Free Printable U13 Parametric

1.

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)

2.

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

a)

(2, 4)

b)

(4, 2)

c)

(-6, 0)

d)

(0,-6)

3.

The variable "t" is called a

a)

parameter

b)

parallel

c)

paralegal

d)

paradise

4.

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

5.

Write x = 2t and y = t² + 3 in rectangular form .

a)

y = 4x² + 3

b)

y = ¼ x² + 3

c)

y = 4t²+ 12

d)

y = (x - 2)² + 3

6.

Eliminate the parameter.

x = t and y = 5t

a)

y=5x²

b)

y=5x

c)

y= x - 5

d)

y=x²

7.

Eliminate the parameter.

x= 2+4t and y=-1+6t

a)

y=(3/2)x - 4

b)

t=(x-2)/4

c)

y=x - 4

d)

y= (2/3)x + 4

8.

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)

9.

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

a)

(2, 4)

b)

(4, 2)

c)

(-6, 0)

d)

(0,-6)

10.

Write the rectangular equation for the following parametric equations.

x = 4 - t

y = 2t + 1

a)

y = 9 - 2x

b)

y = 9 + 2x

c)

y = 7--2x

d)

y = 9 + 2x

11.

Write the rectangular equation for the following parametric equations.

x = 2t - 3

y = 2t + 1

a)

y = x + 4

b)

y = x + 7

c)

y = x - 2

d)

y = mx+ b

12.

Write the rectangular equation for the following parametric equations.

x = 3/t

y = 6t + 1

a)

y = (18/x) + 1

b)

y = 18x + 1

c)

y = 19x

d)

y = 19/x

13.

The horizontal distance a projectile travels is represented by

a)

x

b)

y

c)

t

14.

The vertical distance a projectile travels is represented by

a)

x

b)

y

c)

t

15.

Write x = 2t and y = t² + 3 in rectangular form .

a)

y = 4x² + 3

b)

y = ¼ x² + 3

c)

y = 4t²+ 12

d)

y = (x - 2)² + 3

16.

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

a)

A

b)

B

c)

C

d)

D

17.

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

18.

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)

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

19.

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

a)

(2, 4)

b)

(4, 2)

c)

(-6, 0)

d)

(0,-6)

20.

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)

21.

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

22.

Converting parametric equations to a rectangular equation is called _________________ the parameter.

a)

eliminating

b)

finding

c)

converting

d)

jumping

23.

Write $x=2t$ and $y=t^2+3$ in rectangular form.

a)

$y=4x^2+3$

b)

$y=\frac{1}{4}x^2+3$

c)

$y=4t^2+12$

d)

$y=(x-2)^2+3$

24.

Find the ordered pair based on the parametric equations when t=0

x(t) = e^t - e^-t

y(t) = e^t + e^-t

a)

(0, 2)

b)

(2.35, 3.08)

c)

(7.25, 7.52)

d)

(0, 0)

25.

Eliminate the parameter. $x=\frac{1}{t-2}$ and $y=4t-5$

a)

$y=4x+5$

b)

$y=\frac{4}{x}+3$

c)

$y=-2x+3$

d)

$y=4x+\frac{1}{3}$

26.

Eliminate the parameter

x = 3/t

y = 6t + 1

a)

y = (18/x) + 1

b)

y = 18x + 1

c)

y = 19x

d)

y = 19/x

27.

Eliminate the parameter
$x=\sqrt{t-4},\ y=\sqrt{t}+2$

a)

$y=x+2$

b)

$x=y-4$

c)

$y=x+4$

d)

$x=\sqrt{\left(y-2\right)^2-4}$

28.

The horizontal distance a projectile travels is represented by

a)

x

b)

y

c)

t

29.

What curve do the parametric equations make? What is the direction of motion?
x=1+3sint
y=-2+4cost

a)

Circle. Counterclockwise.

b)

Circle. Clockwise.

c)

Ellipse. Counterclockwise.

d)

Ellipse. Clockwise.

30.

Which half of the curve will be graphed for the parametric equation:
x=1+3cost
y=-2+4sint
π≤t≤2π

a)

Right half

b)

Left half

c)

Top half

d)

Bottom half

31.

The coordinates of a car at time t are given by x = 8 - t and y = 2t - 16. As t increases, which direction and path is the car traveling?

a)

from left to right along the path y = 2x - 16.

b)

from left to right along the path y = 2x.

c)

from right to left along the path y = -2x.

d)

from left to right along the path y = -2x.

32.

Kait hits the golfball at an angle of 27° with the horizontal at an initial speed of 22 m/s. How far has the ball traveled horizontally after 2 seconds?

a)

50.068 meters

b)

19.976 meters

c)

39.204 meters

d)

42.077 meters

33.

What type of graph is the following parametric equations? $x=-2\sin\theta,\ y=-3\cos\theta$

a)

line

b)

parabola

c)

ellipse

d)

hyperbola

e)

square root

34.

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

35.

The height of an object can be modeled by the formula h(t) = -16t² + 70t + 95, where h(t) is in feet after t seconds.

What is the height of the object after 5 seconds?

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

36.

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

37.

A ball is thrown horizontally at a height of 2.2 meters at a velocity of 65 m/s. Assume no air resistance. How long until the ball reaches the ground?

a)

0.45 s

b)

0.67 s

c)

0.22 s

d)

0.47 s

38.

A ball is thrown horizontally at a height of 2.2 meters at a velocity of 65 m/s. Assume no air resistance. How far did the ball travel horizontally when it hit the ground?

a)

14.3 m

b)

30.55 m

c)

65 m

d)

43.55 m

39.

A stone is thrown off a bridge 70 feet above the water at an angle of elevations of 48 $\degree$ with an initial velocity of 40 feet per second. Find the maximum height of the stone.

a)

83.81 feet

b)

84.57 feet

c)

85.02 feet

d)

86.38 feet

40.

A stone is thrown off a bridge 70 feet above the water at an angle of elevations of 48° with an initial velocity of 40 feet per second. Find the horizontal distance the stone traveled at the time it reaches the surface of the water (h = 0)

a)

83.04 fett

b)

83.92 feet

c)

84.56 feet

d)

86.18 feet

41.

A stone is thrown off a bridge 70 feet above the water at an angle of elevations of 48 ° with an initial velocity of 40 feet per second. Find the height of the stone at the time it reaches a horizontal distance of 80 feet.

a)

14.76 feet

b)

15.12 feet

c)

15.84 feet

d)

16.22 feet

42.

Eliminate the parameter. Convert the parametric equation to rectangular. x= t - 1 and y=t² - 2

a)

y=(x+1)² - 2

b)

t=x - 1

c)

x=t - 1

d)

y=t - 2

43.

A soccer ball is kicked with a 36 degree angle and a velocity of 23 f/s. Find the horizontal coordinate of the ball after 1 second.

a)

13.5 f/s

b)

14.1 f/s

c)

18.6 f/s

d)

33.1 f/s

44.

A model rocket is launched from the roof of a building. Its flight path is modeled by the quadratic function h(t)= -16t²+96t+64 where h is the height of the rocket above the ground in feet and t is the time after the launch in seconds. What is the height of the rocket after 3 seconds?

a)

16 feet

b)

208 feet

c)

256 feet

d)

304 feet

45.

Mr. Salaam hits a baseball to Mr. Shakin at 3 ft above the ground with an initial speed of 150 ft/sec and at angle of 18 degrees with the horizontal.

Model the x component with a parametric equation.

a)

x = (3 cos 18) t

b)

x = (150 cos 18)t

c)

x = (150 cos 18)

d)

x = (150 cos 3)t

46.

Identify the starting point of the parametric equation.
x = -2 + 2t
y = 2 - 1t

a)

(-2, 2)

b)

(2, -2)

c)

(2, -1)

d)

(-1, 2)

47.

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

a)

(1, -1)

b)

(4, -3)

c)

(-3, 2)

d)

(-3, 4)

48.

If tanA= 3/4, then secA=...

a)

4/3

b)

4/5

c)

3/4

d)

4/3

49.

Which is NOT true about the graph created by the Parametric equations shown. Select all that apply

a)

It is a horizontal parabola ,opens left, vertex at (0,0)

b)

The graph starts at (-1,10) and ends at (1,-10)

c)

The graph goes through the points (-4,20)

d)

The focus is at (-4,0)

50.

Which is NOT true about the graph created by the Parametric equations shown. Select all that apply

a)

It is a horizontal parabola that opens right

b)

The graph starts at (0,0) and ends at (4,-2)

c)

The graph goes through the point (2,-1)

d)

The graph starts from right to left

51.

What curve do the parametric equations make? What is the direction of motion?
x=1+3cost
y=-2+3sint

a)

Circle. Counterclockwise.

b)

Circle. Clockwise.

c)

Ellipse. Counterclockwise.

d)

Ellipse. Clockwise.

52.

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 reach its maximum altitude?

a)

13.6 seconds

b)

8.8 seconds

c)

5.4 seconds

d)

16.9 seconds

53.

A projectile is fired from a height of 9.5 feet with an initial velocity of 136 ft/sec at an angle of 55° with the horizontal. Determine the maximum height reached by the projectile. Round your answer to the nearest tenth of a foot.

a)

212.9 ft

b)

193.9 ft

c)

397.3 ft

d)

203.4 ft

54.

Determine an appropriate set of parametric equations for the rectangular equation $y=2x^3-5,\ -1\le x\le3$

a)

$x=t^3,\ y=2t-5,\ 1\le t\le8$

b)

$x=t^{\frac{1}{3}},\ y\ =2t-5,\ -1\le t\le8$

c)

$x=\left(\frac{t}{2}\right)^{\frac{1}{3}},\ y=2t-5,\ -1\le t\le8$

d)

$x=\left(\frac{t}{2}\right)^{\frac{1}{3}},\ y\ =t-5,\ -1\le t\le2$

55.

Kait hits the golfball at an angle of 27° with the horizontal at an initial speed of 22 m/s. How far has the ball traveled horizontally after 2 seconds?

a)

50.068 meters

b)

19.976 meters

c)

39.204 meters

d)

42.077 meters

56.

Alex hits the baseball at a 28° angle with an initial velocity of 103 feet per second. The ball is 4 feet off the ground (initial height) at time of impact. The ball is not caught by the outfielder and hits the ground. How far from home plate is the ball, approximately?

a)

282 ft.

b)

347 ft.

c)

188 ft.

d)

226 ft.

57.

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

58.

The coordinates of a car at time t are x = 10 - t and y = 8 - t. Which equation describes the path of the car?

a)

y = 10 - x

b)

y = 8 - x

c)

y = 2 - x

d)

y = x - 2

59.

The coordinates of a train at time t are x = 8 - t and y = 9 - 2t. As t increases, which arrow shows the direction, but not necessarily the path of the train?

a)

Arrow A

b)

Arrow B

c)

Arrow C

d)

Arrow D

60.

The coordinates of a car at time t are given by x = 8 - t and y = 2t - 16. As t increases, which direction and path is the car traveling?

a)

from left to right along the path y = 2x - 16.

b)

from left to right along the path y = 2x.

c)

from right to left along the path y = -2x.

d)

from left to right along the path y = -2x.

61.

The position of a particle at time t is given by x = 3 cos(t) and y = 3 sin(t). Which of the following describes the path of the particle?

a)

a circle of radius 3 centered at the origin

b)

a circle of diameter 3 centered at the origin

c)

an ellipse with minor axis 3 centered at the origin

d)

an ellipse with major axis 3 centered at the origin

62.

A cannonball is fired from a height of 3 feet, at a 45 degree angle with an initial velocity of 625 feet per second. Write an equation to model the horizontal motion of the cannonball.

a)

$y=625\sin\left(45\right)$

b)

$x=625\cos\left(45\right)t$

c)

$x=625\cos\left(45\right)t+3$

d)

$y=625\sin\left(45\right)t+3$

63.

A cannonball is fired at a 45 degree angle with an initial velocity of 625 feet per second. Find the horizontal distance of the cannonball after 2 seconds.

a)

1250

b)

441.9

c)

883.9

d)

328.3

64.

A cannonball is fired from a height of 3 feet, at a 45 degree angle with an initial velocity of 625 feet per second. Write an equation to model the vertical motion of the cannonball.

a)

$y=625\sin\left(45\right)$

b)

$y=-16t^2+625\sin\left(45\right)t$

c)

$y=-16t^2+625\sin\left(45\right)t+3$

d)

$y=625\sin\left(45\right)t+3$

65.

A cannonball is fired from a height of 3 feet, at a 45 degree angle with an initial velocity of 625 feet per second. How long is the cannonball in the air?

a)

27.6 seconds

b)

13.8 seconds

c)

10.3 seconds

d)

20.5 seconds

66.

The height of an object can be modeled by the formula $h\left(t\right)=-16t^2+140\sin\left(30\right)t+95$
What is the height of the object after 5 seconds?

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

67.

An NFL kicker at the 20 yard line kicks a footbal downfield with an initial velocity of 75 ft/sec at an angle of 66 degrees. The ball leaves his foor at a height of 3 feet.

Write a set of parametric equations to model the motion of the ball.

a)

$x=20\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+20\sin\left(66\right)t+75$

b)

$x=75\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+75\sin\left(66\right)t+20$

c)

$x=20\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+20\sin\left(66\right)t+3$

d)

$x=75\cos\left(66\right)t\ \ \ ,\ \ \ \ y=-16t^2+75\sin\left(66\right)t+3$

68.

A ball is thrown horizontally at a height of 2.2 meters at a velocity of 65m/s. How far did the ball travel horizontally when it hit the ground?

a)

14.3 m

b)

30.55 m

c)

65 m

d)

43.55

69.

A ball is kicked with a 36 degree angle and a velocity of 23 f/s. Find the horizontal distance of the ball after 1 second.

a)

13.5

b)

14.1

c)

18.6

d)

33.1

70.

A model rocket is launched from the roof of a building. Its flight path is modeled by the quadratic function $h\left(t\right)=-16t^2+192\sin\left(90\right)+64$

What is the height of the rocket after 3 seconds?

a)

16 feet

b)

208 feet

c)

256 feet

d)

304 feet

71.

Alex hits the baseball at a 28 degree angle with an initial velocity of 103 feet per second from an initial height of 4 feet. The ball is not caught by the outfielder and hits the ground. How far from home plate does the ball land?

a)

282 feet

b)

347 feet

c)

188 feet

d)

226 feet

72.

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

a)

(2, 4)

b)

(4, 2)

c)

(-6, 0)

d)

(0,-6)

73.

Write the rectangular equation for the following parametric equations.

x = 2t - 3

y = 2t + 1

a)

y = x + 4

b)

y = x + 7

c)

y = x - 2

d)

y = mx+ b

74.

Eliminate the parameter from $x(t)=t^2+5$ and $y(t)=t^2-4$ . Which of the following graphs results?

a)

Linear

b)

Quadratic

c)

Quartic

d)

Square Root

75.

What type of graph is the following parametric equations? $x=4-\sqrt{t},\ y=\sqrt{t}$

a)

line

b)

parabola

c)

ellipse

d)

hyperbola

e)

square root

76.

Does this describe a function?

a)

Function

b)

Not a Function

77.

Evaluate f(3).

a)

f(3) = 0

b)

f(3) = -2

c)

f(3) = 3

d)

f(3) = 4

78.

What is the value of x when f(x) = 16?

a)

x = 4 only

b)

x = 4 and x = 8

c)

x = 16

d)

Not on the graph

79.

Evaluate f(2).

a)

f(2) = 5

b)

f(2) = 12

c)

f(2) = 10

d)

f(2) = 0.5

80.

What is the increasing interval on the function shown?

a)

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

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

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

81.

Over what interval is this function constant?

a)

(-5, ∞)

b)

(-3, 4)

c)

(4, ∞)

d)

-5

82.

The function shown contains:

a)

Only one local maximum.

b)

Two local maximums.

c)

Two local minimums.

d)

Three local maximums

83.

What is the domain of the graph?

a)

1≤ x ≤ 4

b)

1 < x < 4

c)

1≤ y ≤ 4

d)

1 < y < 4

84.

Domain of

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

a)

real numbers

b)

$\left[2,\infty\right)$

c)

$\left(2,\infty\right)$

d)

$\left(\infty,2\right]$

85.

What is the range of the function given below?

a)

0 ≤ y ≤ 7

b)

-2 ≤ y ≤ 4

c)

.2 ≤ y ≤ 4

d)

All real numbers

86.

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)

87.

What are the decreasing intervals?

a)

(- ∞, 0) & (2, ∞ )

b)

(-1, 0) & (2,-4)

c)

(0,2)

d)

(0, -4) & (0, 2)

88.

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

a)

b)

c)

d)

89.

The coordinates of a car at time t are x = 10 - t and y = 8 - t. Which equation describes the path of the car?

a)

y = 10 - x

b)

y = 8 - x

c)

y = 2 - x

d)

y = x - 2

U13 Parametric

Total questions: 89

Worksheet time: 3hrs 23mins

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