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BC MCQ Set 10
4 Questions
Question 1 of 4
BC MCQ Set 10 0/4
Question 1 of 4   |  MCQ  · Level 3
The area enclosed by the four-leaved rose \(r = \cos(2 \theta)\) is
A
\(\dfrac{\pi}{4}\)
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B
\(\dfrac{\pi}{2}\)
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C
\(\pi\)
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D
\(2 \pi\)
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E
\(\dfrac{\pi}{2} + \dfrac{1}{2}\)
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Question 2 of 4   |  MCQ  · Level 3
The area bounded by the lemniscate with polar equation \(r^2 = 2 \cos(2 \theta)\) is equal to
A
\(4\)
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B
\(1\)
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C
\(\dfrac{1}{2}\)
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D
\(2\)
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E
None of the above
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Question 3 of 4   |  MCQ  · Level 3
The power series \(x + \dfrac{x^2}{2} + \dfrac{x^3}{3} + ... + \dfrac{x^n}{n} + ...\) converges if and only if:
A
\(-1 < x < 1\)
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B
\(-1 \leq x \leq 1\)
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C
\(-1 \leq x < 1\)
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D
\(-1 < x \leq 1\)
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E
\(x = 0\)
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Question 4 of 4   |  MCQ  · Level 3
The series \(\displaystyle\sum_{n=0}^{\infty} n! (x - 3)^n\) converges if and only if
A
\(x = 0\)
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B
\(2 < x < 4\)
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C
\(x = 3\)
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D
\(2 \leq x \leq 4\)
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E
\(x < 2\) or \(x > 4\)
✕

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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 $2\pi$.

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