Free Printable Parametrics

1.

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

2.

Calculate a rectangular equation (y=mx+b) for the parametric function
x = -2 + 2t
y = 2 - 1t

a)

y = -x +1

b)

y = -x + 2

c)

y = 1/2x +1

d)

y = -1/2x + 1

3.

What variables are involved in parametric equations?

a)

x

b)

t

c)

z

d)

y

4.

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 y component with a parametric equation.

a)

y = -16t²+(150 sin 18)t

b)

y = -16t²+(150 sin 3)t+18

c)

y = -16t²+(150 sin 18)t+3

d)

y = 16t²+(150 sin 3)+18

5.

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

a)

A

b)

B

c)

C

d)

D

6.

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

7.

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)

8.

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.

9.

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

10.

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

a)

eliminating

b)

finding

c)

converting

d)

jumping

11.

What is the slope of the parametric function?

a)

-4/3

b)

-3/2

c)

-2/3

d)

-3/4

12.

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

13.

10.3 You must use ______________ when graphing parametric equations.

a)

arrows

b)

curves

c)

circles

d)

lines

14.

What xy-coordinates are included in this parametric graph? $x=\left|t-1\right|,\ y=t+2$ with $\left[-2,2\right]$ interval.

a)

$\left(3,0\right)$

b)

$\left(0,1\right)$

c)

$\left(1,4\right)$

d)

$\left(-1,2\right)$

e)

$\left(2,1\right)$

15.

What type of graph does the following parametrics equation show ? $x=2+t,\ y=t^2$

a)

Parabola

b)

Line

c)

Ellipse

d)

Rational

e)

Circle

16.

What is the domain value of these parametric equations in rectangular form? $x=t^3,\ y=3\ln\left(t\right)$
(Hint: Graph to determine domain)

a)

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

b)

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

c)

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

17.

What is the rectangular equation for $x=1-t,\ y=1+t$ ?

a)

$y=x$

b)

$y=-x+2$

c)

$y=2x+3$

18.

What is the rectangular equation for $x=2t-5,\ y=4t-7$ ?

a)

$y=-\frac{2}{3}x+2$

b)

$y=-x+2$

c)

$y=2x+3$

19.

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

a)

line

b)

parabola

c)

ellipse

d)

hyperbola

e)

square root

20.

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

a)

line

b)

parabola

c)

ellipse

d)

hyperbola

e)

square root

21.

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

22.

What type of graph is the following parametric equations? $x=t^2,\ y=\sqrt{4-t^2}$

a)

line

b)

parabola

c)

ellipse

d)

hyperbola

e)

square root

23.

What is the rectangular equation for $x=\sec^2\theta-1,\ y=\tan\theta$ ?

a)

$y^2=x-2$

b)

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

c)

$x+y=9$

24.

What is the coordinate for the following conditions? $x=t^2+t,\ y=t^2-t\$ where $t=-1$

a)

$\left(-\frac{3}{2},-1\right)$

b)

$\left(-2,3\right)$

c)

$\left(0,2\right)$

d)

$\left(1,-2\right)$

25.

What is the coordinate for the following conditions? $x=3t,\ y=8t^3\$ where $t=-\frac{1}{2}$

a)

$\left(-\frac{3}{2},-1\right)$

b)

$\left(-2,3\right)$

c)

$\left(2,\frac{1}{3}\right)$

d)

$\left(1,-2\right)$

26.

What is the coordinate for the following conditions? $x=\frac{1}{t},\ y=-2+\ln\left(t\right)$ where $t=1$

a)

$\left(2\sqrt{2},\sqrt{2}\right)$

b)

$\left(e,1\right)$

c)

$\left(2,\frac{1}{3}\right)$

d)

$\left(1,-2\right)$

27.

What is the coordinate for the following conditions? $x=2e^t,\ y=\frac{1}{3}e^{-t}$ where $t=0$

a)

$\left(2\sqrt{2},\sqrt{2}\right)$

b)

$\left(e,1\right)$

c)

$\left(2,\frac{1}{3}\right)$

d)

$\left(\sqrt{2},-\sqrt{2}\right)$

28.

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

29.

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.

30.

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)

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

31.

Determine an appropriate set of parametric equations and window for the rectangular equation $y=\left|2x+3\right|,\ 0\le x\le4$

a)

$x=\frac{t}{2},\ y=\left|t+\ 3\right|,\ 0\le t\le8$

b)

$x=\frac{t}{2},\ y=\left|t+3\right|,\ 0\le t\le2$

c)

$x=t,\ y=\left|t+3\right|,\ 0\le t\le4$

d)

$x=2t,\ y\ =\left|\frac{t}{2}+3\right|,\ 0\ \le t\le2$

32.

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)

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

33.

Given two points P=(-1,5) and Q=(-3,11), find a Parameterization for the ray QP.

a)

x=-1-2t
y=5+6t

b)

x=-1-2t
y=5+6t
t≥0

c)

x=-3+2t
y=11-6t

d)

x=-3+2t
y=11-6t
t≥0

34.

Using the equation for horizontal distance: x = v₀tcosθ , find the distance a ball travels if thrown at an initial velocity of 65 ft/s at an angle of 29 degrees at 2 seconds.

a)

166.177 ft

b)

5.055 ft

c)

56.85 ft

d)

113.700 ft

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.

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.

How high will the ball be when it reaches the crossbar of the goalposts, which are 25 yards (75 feet) away from the kicker?

a)

-81.516

b)

74.734

c)

28.236

d)

25

38.

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

39.

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

40.

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

41.

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

42.

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)

43.

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

44.

The variable "t" is called a

a)

parameter

b)

parallel

c)

paralegal

d)

paradise

45.

Curve orientation indicates the

a)

direction the particle is travelling.

b)

distance the particle is travelling.

c)

shape the particle is travelling

46.

A soccer ball is kicked with a 36^o angle and a velocity of 23 feet/sec.

Find the horizontal coordinate of the ball after 1 second.

a)

13.5 feet

b)

14.1 feet

c)

18.6 feet

d)

33.1 feet

47.

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.

How far away is the ball from Mr. Salaam

after 1.5 seconds?

a)

180.988 feet

b)

36.529 feet

c)

46.353 feet

d)

213.988 feet

48.

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.

How long does it take the ball to

travel 100 feet horizontally?

a)

0.206 sec

b)

0.701 sec

c)

0.634 sec

d)

2.157 sec

49.

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.

What is the coordinate location of the ball after 3 seconds?

a)

(139.058,286.975)

b)

(2.853,-133.150)

c)

(427.975,-1.942)

d)

(427.975,-94.647)

50.

There are 3 apples on an apple tree. You take 2. How many do you have?

a)

2

b)

1

c)

3

d)

5

51.

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

52.

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

53.

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

54.

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

Parametrics

Total questions: 54

Worksheet time: 3hrs 19mins

Similar Resources on Wayground