Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Considering the given value
of t, choose the ordered pair that lies on the graph of the given pair of parametric
equations.
x = -4t
+ 8, y = 3t - 3; t = -7
a. | ( 20,
-18) | c. | ( 4,
0) | b. | ( -3,
-7) | d. | ( 36,
-24) |
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2.
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Considering the given value
of t, choose the ordered pair that lies on the graph of the given pair of parametric
equations.
x = sin t, y = cos
t; t = 
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3.
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Considering the given value
of t, choose the ordered pair that lies on the graph of the given pair of parametric
equations.
x = t, y =  ; t = -2
a. | ( -2,
4) | c. | ( 2,
8) | b. | ( -8,
-2) | d. | ( -2,
-8) |
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4.
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Use a table of values to
graph the plane curve defined by the following parametric equations. Find a rectangular equation for
the curve.
x = 3t, y =
t + 1, for t in [-2, 3]
a. | 
y =  x - 1, for x in [ -6, 9] | b. | 
y =  x + 1, for x in [ -6, 9] | c. | 
y = -3x + 1,
for x in [ -9, 6] | d. | 
y = x2 + 1, for x in [-2,
2] |
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5.
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Use a table of values to
graph the plane curve defined by the following parametric equations. Find a rectangular equation for
the curve.
x = t2, y =  + 2, for t in [0, 4]
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6.
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Use a table of values to
graph the plane curve defined by the following parametric equations. Find a rectangular equation for
the curve.
x = 8 sin t, y = 8 cos t, for t in [0, 2ð]
a. | 
y2 - x2
= 64, for x in [ -8, 8] | b. | 
y =  = 64, for x in
[-8, 8] | c. | 
x2 + y2 = 64, for
x in [ -8, 8] | d. | 
y = x2 - 9, for x in [-2,
2] |
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7.
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Use a table of values to
graph the plane curve defined by the following parametric equations. Find a rectangular equation for
the curve.
x =  ,
y = 4t + 3, for t in [0, 4]
a. | 
y =
-3x + 19, for x in [0, 2] | b. | 
y = 4x2 + 3,
for x in [0, 2] | c. | 
y = -3x2 + 19, for x in
[0, 2] | d. | 
y = 3x2 + 4, for x in
[-1, 2] |
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8.
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Find a rectangular equation
for the plane curve defined by the parametric equations.
x =  , y = 2t +
5
a. | y = 2x2 -
5 | c. | y = 2x2 +
5 | b. | y = 2 - 5, x =
0 | d. | y = 2 + 5, x =
0 |
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9.
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Find a rectangular equation
for the plane curve defined by the parametric equations.
x = t - 3, y = t2 + 5
a. | y = x2 - 6x -
14 | c. | y = x2 +
14 | b. | y = x2 + 6x +
14 | d. | y = x2 - 14 |
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10.
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Find a rectangular equation
for the plane curve defined by the parametric equations.
x = 5 tan t, y = 4 cot t
a. | y =  cos
x | c. | y =  sin
x | b. | y =  | d. | y =  |
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11.
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Find a rectangular equation
for the plane curve defined by the parametric equations.
x = t2 + 1, y = t2 - 1
a. | y = x2 - 2, x =
1 | c. | y = x2 + 2, x =
1 | b. | y = x - 2, x =
1 | d. | y = x + 2, x =
1 |
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12.
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Give two parametric
representations for the equation of the parabola.
y =  +
10
a. | x = t, y =  + 10 for t in (-8, 8); x = t + 5, y =  + 10
for t in (-8, 8) | b. | x = t, y =  + 10 for t in (-8, 8); x = t - 5,
y =  + 10 for t in (-8,
8) | c. | x = t, y =  + 10 for t in (-8, 8); x = t + 5, y =  + 10
for t in (-8, 8) | d. | x = t, y =  + 10 for t in (-8, 8); x = t - 5,
y =  + 10 for t in (-8,
8) |
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13.
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Give two parametric
representations for the equation of the parabola.
y =  - 4x +
7
a. | x = t, y =  - 4t - 7 for t in (-8, 8); x = t - 2, y =  - 3
for t in (-8, 8) | b. | x = t, y =  + 4t + 7 for t in (-8, 8); x =
t - 2, y =  + 3 for t in (-8,
8) | c. | x = t, y =  - 4t + 7 for t in (-8, 8); x = t - 2, y =  + 3
for t in (-8, 8) | d. | x = t, y =  + 4t + 7 for t in (-8, 8); x =
t - 2, y =  - 3 for t in (-8,
8) |
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14.
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Graph the cycloid for t in
the indicated interval.
x = 2(t - sin t), y= 2(1 - cos t), 0 = t =
6ð
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15.
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Graph the cycloid for t in
the indicated interval.
x = 6t - 6 sin t, y= 6 - 6 cos t,
-2ð = t = 2ð
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16.
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A projectile is fired with an
initial velocity of 500 feet per second at an angle of 45° with the horizontal. To the
nearest 10 feet, find the horizontal distance covered by the projectile.
a. | 8320 ft | c. | 7470 ft | b. | 8550 ft | d. | 7810 ft |
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17.
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A projectile is fired with an
initial velocity of 300 feet per second at an angle of 70° with the horizontal. In how
many seconds will the projectile strike the ground? (Round your answer to the nearest tenth of a
second.)
a. | 17.6
sec | c. | 14.2
sec | b. | 20.4 sec | d. | 21.7 sec |
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18.
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A projectile is fired with an
initial velocity of 400 feet per second at an angle of 70° with the horizontal. To the
nearest foot, find the maximum altitude of the projectile.
a. | 2191 ft | c. | 2224 ft | b. | 2200 ft | d. | 2208 ft |
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19.
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True or false? The parametric
equations x = t3, y = t3 - 8 will graph a circle.
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