.

Which of the following could be the equation of the graph shown?

a)

f(x) = x² + 3x

b)

f(x)=x³ + 6x² + 9x

c)

f(x) = x² - 3x

d)

f(x)=x³ - 6x² + 9x

10.

Which of the following could be the factored form for the equation representing the graph shown?

a)

(x+3)(x-2)(x-5)

b)

(x-5)²(x-2)(x+3)

c)

(x-3)(x+2)(x+5)²

d)

none of these

11.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

12.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

13.

Which function matches the graph?

a)

$y=x^{\frac{1}{2}}$

b)

$y=x^{\frac{1}{3}}$

c)

$y=x^{\frac{2}{3}}$

14.

Which function matches the graph?

a)

$y=x^{\frac{1}{2}}$

b)

$y=x^{\frac{1}{3}}$

c)

$y=x^{\frac{2}{3}}$

15.

Which function matches the graph?

a)

$y=x^{-\frac{1}{2}}$

b)

$y=x^{-2}$

c)

$y=x^{-3}$

16.

Which function matches the graph?

a)

$y=x^{-\frac{1}{2}}$

b)

$y=x^{-2}$

c)

$y=x^{-3}$

17.

Find the graph of $f\left(x\right)=x^{\frac{1}{3}}$

a)

b)

c)

d)

18.

This graph shown is increasing on the interval

a)

$\left(-\infty,\ 0\right)$

b)

$\left(0,\ \infty\right)$

c)

$\left(-\infty,\ \infty\right)$

19.

This graph shown is increasing on the interval

a)

$\left(-\infty,\ 0\right)$

b)

$\left(0,\ \infty\right)$

c)

$\left(-\infty,\ \infty\right)$

20.

Which of the following could be the factored form for the equation representing the graph shown?

a)

f(x)=(x+3)(x-2)(x-5)

b)

f(x)=(x-5)²(x-2)(x+3)

c)

f(x)=(x-3)(x+2)(x+5)²

d)

none of these

21.

Which of the following could be the function for the graphed polynomial?

a)

$f\left(x\right)=x^2\left(x-3\right)^3\left(x+1\right)$

b)

$f\left(x\right)=x^2\left(x-3\right)\left(x+1\right)$

c)

$f\left(x\right)=x\left(x-3\right)\left(x+1\right)$

d)

$f\left(x\right)=-x^2\left(x-3\right)\left(x+1\right)$

22.

What is the reference angle for 240 degrees?

a)

60 degrees

b)

30 degrees

c)

45 degrees

d)

210 degrees

23.

Find the reference angle for an angle measuring -300⁰

a)

60⁰

b)

-60⁰

c)

30⁰

d)

45⁰

24.

Find a coterminal angle to -180 degrees.

a)

180

b)

90

c)

270

d)

360

25.

Find a coterminal angle to 200 degrees.

a)

-520

b)

-200

c)

160

d)

-380

26.

Which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

27.

What is the sin(120)?

a)

-1/2

b)

1/2

c)

-root(3)/2

d)

root(3)/2

28.

What is the cos(585)?

a)

1/2

b)

root(2)/2

c)

-root(2)/2

d)

-root(3)/2

29.

Find an angle coterminal with an angle which measures 11π ∕ 3.

a)

17 π / 3

b)

4π ∕ 3

c)

π ∕ 3

d)

8π ∕ 3

30.

What quadrant is 7π/3?

a)

I

b)

II

c)

III

d)

^IV

31.

What is the reference angle for 5pi/4?

a)

pi/4

b)

7pi/4

c)

pi/6

d)

pi/3

32.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

33.

cos(π)=

a)

0

b)

1

c)

-1

d)

1/2

34.

a)

√3/3

b)

√3

c)

1

d)

undefined

35.

cscθ=

a)

1/cosθ

b)

1/sinθ

c)

1/tanθ

d)

1/secθ

36.

secθ=

a)

1/cosθ

b)

1/sinθ

c)

1/tanθ

d)

1/cscθ

37.

$1+\tan^2x=$

a)

$\csc^2x$

b)

$\cot^2x$

c)

$\sin^2x$

d)

$\sec^2x$

38.

$1+\cot^2x\ =$

a)

$\csc^2x$

b)

$\sec^2x$

c)

$\cos^2x$

d)

$\tan^2x$

39.

Simplify

$\cot\theta\tan\theta$

a)

sin²θ/cos²θ

b)

1

c)

0

d)

cos²θ/sin²θ

40.

Simplify
$\sec\theta\cot\theta\sin\theta$

a)

-1

b)

sin θ

c)

csc θ

d)

1

41.

Simplify

$\cot^2\theta\left(1+\tan^2\theta\right)$

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

42.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

2secθ

b)

cot²θ

c)

tan²θ

d)

sec²θ + 1

43.

Simplify

$\csc\ x\left(\cos x+\sin x\right)$

a)

csc x

b)

tan x + 1

c)

cot x

d)

cot x + 1

44.

Simplify $\left(\csc x+1\right)\left(\csc x-1\right)$

a)

$\csc^2x+1$

b)

$\tan^2x$

c)

$\cot^2x$

d)

$2\csc x$

45.

$1-\sin^2x\ =$

a)

$\sin^2x$

b)

$\cos^2x$

c)

$\sec^2x$

d)

$\csc^2x$

46.

$\cos70^o\cos40^o-\sin70^o\sin40^o\$ is equivalent to

a)

$\cos30^o$

b)

$\cos70^{o\ }$

c)

$\cos110^o$

d)

$\sin70^{o\ }$

47.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

a)

$-\frac{2}{3}$

b)

$\frac{4\sqrt{5}-6}{15}$

c)

$\frac{4\sqrt{5}+2}{5}$

d)

$\frac{4\sqrt{5}+6}{15}$

48.

$\sin96^o\cos24^o+\cos96^o\sin24^o\$ is equivalent to

a)

$\sin120^o$

b)

$\sin72^{o\ }$

c)

$\cos120^o$

d)

$\cos72^o$

49.

How many radians is 250 degrees?

a)

4π/3

b)

25π/18

c)

5π/6

d)

50π/9

50.

What is the equation of the graph?

a)

y = -2 cos (x) - 3

b)

y = 3 cos (x) - 2

c)

y = -7 cos (x) - 3

d)

y = -3 cos (x) - 4

51.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

52.

What is the period?

a)

π/4

b)

π/2

c)

3π/4

d)

π

53.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

54.

The hour hand of the large clock on the wall in Union Station measures 24 inches in length.

At noon, the tip of the hour hand is 30 inches from the ceiling. At 3 PM, the tip is 54 inches from the ceiling, and at 6 PM, 78 inches. At 9 PM, it is again 54 inches from the ceiling, and so forth.

Let y equal the distance from the tip of the hour hand to the ceiling and x be the number of hours after noon.

Find the equation that models the motion of the hour hand.

a)

y=-24\cos\left(\frac{\pi}{6}x\right)+54

b)

$y=30\cos\left(\frac{\pi}{6}x\right)+54$

c)

$y=30\sin\left(\frac{\pi}{6}x\right)+54$

d)

$y=24\sin\left(\frac{\pi}{6}x\right)+54$

55.

Find sin(-240°)

a)

(√3)/2)

b)

(-1/2)

c)

(√2/2)

d)

(1/2)

56.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

57.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

58.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

59.

How many triangles can you make if A=53, b=6, and a=4?

a)

0

b)

1

c)

2

d)

Infinitely many

60.

How many triangles can you make if A=53, b=6, and a=5?

a)

0

b)

1

c)

2

d)

Infinitely many

61.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

62.

Find the oblique asymptote.

a)

y = 3x - 12

b)

y = x + 5

c)

y = 3x - 5

d)

y = 3x - 7

63.

Find the oblique asymptote.
(3x³ - 2x + 1) / (x² + 4x + 2)

a)

y = 3x - 12

b)

y = 40x + 25

c)

y = 3x - 10

d)

y = 3x - 14

64.

What type(s) of asymptotes does this function have? (Check all that apply.)

a)

Vertical

b)

Horizontal

c)

Oblique

65.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

66.

Find the Vertical Asymptotes

a)

x= 0, -2

b)

x= 2

c)

x= -3, 2

d)

x = -3,1

67.

Where does the hole occur?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

68.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

69.

a)

Does not exist

b)

2

c)

0

d)

1

70.

a)

-7

b)

0

c)

1

d)

DNE

71.

a)

0

b)

0/0

c)

1/4

d)

DNE

72.

$\lim_{x\rightarrow3^-}f\left(x\right)=$

a)

0

b)

$\sqrt{6}$

c)

6

d)

DNE

73.

Select all statements that are TRUE.

a)

b)

c)

d)

74.

$find\ the\lim_{x\rightarrow4}\sqrt{3-x}$

a)

DNE

b)

$\frac{3}{4}$

c)

$1$

d)

$\sqrt{-1}$

75.

what is the limit of the function

a)

0

b)

10/11

c)

DNE

d)

25/26

76.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

77.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(f\circ g\right)\left(2\right)$

a)

$\frac{1}{4}$

b)

$\frac{1}{8}$

c)

$\frac{7}{2}$

d)

8

78.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

79.

Which functions are even? Check all of the boxes that apply.

a)

$f\left(x\right)=x^4-x^2$

b)

$f\left(x\right)=x^2-3x+2$

c)

$f\left(x\right)=\sqrt{\left(x-2\right)}$

d)

$f\left(x\right)=\left|x\right|$

80.

Check all of the functions that are odd.

a)

$f\left(x\right)=x^3-x^2$

b)

$f\left(x\right)=x^5-3x^3+2x$

c)

$f\left(x\right)=4x+9$

d)

$f\left(x\right)=\frac{1}{x}$

81.

Label the function as even, odd or neither
f(x) = x³+ 4x

a)

Even

b)

Odd

c)

Neither

82.

Label the function as even, odd or neither
f(x) = 3x⁴ - 2x²+ 5

a)

Even

b)

Odd

c)

Neither

83.

Label the function as even, odd or neither
f(x) = 8x³ - 7x + 2

a)

Even

b)

Odd

c)

Neither

84.

log (2 * 3) = ?

a)

log 2 + log 3

b)

log 2 * log 3

c)

log 2 - log 3

d)

log 5

85.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

86.

Expand log(x²/y³). Choose the best answer.

a)

log x²+log y³

b)

2 log x - 3 log y

c)

log x + log y

d)

2log x² +3 logy³

87.

ln(4xy)

a)

ln4+lnx+lny

b)

4lnxy

c)

4lnx+lny

d)

4ln(x+y)

88.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

89.

Rewrite in exponential form:
2=log₉x

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

90.

Solve for x:
8^x+1= 3

a)

0.528

b)

0.893

c)

-0.472

d)

1.893

91.

2 * 4^{3x – 6}– 8 = 120

a)

x = 3

b)

x = 4

c)

x = 2.9

d)

x = 8

92.

Rewrite the exponential as a log.

2^3x+1= 12

a)

log(2)= 3x+1

b)

log₂(12)= 3x+1

c)

log(6)=3x+1

d)

log₁₂(2)= 3x+1

93.

Solve for x.
$\log_52+\log_5x=\log_520$
x = (a)

94.

Eliminate the parameter from x(t) = t² + 5 and y(t) = t² - 4. Which of the following sketches results?

a)

Linear

b)

Quadratic

c)

Quartic

d)

Square Root

95.

Find the point based on the parametric equations. t = 3

x = 1 - 2t

y =4t + 1

a)

(-5, 13)

b)

(13, -5)

c)

(5, 13)

d)

(13, 5)

96.

Write the rectangular equation for the following parametric equations.

x = 4cosθ

y = 3sinθ

a)

$\frac{x^2}{9}+\frac{y^2}{16}=1$

b)

$\frac{y^2}{9}+\frac{x^2}{16}=1$

c)

$\cos^2\theta+\sin^2\theta=1$

d)

$\frac{x^2}{9}-\frac{y^2}{16}=1$

97.

What is the center and radius of the curve:
x=1+3cost
y=-2+3sint

a)

(-1,2) , r=3

b)

(-1,2) , r=9

c)

(1,-2) , r=3

d)

(1,-2) , r=9

98.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

99.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

100.

Find the dot product of the given vectors:

a)

92

b)

0

c)

-92

d)

none of the above

101.

Find the angle between v and w

a)

21.8 degrees

b)

111.8 degrees

c)

68.2 degrees

102.

A cannonball is fired at a 45.0° angle and an initial velocity of 625 f/s. Assume no air resistance. Find the horizontal coordinate of the cannonball after 2 seconds.

a)

1250 f/s

b)

883.9 f/s

c)

441.9 f/s

d)

328.3 f/s

103.

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.

Model the scenario using parametric equations.

a)

x = (20cos(66⁰))t; y=-16t² + (20sin(66⁰)t + 75

b)

x = (20cos(66⁰))t; y=-16t² + (20sin(66⁰)t + 3

c)

x = (75cos(66⁰))t; y=-16t² + (75sin(66⁰)t + 20

d)

x = (75cos(66⁰))t; y=-16t² + (75sin(66⁰)t + 3

104.

Any vector with initial point (x₁, y₁) and terminal point (x₂, y₂) can be written in component form as:

a)

b)

c)

d)

105.

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

a)

6

b)

8.2

c)

10

d)

10.4

106.

Find the direction angle for the vector initial point (-3, 4) and terminal point (-10, 4). Hint: you can use the formula or sketch a graph

a)

0 degrees

b)

90 degrees

c)

180 degrees

d)

270 degrees

107.

A vector has initial point (4, -3) and terminal point (-3, -1). Find the direction angle to the nearest tenth.

(a)

PreCalc Final Review (F21)

Total questions: 107

Worksheet time: 7hrs 24mins

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