ilearnmathnet AB MCQ Set 10

Question 1 of 10 | MCQ · Level 3

Let $f$ be a differentiable function such that $f(3) = 15$, $f(6) = 3$, $f'(3) = -8$, and $f'(6) = -2$. The function $g$ is differentiable and $g(x) = f^{-1}(x)$ for all $x$. What is the value of $g'(3)$?

$\dfrac{-1}{2}$

$\dfrac{-1}{8}$

$\dfrac{1}{6}$

$\dfrac{1}{3}$

Cannot be determined.

Question 2 of 10 | MCQ · Level 2

The slope of the tangent to $y = \arctan(4x)$ at $x = \dfrac{1}{4}$ is:

$2$

$\dfrac{1}{2}$

$0$

$\dfrac{-1}{2}$

$-2$

Question 3 of 10 | MCQ · Level 3

If $f'(x) = (x-1)(x+2)(3-x)$, which of the following is NOT true about $f(x)$?

$f(x)$ has a horizontal tangent at $x = 1$

$f(x)$ is a polynomial of degree 4

$f(x)$ has a relative maximum at $x = 3$

$f(x)$ is decreasing on $(-2, 1)$

$f(x)$ is concave up on $(-2, 1)$

Question 4 of 10 | MCQ · Level 3

At the point of intersection of $y = \sin\left(x + \dfrac{\pi}{2}\right)$ and $y = 1 - \dfrac{x^2}{2}$, the tangent lines are:

identical

parallel

perpendicular

intersecting but not perpendicular

none of the above

Question 5 of 10 | MCQ · Level 1

The graph of an even function passing through $(3, -2)$ must also contain:

$(-3, -2)$

$(-3, 2)$

$(3, 2)$

$(2, 3)$

$(0, 0)$

Question 6 of 10 | MCQ · Level 3

$\operatorname*{lim}\limits_{x \rightarrow 0} \dfrac{\cos\left(\dfrac{\pi}{2} + x\right) - \cos\left(\dfrac{\pi}{2} - x\right)}{x} =$

$1$

$-2$

$-1$

$0$

$2$

Question 7 of 10 | MCQ · Level 3

$\int 5^{2x} d x =$

$\dfrac{5^{2x}}{\ln 5} + C$

$\dfrac{5^{2x}}{2 \ln 5} + C$

$\dfrac{5^{2x+1}}{2x+1} + C$

$\dfrac{5^{2x}}{2} + C$

$(\ln 5) 5^{2x} + C$

Question 8 of 10 | MCQ · Level 3

$f(x) = \dfrac{25 - x^2}{5 - x}$ for $x \neq 5$ and $f(x) = 5$ when $x = 5$. Which of the following is correct?

$f(x)$ is continuous at 5 since $f(x)$ is defined at $x = 5$

$f(x)$ is continuous at 5 since $\operatorname*{lim}\limits_{x \rightarrow 5} f(x)$ exists

$f(x)$ is discontinuous at 5 since $f(5)$ does not exist

$f(x)$ is discontinuous at 5 since $\operatorname*{lim}\limits_{x \rightarrow 5} f(x)$ DNE

$f(x)$ is discontinuous at 5 since $\operatorname*{lim}\limits_{x \rightarrow 5} f(x) \neq f(5)$

Question 9 of 10 | MCQ · Level 3

If $y = \ln(2x+3)$, then $\dfrac{d^2 y}{d x^2} =$

$\dfrac{2}{2x+3}$

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

$\dfrac{4}{(2x+3)^2}$

$\dfrac{-4}{(2x+3)^2}$

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

Question 10 of 10 | MCQ · Level 3

$\operatorname*{lim}\limits_{h \rightarrow 0} \dfrac{5^{2+h} - 25}{h} =$

$0$

$1$

$25$

$25 \ln 5$

$25 e^5$

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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

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