BC MCQ Set 10 - PyQuiz

Question 1 of 10 | MCQ · Level 3

The equation of the tangent line to the curve with parametric equations $x(t) = 2 t + 1$, $y(t) = 3 - t^3$ at $t = 1$ is:

$2 x + 3 y = 12$

$3 x + 2 y = 13$

$6 x + y = 20$

$3 x - 2 y = 5$

None of the above.

Question 2 of 10 | MCQ · Level 4

If $x(t) = 4 \cos t$, $y(t) = 3 \sin t$, then $\displaystyle\int_{2}^{4} x y d x$ is equivalent to

$48 \displaystyle\int_{\dfrac{\pi}{3}}^0 \sin t \cos^2 t d t$

$48 \displaystyle\int_{2}^{4} \sin^2 t \cos t d t$

$36 \displaystyle\int_{2}^{4} \sin t \cos^2 t d t$

$-48 \displaystyle\int_{0}^{\dfrac{\pi}{3}} \sin t \cos^2 t d t$

$48 \displaystyle\int_{0}^{\dfrac{\pi}{3}} \sin^2 t \cos t d t$

Question 3 of 10 | MCQ · Level 4

The length of $x = e^t \cos t$, $y = e^t \sin t$ from $t = 2$ to $t = 3$ is

$\sqrt{2} e^2 \sqrt{e^2 - 1}$

$\sqrt{2} (e^3 - e^2)$

$2 (e^3 - e^2)$

$e^3 (\cos 3 + \sin 3) - e^2 (\cos 2 + \sin 2)$

None of the above.

Question 4 of 10 | MCQ · Level 3

The area enclosed by the four-leaved rose $r = \cos(2 \theta)$ is

$\dfrac{\pi}{4}$

$\dfrac{\pi}{2}$

$\pi$

$2 \pi$

$\dfrac{\pi}{2} + \dfrac{1}{2}$

Question 5 of 10 | MCQ · Level 3

The rectangular equation of the parametric curve $x = 1 - \sin t$ and $y = 4 - 2 \cos t$ is:

$4(x - 1)^2 + (y - 4)^2 = 1$

$4(x - 1)^2 + (y - 4)^2 = 4$

$(x - 1)^2 + (y - 4)^2 = 4$

$(x - 1)^2 + (y - 4)^2 = 2$

none of the above

Question 6 of 10 | MCQ · Level 3

The area bounded by the lemniscate with polar equation $r^2 = 2 \cos(2 \theta)$ is equal to

$4$

$1$

$\dfrac{1}{2}$

$2$

None of the above

Question 7 of 10 | MCQ · Level 2

The graph of the polar equation $r = \dfrac{1}{\sin \theta - 2 \cos \theta}$ is:

a circle

a line with slope $1$

a line with slope $2$

a parabola

a semi-circle

Question 8 of 10 | 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 9 of 10 | MCQ · Level 4

The power series $(x + 1) - \dfrac{(x + 1)^2}{2!} + \dfrac{(x + 1)^3}{3!} - \dfrac{(x + 1)^4}{4!} + ...$ diverges:

for no real $x$ values

if $-2 < x \leq 0$

if $x < -2$ or $x > 0$

if $-2 \leq x < 0$

if $x \neq -1$

Question 10 of 10 | 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 $x > 4$

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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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