⌛ 5 minutes remaining. The timer is now always visible.
BC MCQ Set 40 (Brandeis)
5 Questions
Question 1 of 5
BC MCQ Set 40 (Brandeis) 0/5
Question 1 of 5   |  MCQ  · Level 3
A commercial nursery has \(1000\) yards of fencing which the owners plan to use to enclose as large a rectangular garden as possible. The garden will be bounded on one side by a barn, so no fencing is needed on that side. How large will the garden be (in square yards)?
A
\$125,000$ sq yds
✕
B
\$250,000$ sq yds
✕
C
\$111,088.89$ sq yds
✕
D
\$62,500$ sq yds
✕
E
none of the above
✕
Question 2 of 5   |  MCQ  · Level 3
Which of the following statements about indefinite integrals are true?
I. \(\int f(x) + g(x) d x = \int f(x) d x + \int g(x) d x\)
II. \(\int f(x) g(x) d x = \int f(x) d x \cdot \int g(x) d x\)
III. \(\int f'(g(x)) g'(x) d x = f(g(x)) + C\)
IV. \(\int [f(x)]^n d x = \dfrac{[f(x)]^{n+1}}{n + 1} + C\)
A
only I and II are true
✕
B
only I and III are true
✕
C
only I and IV are true
✕
D
only I, II and IV are true
✕
E
only I, III and IV are true
✕
Question 3 of 5   |  MCQ  · Level 2
The integral \(\int x \sin x d x\) can be found by
A
making the substitution \(u = x\)
✕
B
making the substitution \(u = \sin x\)
✕
C
using integration by parts, with \(u = \sin x\) and \(d v = x d x\)
✕
D
using integration by parts, with \(u = x\) and \(d v = \sin x d x\)
✕
E
none of the above
✕
Question 4 of 5   |  MCQ  · Level 3
Find \(\displaystyle\int_{0}^{\ln \sqrt{3}} \dfrac{e^x}{1 + e^{2 x}} d x\).
A
\(\ln 2\)
✕
B
\(1\)
✕
C
\(\dfrac{\pi}{12}\)
✕
D
\(\dfrac{\pi}{4}\)
✕
E
\(0\)
✕
Question 5 of 5   |  MCQ  · Level 3
Which of the following improper integrals converge to a finite value? (I) \(\displaystyle\int_{1}^{\infty} e^{-x} d x\) (II) \(\displaystyle\int_{-\infty}^{\infty} x^3 d x\) (III) \(\displaystyle\int_{-\infty}^{\infty} \dfrac{1}{1 + x^2} d x\)
A
I only
✕
B
III only
✕
C
I and II only
✕
D
I and III only
✕
E
all of them
✕

Review Your Answers

Check your work before submitting. You can return to any question.

Answered: 0 Unanswered: 0 Flagged: 0
—

Report an issue with this question

Question ID: —
Questions
Answered Unanswered ⚑ Flagged
Graphing Calculator
Reference Sheet

Area & Circumference

Circle$A = \pi r^2$,  $C = 2\pi r$
Rectangle$A = lw$
Triangle$A = \tfrac{1}{2}bh$
Trapezoid$A = \tfrac{1}{2}(b_1+b_2)h$

Volume

Box$V = lwh$
Cylinder$V = \pi r^2 h$
Sphere$V = \tfrac{4}{3}\pi r^3$
Cone$V = \tfrac{1}{3}\pi r^2 h$
Pyramid$V = \tfrac{1}{3}lwh$

Triangles

Pythagorean Thm$a^2 + b^2 = c^2$
30-60-90sides: $1,\, \sqrt{3},\, 2$
45-45-90sides: $1,\, 1,\, \sqrt{2}$
Triangle Anglessum $= 180°$

Other Facts

Circle Degrees$360° = 2\pi \text{ rad}$
Exterior Angle= sum of non-adjacent interior angles

The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is $2\pi$.

Submit Exam?

Answered: 0 / 5

Exam Paused

Your timer is paused. Click Resume to continue from where you left off — your answers and current position are saved.

Time is up

This exam was already started and the time limit has passed. Submit your answers as they are, or open the review panel to inspect them before submitting.