Free Printable MAT 172 Exam Part 1 Review

1.

What is the t value shown?

a)

π/2

b)

π/3

c)

π/4

d)

π/6

2.

Which quadrant is $t=-\frac{5\pi}{3}$

a)

I

b)

II

c)

III

d)

IV

3.

The reference number for $t=\frac{17\pi}{3}$

a)

3

b)

$\frac{\pi}{3}$

c)

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

d)

$2\pi$

e)

$\frac{3\pi}{17}$

4.

What is the terminal point for $t=\frac{3\pi}{4}$ ?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

5.

What quadrant is 7π/3?

a)

I

b)

II

c)

III

d)

^IV

6.

The sine of any angle on the unit circle is the y-coordinate.

a)

True

b)

False

7.

What is the value of cosine at 0?

a)

$0$

b)

$\frac{1}{2}$

c)

$1$

d)

$\frac{\sqrt{3}}{2}$

8.

What is $\sin\left(\frac{\pi}{6}\right)$ ?

a)

1

b)

1/2

c)

√3/2

d)

√2/2

9.

$\cos\left(\frac{4\pi}{3}\right)$

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

10.

$\tan\left(\frac{5\pi}{4}\right)$

a)

√2/2

b)

-√2/2

c)

-1

d)

1

11.

Find the exact value for $\sec\ \frac{3\pi}{2}$ .

a)

0

b)

undefined

c)

1

d)

-1

12.

Which does not belong?

a)

$\frac{\pi}{2}$

b)

(-1,0)

c)

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

d)

(0,1)

13.

Given the Cos(x) = -2/3, then the Sec(x) = ?

a)

-2/3

b)

-3/2

c)

3/2

d)

2/3

14.

If $\sec\theta=-2$ , find $\cos\theta$ .

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

$2$

d)

$-\frac{1}{4}$

15.

Rewrite tan(x) in terms of sin(x) and cos(x).

a)

tan(x) = cos(x)/sin(x)

b)

tan(x) = 1/cot(x)

c)

tan(x) = sin(x)/cos(x)

d)

tan(x) = opp/adj

16.

sin x =

a)

cos x

b)

1/cosx

c)

1/secx

d)

1/cscx

17.

sec x =

a)

1/cosx

b)

1/sinx

c)

1/cscx

d)

1/tanx

18.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

19.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

20.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

21.

sin²x + cos²x =

a)

1

b)

1/sinx

c)

sec²x

d)

csc²x

22.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

23.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

24.

Which equation?

a)

y= sin(1/3x)

b)

y= (1/3)sinx

c)

y= 3sinx

d)

y= sin(3x)

25.

What is the equation of the graph shown?

a)

y = 4cosθ/2 - 6

b)

y = 4cosθ/2 - 2

c)

y = -2cosθ/4 - 2

d)

y = 4cosθ/4 + 2

26.

What is the period?

a)

4π

b)

2π

c)

π

d)

8π

27.

What is the vertical shift?

a)

Down 1

b)

Down 5

c)

Down 3

d)

Down 4

28.

What is the vertical shift for y = 4cos(¹/₂x +π) - 2?

a)

up 2

b)

left 2

c)

right 2

d)

down 2

29.

What is the phase shift for $y=4\cos\left(\frac{1}{2}\left(x-2\pi\right)\right)-2$ ?

a)

left pi/2

b)

right pi/2

c)

right 2pi

d)

left 2pi

30.

What is the amplitude of

y = -3sin (7x) -2

a)

7

b)

-2

c)

3

d)

-3

31.

What is another name for a phase shift?

a)

Horizontal Dilation

b)

Horizontal Shift/Translation

c)

Vertical Dilation

d)

Vertical Shift/Translation

32.

The __________ represents half the distance between the max and min of a sine or cosine graph.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

33.

The period of a function is

a)

the length of one cycle

b)

how high and low the function goes from the center line

c)

the range of the function

34.

Does the graph of sine have asymptotes?

a)

no

b)

yes, at multiples of π

c)

sometimes

d)

yes at multiples of 2π

35.

Determine an equation for this graph:

a)

y=sec(x)

b)

y=csc(x)

c)

y=cos(x)

d)

y= cot(x)

36.

Determine an equation for this graph:

a)

y=sec(x)

b)

y=csc(x)

c)

y=cot(x)

d)

y= tan(x)

37.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

38.

What are the vertical asymptotes for y = tan(x)?

a)

x = ... pi/2, 3pi/2, ....

b)

x = ... 0, pi, 2pi, ....

c)

There are no vertical asymptotes.

d)

x = infinity, x = - infinity

39.

What is the period for $y=4\cos\left(\frac{1}{2}\left(x-2\pi\right)\right)-2$ ?

a)

pi/2

b)

pi

c)

3pi

d)

4pi

40.

What is the amplitude and period of the function: $y=\frac{2}{5}\sin9x$ ?

a)

Amplitude: $\frac{2}{5}$ Period: $\frac{2\pi}{9}$

b)

Amplitude: $\frac{2}{5}$ Period: $\frac{\pi}{6}$

c)

Amplitude: $\frac{5}{2}$ Period: $\frac{2\pi}{9}$

d)

Amplitude: $\frac{5}{2}$ Period: $\frac{\pi}{6}$

41.

Describe the horizontal and vertical shifts.

a)

left π , up 4

b)

left π , down 3

c)

right π , up 4

d)

right π , down 3

42.

Where is the midline for $y=3\cos\left(\frac{1}{3}\left(x-\frac{\pi}{6}\right)\right)+2$

a)

1/3

b)

-2

c)

2

d)

3

43.

What is the radian equivalent of 210 degrees?

a)

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

b)

$\frac{7\pi}{6}$

c)

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

d)

$\frac{6\pi}{7}$

44.

What is the radian equivalent of -460 degrees?

a)

$\frac{9\pi}{23}$

b)

$\frac{23\pi}{9}$

c)

$-\frac{23\pi}{9}$

d)

$-\frac{9\pi}{23}$

45.

\frac{5\pi}{6}

a)

140

b)

150

c)

210

d)

216

46.

What is 45 degrees in radians?

a)

π/2

b)

π/6

c)

π/4

d)

3π/4

47.

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

a)

17 π / 3

b)

4π ∕ 3

c)

π ∕ 3

d)

8π ∕ 3

48.

What is the reference angle for -30 degrees?

a)

150 degrees

b)

30 degrees

c)

80 degrees

d)

60 degrees

49.

Which of the following angles are co-terminal to 450^o?

a)

450^o, -450^o

b)

90^o, -270^o

c)

270^o, -90^o

d)

420^o, -330^o

50.

Find the arc length of arc AB.

a)

12.57 units

b)

75.40 units

c)

24 units

d)

125.66 units

51.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

52.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

53.

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot?

a)

40

b)

35

c)

55

d)

69

54.

A pizza has a diameter of 6 inches and is cut into 8 slices. What is the area of each slice?

a)

2.36in

b)

7in

c)

3.53in

55.

In the equation

s=\theta r,\ \ \theta\ represents...

a)

Angular velocity measured in radians

b)

The central angle measured in degrees

c)

The central angle measured in revolutions

d)

The central angle measured in radians

56.

A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute. What is the angular speed in radians per hour?

a)

90π rad / 1 hr

b)

2700π rad / 1 hr

c)

5400π rad / 1 hr

d)

97200π rad / 1 hr

57.

A ceiling fan has 18 inch blades and turns at a rate of 5400π radians per hour. What is the linear speed in feet per hour?

a)

90π ft / 1 hr

b)

4010π ft / 1 hr

c)

5400π ft / 1 hr

d)

8100π ft / 1 hr

58.

If you know how fast a wheel is turning in revolutions per minutes, what do you multiply by the find angular speed?

a)

circumference

b)

π times radius

c)

2π

d)

360

59.

What is the value of "x" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

60.

What is the value of "y" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

61.

Determine the value of: cos(C)

a)

7 / 25

b)

24 / 25

c)

25 / 7

d)

24 / 7

62.

Which trigonometric function would you use to find "h", the height of the tree?

a)

sine

b)

cosine

c)

tangent

d)

none of these

63.

Which inverse trig function would you use to find the measure of Angle A?

a)

inverse sine

b)

inverse cosine

c)

inverse tangent

d)

It is not possible to determine m<A

64.

Which expression is correct for "y"?

a)

y = tan^–1(31/23)

b)

y = sin^–1(31/23)

c)

y = cos^–1(31/23)

65.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

66.

Solve for the misssing distance

a)

18.9

b)

19.5

c)

47

d)

27.5

67.

Solve for the missing angle.

a)

50.5 degrees

b)

12.7 degrees

c)

36.9 degrees

d)

72.2 degrees

68.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

c)

An 8 foot ramp leans
against a building 5 feet away. What angle does the ramp make with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

69.

Find the area of the triangle

a)

24.0 cm²

b)

47.9 cm²

c)

19.7 cm²

d)

23.967 cm²

70.

Find the area of ABC to the nearest tenth, if necessary.

a)

72.4cm²

b)

71.5cm²

c)

82.1cm²

d)

79.4cm²

71.

Domain of function $\sin^{-1}x\ is$

a)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

72.

Range of function $\cos^{-1}x\ is$

a)

$\left[0,\ \pi\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

73.

Range of function $\sin^{-1}x\ is$

a)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

74.

sin^-1[cosπ]

a)

0

b)

π

c)

π/2

d)

-π/2

75.

What is cos^-1(½)?

a)

¼π, 45⁰

b)

⅓π, 60⁰

c)

½π, 90⁰

d)

π, 180⁰

76.

sin[arcsin( $\frac{1}{2}$ )]

a)

$\frac{\pi}{6}$

b)

$\frac{1}{2}$

c)

$60\degree$

d)

no solution

77.

Find the length of side AB. m<C = 53 degrees. m<B = 44 degrees. AC = 7.

a)

8.0

b)

8.8

c)

9.2

d)

10.3

78.

Which Law would you use to find side length BC?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

SOHCAHTOA

79.

Which Law would you use to solve for Angle B?

a)

SOHCAHTOA

b)

Law of Cosines

c)

Laws of the Masked Singer

d)

Law of Sines

80.

What is the measure of angle A? BC = 37 cm, AB = 29 cm and m<C = 50 degrees.

a)

70.7 degrees

b)

74.5 degrees

c)

77.8 degrees

d)

80.2 degrees

81.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

82.

Which Law would you use to solve for side AC?

a)

Law of Sines

b)

Law of Cosines

c)

Newton's Laws

d)

SOHCAHTOA

83.

What is the distance across the river? The two sides are 4.15 miles and 5.33 miles. The included angle measure is 37 degrees.

a)

2.9 miles

b)

3.2 miles

c)

3.6 miles

d)

3.9 miles

84.

Identify the Law of Sines

a)

Sin²x + Cos²x =1

b)

Sin(A)/a = Sin(B)/b = Sin(C)/c

c)

Sin(A)Sin(B)Sin(C) = 1

d)

Soh-Cah-Toa

85.

Use the Law of Cosines to find the measure of angle x. The side lengths shown are 25, 32 and 37. <x is opposite the 25 length side.

a)

38.5^o

b)

41.7^o

c)

45.1^o

d)

51.3^o

86.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

87.

Find the equation of the figure shown.

a)

(x-5)² + (y-3)²= 25

b)

(x+5)²/4 + (y+3)²/9= 1

c)

(x-5)²/2 + (y-3)²/3= 1

d)

(x-5)²/4 + (y-3)²/9= 1

88.

Classify the conic section.

a)

Circle

b)

Ellipse

c)

Line

d)

None of these

89.

Which is the equation of a circle with center (2, 1) that passes through (2, 4)?

a)

(x – 2)² + (y – 1)² = 9

b)

(x – 2)² + (y – 1)² = 3

c)

(x + 2)² + (y + 1)² = 9

d)

(x + 2)² + (y + 1)² = 3

90.

Is the hyperbola vertical or horizontal?

a)

Vertical

b)

Horizontal

91.

What is the radius of (x + 2)²+(y - 5)² = 5

a)

5

b)

25

c)

√5

d)

(-2,5)

92.

a)

(x - 3)²+ (y + 4)² = 9

b)

(x - 3)²+ (y + 4)² = 3

c)

(x)²+ (y)² = 9

d)

(x - 1)²+ (y + 1)² = 7

93.

a)

Vertical Ellipse

b)

Vertical Hyperbola

c)

Horizontal Ellipse

d)

Horizontal Hyperbola

94.

What conic section is pictured?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

95.

Identify this conic section

a)

Circle

b)

Degenerate Conic Section

c)

Parabola

d)

Hyperbola

96.

Identify the center and the length of a and b.

a)

C: (0,0) a= 25, b=4

b)

C: (0,0) a= 4, b=25

c)

C: (0,0) a= 2, b=5

d)

C: (0,0) a= 5, b=2

97.

What are the vertices of the hyperbola?

a)

(0, 5) and (0, -5)

b)

(5, 0) and (-5, 0)

c)

(0, 25) and (-25, 0)

d)

(0, 0) and (0, 5)

98.

Find the foci of this ellipse?

a)

(8, -1), (0, -1)

b)

(4±√7, -1)

c)

(4, 3), (4, -5)

d)

(4, -1)

99.

What is the equation used to find the focal points on an ELLIPSE?

a)

c² = a² + b²

b)

c² = a² - b²

c)

1/4d

d)

(x-h)² + (y-k)² = r²

100.

What is the directrix of the parabola, careful to put in proper form
(x - 4)²= 8(y + 3)

a)

y = - 3

b)

x= 5

c)

y= - 5

d)

y= 2

101.

What is the focus of the following parabola? careful to put in proper form!
(y + 5)²= -12 (x - 2)

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

102.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -2, -4), (-2, 8)
Length of minor axis is 10
What is the center of the ellipse?

a)

( - 2, 2)

b)

(- 2, 4)

c)

(2, -2)

d)

(-2, 1)

103.

What are the equations of the asymptotes for this conic section?16x² - 9y² + 144 = 0

a)

y = (4/3)x; y = -(4/3)x

b)

y = (3/4)x; y = -(3/4)x

c)

y = 0; x = 0

d)

y = (16/9)x; y = -(16/9)x

104.

What are the vertices of the ellipse?

a)

(0, 0)

b)

(7, 1) and (-1, 1)

c)

(3, -5) and (3, 7)

d)

(3, 1)

105.

Given the equation of the parabola, where would the VERTEX be?

a)

( 3 , 3)

b)

(24, 3)

c)

( - 24, 3)

d)

(-3, 3)

106.

Name the conic section and find the center.25x²+ 9y²+ 50x - 36y - 164 = 0

a)

ellipse; C(-1, 2)

b)

hyperbola; C(-1, -2)

c)

ellipse; C(-2, 4)

d)

ellipse; C(1, 2)

107.

Name the conic section and determine the vertices.9x² - 4y² - 54x-16y - 79 = 0

a)

hyperbola; (3, 4), (3, -8)

b)

hyperbola; (7, -2), (-1, -2)

c)

hyperbola; (9, -2), (-3, -2)

d)

hyperbola; (3, 2), (3, -6)

108.

(y-4)² = -8(x+1)
What are the coordinates for the focus?

a)

(1,4)

b)

(-1,6)

c)

(-1,2)

d)

(-3,4)

109.

(x+3)² = 4(y+5)
What is the equation of the directrix?

a)

x = 4

b)

x = 2

c)

y = -4

d)

y = -6

110.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

a)

y² = 24(x+4)

b)

(y+4)² = -12x

c)

x² = 16(y+4)

d)

(x+4)² = -20y

111.

What is the focus of the following parabola?
(y + 5)²= -12 (x - 2)

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

112.

Which direction does this parabola open?

a)

Up

b)

Down

c)

Left

d)

Right

MAT 172 Exam Part 1 Review

Total questions: 112

Worksheet time: 5hrs 48mins

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