BC MCQ Set 10 - PyQuiz

Question 1 of 3 | 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 2 of 3 | 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 3 of 3 | 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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Area & Circumference

Volume

Triangles

Other Facts

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