BC MCQ Set 20 - PyQuiz

Question 1 of 7 | MCQ · Level 3

The area of one loop of the graph of the polar equation $r = 2 \sin(3 \theta)$ is given by which of the following?

$4 \displaystyle\int_{0}^{\dfrac{\pi}{3}} \sin^2(3 \theta) d \theta$

$2 \displaystyle\int_{0}^{\dfrac{\pi}{3}} \sin(3 \theta) d \theta$

$2 \displaystyle\int_{0}^{\dfrac{\pi}{3}} \sin^2(3 \theta) d \theta$

$2 \displaystyle\int_{0}^{2 \dfrac{\pi}{3}} \sin^2(3 \theta) d \theta$

$2 \displaystyle\int_{0}^{2 \dfrac{\pi}{3}} \sin(3 \theta) d \theta$

Question 2 of 7 | MCQ · Level 2

Identify the false statement.

$\dfrac{d \sinh(x)}{d x} = \cosh(x)$

$\dfrac{d \cosh(x)}{d x} = \sinh(x)$

$\displaystyle\int_{a}^{t} sech^2(x) d x = \tanh(t) - \tanh(a)$

$\cosh^2(x) - \sinh^2(x) = 1$

All four statements are true.

Question 3 of 7 | MCQ · Level 3

Evaluate $\displaystyle\int_{0}^{6} \sqrt{6 x - x^2} d x$

$\pi$

$2 \pi$

$\dfrac{5 \pi}{2}$

$\dfrac{9 \pi}{2}$

$3 \pi$

Question 4 of 7 | MCQ · Level 4

Find $\int e^{m x} \cos(n x) d x$

$e^{m x} \dfrac{m \cos(n x) - n \sin(n x)}{m^2 + n^2} + C$

$e^{m x} \dfrac{\cos(n x) - \sin(n x)}{m^2 + n^2} + C$

$e^{m x} \dfrac{n \sin(n x) + m \cos(n x)}{m^2 + n^2} + C$

$\dfrac{-e^{m x} \cos(n x)}{n} + C$

None of the above.

Question 5 of 7 | MCQ · Level 3

The power series $x + \dfrac{x^2}{2} + \dfrac{x^3}{3} + ... + \dfrac{x^n}{n} + ...$ converges if and only if:

$-1 < x < 1$

$-1 \leq x \leq 1$

$-1 \leq x < 1$

$-1 < x \leq 1$

$x = 0$

Question 6 of 7 | MCQ · Level 3

The series $\displaystyle\sum_{n=0}^{\infty} n! (x - 3)^n$ converges if and only if

$x = 0$

$2 < x < 4$

$x = 3$

$2 \leq x \leq 4$

$x < 2$ or $x > 4$

Question 7 of 7 | MCQ · Level 3

The Taylor polynomial of order 3 at $x = 1$ for $e^x$ is:

$1 + (x - 1) + \dfrac{(x - 1)^2}{2} + \dfrac{(x - 1)^3}{3}$

$e[1 + (x - 1) + \dfrac{(x - 1)^2}{2} + \dfrac{(x - 1)^3}{3}]$

$e[1 + (x + 1) + \dfrac{(x + 1)^2}{2} + \dfrac{(x - 1)^3}{3!}]$

$e[1 + (x - 1) + \dfrac{(x - 1)^2}{2!} + \dfrac{(x - 1)^3}{3!}]$

$e[1 - (x - 1) + \dfrac{(x - 1)^2}{2!} - \dfrac{(x - 1)^3}{3!}]$

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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 $2\pi$.

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