Free Printable Second Semester PreCalc Final

1.

What range of angles can you get from inverse sine?

a)

0 to π

b)

0 to 2π

c)

-π/2 to π/2

d)

π/2 to 3 π/2

2.

a)

A

b)

B

c)

C

d)

D

3.

a)

A

b)

B

c)

C

d)

D

4.

Solve
cosθ = - √(3)/2
on θ∈[0, 2π)

a)

θ = π /3, 2π /3

b)

θ = 2π /3, 4π /3

c)

θ = π /6, 5π /6

d)

θ = 5π /6, 7π /6

5.

Solve on the Interval [0,2π)
1/2sec x - 1 = 0

a)

π/6, 5π/6

b)

π/3, 5π/3

c)

2π/3, 4π/3

d)

7π/6, 11π/6

6.

What is one possible solution?

a)

π

b)

π/3

c)

π/2

d)

-π

7.

Solve

sin²θ = ½

on θ∈[0, 2π)

a)

θ = π /4, 7π /4

b)

θ = π /4, 3π /4

c)

θ = 3π /4, 5π /4

d)

θ = π /4, 3π /4, 5π /4, 7π /4

8.

a)

A

b)

B

c)

C

d)

D

9.

a)

A

b)

B

c)

C

d)

D

10.

Which of the following angles are solutions to:

4cos²(2x) - 2 = 0? From 0 - 2π

a)

π/4, 3π/4, 5π/4, 7π/4

b)

π/4, 3π/4, 5π/4, 7π/4, 9π/4, 11π/4, 13π/4, 15π/4

c)

π/8, 3π/8, 5π/8, 7π/8

d)

π/8, 3π/8, 5π/8, 7π/8, 9π/8, 11π/8, 13π/8, 15π/8

11.

a)

5π∕6 + 2πn, 7π/6 + 2πn

b)

π/3 + 2πn, 2π/3 + 2πn

c)

5π/12 +πn, 7π/12 +πn

d)

2π/3 +πn, 4π/3 +πn

12.

cos 150^o

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

13.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

14.

What is the exact value of sin 150°

a)

-1/2

b)

-√3/2

c)

1/2

d)

√3/2

15.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

16.

cos (π/4)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

17.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

18.

tan 7π/4

a)

-1

b)

1

c)

√2/2

d)

undefined

19.

cot π/2

a)

undefined

b)

0

c)

1

d)

1/2

20.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

21.

Simplify

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

22.

a)

1/cos x

b)

1

c)

cot x

d)

-1

23.

Which of the following would be a step to prove the following identity?

a)

(1/ sin x) - (1 / cos x)

b)

(cos x - sin x) / ( sin x)

c)

(cos x - sin x) / (cos x)

d)

(1/ sin x cos x)

24.

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

a)

sin(120)

b)

cos(120)

c)

cos(230)

d)

sin(230)

25.

Find the exact value of the expression.
cos(20)cos(40) - sin(20)sin(40)

a)

1/4

b)

1/2

c)

√(3)/2

d)

√(3)

26.

a)

A

b)

B

c)

C

d)

D

27.

a)

A

b)

B

c)

C

d)

D

28.

find X

a)

52

b)

33

c)

41

d)

29

29.

Find m<A

a)

A

b)

B

c)

C

d)

D

30.

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

a)

0

b)

1

c)

2

d)

Infinitely many

31.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

32.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

33.

Which is the correct ratio?

a)

sin 28 = x/14

b)

cos 28 = x/14

c)

tan 28 = x/14

d)

tan 28 = 14/x

34.

What is the correct ratio?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

35.

FInd tan X

a)

32/40

b)

40/24

c)

32/24

d)

24/32

36.

Which of these coordinates do not belong?

a)

(4, -150^o)

b)

(-4, -210^o)

c)

(4, 690^o)

d)

(4,-30^o)

37.

Which equation represents the polar graph?

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 4 - 3 sin θ

d)

r = 4 + 5 sin θ

38.

Convert

a)

A

b)

B

c)

C

d)

D

39.

Convert the rectangular coordinates to polar form

a)

(√2 , 315^o)

b)

(2 , 135^o)

c)

(4 , 45^o)

d)

(4 , 225^o)

40.

Describe the curve

a)

Rose with 3 leaves

b)

Rose with 6 leaves

c)

Inner loop limacon

d)

Circle

41.

Describe the curve

a)

Rose with 3 leaves

b)

Circle

c)

Cardioid

d)

Inner loop limacon

42.

Which equation represents the polar graph?

a)

r = sin 4θ

b)

r = 6 sin 2θ

c)

r = 6 cos 2θ

d)

r = cos 4θ

43.

Choose the correct equation.

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 3cosθ

44.

Choose a correct equation for this rose curve.

a)

r = sin(7θ)

b)

r = 7sin(2θ)

c)

r = 2sin(7θ)

d)

r = 2sin(14θ)

45.

Find the angle between the two vectors:

a)

-0.789

b)

142.1

c)

100

d)

0.789

46.

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

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

47.

How do you know if two vectors are orthogonal?

a)

Their sum is 0.

b)

The dot product is 1.

c)

The angle between them is 0°.

d)

The dot product is 0.

48.

a)

69

b)

63

c)

57

d)

-27

49.

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

50.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

51.

If c=<-5, 4> and d=<8, 0>, calculate 2c+d

a)

<-2, 8>

b)

<-2, 0>

c)

<6, 8>

d)

<6, 0>

52.

What is the "starting point" of this parametric function? (t=0)

a)

(1, -1)

b)

(4, -3)

c)

(-3, 2)

d)

(-3, 4)

53.

A ball rolls across the floor.
The coordinates of the ball are given by x = t and y = 10 - 2t.
What is the position of the ball at time t = 3?

a)

Point A

b)

Point B

c)

Point C

d)

Point D

54.

Which set of parametric equations satisfies the given data table?

a)

x(t) = t³ - 1
y(t) = 2t

b)

x(t) = t³ - 1
y(t) = t + 2

c)

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

d)

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

55.

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

a)

A

b)

B

c)

C

d)

D

56.

Where is the graph continuous yet NOT differentiable?

a)

x = a, b, c, d

b)

x = b, c, d

c)

x = a, b,

d)

x = b, d

57.

Find h'(3)

a)

-2

b)

0

c)

1

d)

3

58.

What is the limit?

a)

5/2

b)

-2/3

c)

Infinity

d)

17/3

59.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

60.

a)

1/2

b)

0

c)

Positive Infinity

d)

Negative Infinity

61.

a)

I only

b)

I and II Only

c)

I, II, and III

d)

II Only

62.

Find f'(x)

a)

A

b)

B

c)

C

d)

D

63.

A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?

a)

2

b)

4

c)

6.5

d)

7

64.

Find dy/dx

a)

A

b)

B

c)

C

d)

D

65.

If A = 2x³, what is (dA/dt)?

a)

6x²

b)

6x²(dA/dx)

c)

6x²(dx/dt)

d)

6x (dx/dt)

66.

f' is given, which could be f?

a)

A

b)

B

c)

C

67.

Where is the graph not differentiable?

a)

x = -2, -1, 0, 1

b)

x = -2, -1, 1

c)

x = -2, -1

d)

x = -1,

68.

Find the second derivative of f(x) = x²+ e^x - cosx

a)

f"(x) = 2 + e^x + cosx

b)

f"(x) = 2x + e^x + cosx

c)

f"(x) = 2x + xe^x - cosx

d)

f"(x) = 2x + e^x + sinx

69.

Which of the following are synonyms for find the derivative?

a)

f'(x)

b)

dy/dx

c)

y'

d)

slope of the tangent line

e)

instantaneous rate of change

70.

Given u(x) = f(x)g(x), f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,

then u'(2) = ?

a)

-12

b)

4

c)

5

d)

12

71.

If f has a derivative at x = a, then f is continuous at x = a?

a)

True

b)

False

72.

An objects distance from its starting point at time t is given by the equation

s(t) = t³ - 6t² - 4.

What is the speed of the object when its acceleration is 0?

a)

2

b)

-24

c)

12

d)

44

73.

If H(x) = f ^-1(x), then H'(3) equals

a)

4

b)

1/4

c)

- 1/4

d)

-4

74.

Find dy/dx at a given point.

a)

5/4

b)

4/5

c)

1

d)

-5

75.

Find the derivative of the inverse

a)

12

b)

1/12

c)

146

d)

1/146

76.

find y'

a)

A

b)

B

c)

C

d)

D

77.

Find the Derivative

a)

A

b)

B

c)

C

d)

D

78.

Evaluate the derivative at

x = π

a)

-1 - 3/(π³)

b)

9/(π⁴)

c)

3/(π⁴)

d)

9

79.

a)

Only the Quotient Rule

b)

The Quotient and Product Rules

c)

The Quotient and Chain Rules

d)

Only the Chain Rule

80.

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec. How fast is the area of the outer circle changing when the diameter is 8 in?

a)

80π in/sec

b)

20π in/sec

c)

60π in/sec

d)

40π in/sec

81.

A hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 4 m/min. At what rate is the volume of the cube changing when the sides are 5 m each?

a)

-296 m³/min

b)

-297 m³/min

c)

-300 m³/min

d)

-307 m³/min

82.

Find

a)

0

b)

1/ln(5)

c)

1

d)

ln(5)

83.

a)

0

b)

1

c)

-32/3

d)

32/3

84.

a)

5/3

b)

0

c)

DNE

d)

1

85.

If the sides of a triangle are 8, 8, and 8, what is the area?

a)

8

b)

15.58

c)

27.71

d)

62.91

86.

If the sides of a triangle are 3, 9, and 10, what is the area?

a)

13.3

b)

15.75

c)

124.62

Second Semester PreCalc Final

Total questions: 86

Worksheet time: 7hrs 22mins

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