Pre-AP Calculus 10.6-10.7 Review Worksheet (Due Monday, April 6)
Name: _______________________________________
46 pts, 2 pts each
1. Evaluate the set of parametric equations for the given value of the parameter.
x  2t , y  2t 2  5t , t  – 2
[A] x  –2, y  18
[B] x  –2, y  42
[C] x  –4, y  42
[D] x  –4, y  18
2. Evaluate the set of parametric equations for the given value of the parameter.
x  1  4t , y  2t 3 , t  2
[A] x  10, y  16
[B] x  9, y  16
[C] x  10, y  12
[D] x  9, y  4
3. Eliminate the parameter and obtain the standard form of the rectangular equation.
x  – 5t  1
y  3t
[A] y  
10
5
x
3
3
[B] y 
3
3
x
5
5
3
3
[C] y   x 
5
5
6
3
[D] y   x 
5
5
4. Eliminate the parameter and obtain the standard form of the rectangular equation.
x  2cost
y  2sint
[A] x 2  y 2  4
[B] x 2  y 2  4
[C] x 2  y 2  4
[D] x 2  y 2  4
5. Identify the set of parametric equations for the given rectangular equation.
x 2  y 2  16
[A] x  4cott
y  4tant
[B] x  4t
y  4t
[C] x  4cost
y  4sint
[D] x  t
y4
6. Identify the set of parametric equations for the given rectangular equation.
y  x 3  3x
[A] x  0, y  3x [B] x  t , y  t 3  3t [C] x  x 3 , y  3x
#7-11. Eliminate the parameter
7. x  x1  t ( x2  x1 ) y  y1  t ( y2  y1 )
8. x  h  r cos   y  k  r sin 
9. x  cos   y  2sin 
10. x  3cos   y  5sin 
11. x  6t 2   y  2t  5
[D] x  t 3  3t , y  t
12. Projectile Motion: Eliminate the parameter t from the parametric equations
x  (v0 cos  )t and y  h  (v0 sin  )t  16t 2 for the motion of a projectile to show the
rectangular equation
13. Identify the graph of the given point.

– 3,
3
FG
H
IJ
K
[A]
[B]
[C]
[D]




2
2
2
2
6
0
6
0
6
14. Identify the point graphed.

2
6
FG
H
[A] 4,
7
12
IJ
K
FG
H
[B] 4,
0
3
4
IJ
K
FG
H
[C] – 4,
IJ
K
FG
H
3
7
[D] – 4,
4
12
IJ
K
0
6
0
15. Plot the point given in polar coordinates and find the other three representations.
(-5, -1.4)
16. A point in rectangular coordinates is given. Convert the point to polar coordinates.
6, – 6
b
g
FG
H
[A] – 6 2 ,
7
4
IJ
K
FG
H
[B] 6 2 ,
5
4
IJ
K
FG
H
[C] 6 2 ,
9
4
IJ
K
FG
H
[D] 6 2 ,
7
4
IJ
K
17. A point in rectangular coordinates is given. Convert the point to four equivalent polar
coordinates. FGH – 3, 3 3IJK
18. A point in polar coordinates is given. Convert the point to rectangular coordinates.
3, 0.92
b
b
g
[A] 3.000, 0.048
g
b
[B] – 0.048, – 3.000
g
b
[C] 1817
. , 2.387
g
b
[D] 0.606, 0.796
g
19. Convert the polar equation to rectangular form.
r  –12cos
b g
b g
[A] x 2  y  6  36
[B] x  6  y 2  36
[D] y  x
[E] None of these
2
2
b g
[C] x  6  y 2  36
2
20. Convert the rectangular equation to polar form. y   x
[A] r  4
[B]   


[C]  
4
4
[D] r  –8sin [E] None of these
21. Convert the rectangular equation to polar form.
[A] r  7
[B] r  14cos
[C] r  –14cos
b x  7g  y
2
2
[D]  
 49

4
[E] None of these
22.
Convert the rectangular equation to polar form.
23. Convert the polar equation to rectangular form.
2sec 
r
4sec   3
b x  2g  y
2
2
4