Exam (elaborations)
AP Calculus Chapter 10 Test Bank Mr. Surowski
- Institution
- 123 University
AP Calculus Chapter 10 Test Bank Mr. Surowski
[Show more]
Seller
Follow
Content preview
AP Calculus Testbank(Chapter 10)
(Mr. Surowski)
Part I. Multiple-Choice Questions
1. The graph in the xy-plane represented by x = 3 sin t and y =
2 cos t is
(A) a circle (B) an ellipse (C) a hyperbola (D) a parabola (E) a line
2. If a particle moves in the xy-plane so that at time t > 0 its po-
2 3
sition vector is (et , e−t ), then its velocity vector at time t = 3
is
(A) (ln 6, ln(−27))
(B) (ln 9, ln(−27))
(C) (e9 , e−27 )
(D) (6e9 , −27e−27 )
(E) (9e9 , −27e−27 )
3. A particle moves along a path described by x = cos3 t and y =
sin3 t. The distance that the particle travels along the path from
π
t = 0 to t = is
2
(A) 0.75 (B) 1.50 (C) 0 (D) −3.50 (E) −0.75
4. The area enclosed by the polar equation r = 4 + cos θ, for 0 ≤
θ ≤ 2π, is
9π 33π 33π
(A) 0 (B) (C) 18π (D) (E)
2 2 4
dy
5. If, for t > 0, x = t2 and y = cos t2 , then =
dx
(A) cos t2 (B) − sin t2 (C) − sin 2t (D) sin t2 (E) cos 2t
,6. Find the area inside one loop of the curve r = sin 2θ.
π π π π
(A) (B) (C) (D) (E) π
16 8 4 2
1
7. Find the length of the arc of the curve defined by x = t2 and
2
1 3
y = (6t + 9) 2 , from t = 0 to t = 2.
9
(A) 8 (B) 10 (C) 12 (D) 14 (E) 16
8. If f is a vector-valued function defined by f (t) = (sin 2t, sin2 t),
then f 00 (t) =
(A) (−4 sin 2t, 2 cos 2t)
(B) (− sin 2t, − cos2 t)
(C) (4 sin 2t, cos2 t)
(D) (4 sin 2t, −2 cos 2t)
(E) (2 cos 2t, −4 sin 2t)
9. A solid is formed by revolving the region bounded by the x-axis,
the lines x = 0 and x = 1 and the parametric curve x = sin t, y =
1 + cos2 (2t) about the x-axis. Write down the integral which will
compute the volume of the solid.
Z π Z π
2 2
4
(A) π (1 + cos (2t)) dt (C) π (sin2 t + (1 + cos2 (2t))2 ) dt
0 0
Z π
2
(D) 2π (1 + cos2 (2t))2 dt
0
π
π
Z
2 Z
2
(B) π (1 + cos2 (2t))2 dt (E) π cos t(1 + cos2 (2t))2 dt
0 0
, 10. The length of the curve determined by x = 3t and y = 2t2 from
t = 0 to t = 9 is
Z 9p
(A) 9t2 + 4t4 dt
0
Z 162 p
(B) 9 − 16t2 dt
0
Z 162 p
(C) 9 + 16t2 dt
0
Z 3p
(D) 9 − 16t2 dt
0
Z 9p
(E) 9 + 16t2 dt.
0
11. The length of the curve determined by x = 2t3 and y = t3 from
t = 0 to t = 1 is
√
5 5 3 √
(A) (B) (C) (D) 5 (E) 3
7 2 2
12. The area of the region inside
√ the polar curve r = 4 sin θ but out-
side the polar curve r = 2 2 is given by
Z 3π/4
(A) 2 (4 sin2 θ − 1) dθ
π/4
1
Z 3π/4 √ 2
(B) (4 sin θ − 2 2) dθ
2 π/4
1
Z 3π/4 √
(C) (4 sin θ − 2 2) dθ
2 π/4
1 3π/4
Z
(D) (16 sin2 θ − 8) dθ
2 π/4
1 3π/4
Z
(E) (4 sin2 θ − 1) dθ.
2 π/4
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Exammate. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
65040 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now
Recently viewed by you
Summary ·
Samenvatting KT4 - HBO v jaar 2 - (cijfer 8,7)
Summary ·
Samenvatting strafprocesrecht 2020-2021
Exam (elaborations) ·
MCAT PRACTICE QUESTIONS well answered to pass
Summary ·
Plichtenleer en ethisch handelen 12/20 behaald!!
Summary ·
Samenvatting taal- en onderzoeksvaardigheden 2
Class notes ·
Samenvatting financieel recht 2021-2022
Exam (elaborations) ·
Hondros HESI Exit Preparation Condensed
Exam (elaborations) ·
CAAN exam 2023 with 100% correct answers
