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AB MCQ Set 50
20 Questions
Question 1 of 20
AB MCQ Set 50 0/20
Question 1 of 20   |  Limits and Continuity  · Level 1
The graph of the function \(y = \dfrac{10 x + 3}{2 x - 5}\) has a horizontal asymptote at:
A
\(y = 5\)
✕
B
\(y = \dfrac{3}{5}\)
✕
C
\(y = -\dfrac{3}{5}\)
✕
D
\(y = -5\)
✕
E
\(y = 0\)
✕
Question 2 of 20   |  Limits and Continuity  · Level 1
\(\operatorname*{lim}\limits_{x \rightarrow 6} 7 =\)
A
\(1\)
✕
B
\(-1\)
✕
C
\(7\)
✕
D
Does not exist
✕
E
\(-7\)
✕
Question 3 of 20   |  Limits and Continuity  · Level 2
\(\operatorname*{lim}\limits_{x \rightarrow 3} \dfrac{x}{x - 3} =\)
A
\(1\)
✕
B
\(0\)
✕
C
\(+\infty\)
✕
D
Does not exist
✕
E
\(-\infty\)
✕
Question 4 of 20   |  Limits and Continuity  · Level 1
TRUE or FALSE: The equation \(f(x) = x^3 + x - 3 = 0\) has at least one solution on the interval \([1, 2]\).
A
TRUE
✕
B
FALSE
✕
Question 5 of 20   |  Limits and Continuity  · Level 2
TRUE or FALSE: \(\operatorname*{lim}\limits_{x \rightarrow 0} \dfrac{1 - \cos x}{\sin x} = 0\).
A
TRUE
✕
B
FALSE
✕
Question 6 of 20   |  Differentiation: Definition and Fundamental Properties  · Level 1
Find the equation of the tangent line to the curve \(y = 2 x\) at \(x = 3\).
A
\(y = 2 x\)
✕
B
\(y = 2 x - 3\)
✕
C
\(y = 2 x + 3\)
✕
D
\(y = 2\)
✕
E
\(y = 3\)
✕
Question 7 of 20   |  Differentiation: Definition and Fundamental Properties  · Level 1
Find \(\dfrac{d y}{d x}\) if \(y = e^8\).
A
\(7 e^7\)
✕
B
\(8 e^7\)
✕
C
\(-8\)
✕
D
\(8\)
✕
E
\(0\)
✕
Question 8 of 20   |  Differentiation: Definition and Fundamental Properties  · Level 2
Suppose that \(g(x) = \sqrt{x} f(x)\). Find \(g'(1)\), given that \(f(1) = 8\) and \(f'(1) = 5\).
A
\(5\)
✕
B
\(4\)
✕
C
\(9\)
✕
D
\(13\)
✕
E
\(0\)
✕
Question 9 of 20   |  Differentiation: Definition and Fundamental Properties  · Level 2
Find \(f'(x)\) if \(f(x) = x^3 \cos x\).
A
\(3 x^2 \cos x\)
✕
B
\(-3 x^2 \cos x\)
✕
C
\(3 x^2 \cos x + x^3 \sin x\)
✕
D
\(3 x^2 \cos x - x^3 \sin x\)
✕
E
\(3 x^2 \sin x\)
✕
Question 10 of 20   |  Differentiation: Definition and Fundamental Properties  · Level 3
TRUE or FALSE: \(\dfrac{d^{71}}{d x^{71}}(\sin x) = \cos x\).
A
TRUE
✕
B
FALSE
✕
Question 11 of 20   |  Contextual Applications of Differentiation  · Level 3
Find \(\dfrac{d V}{d t}\) for a spherical balloon of radius \(2\) ft if \(\dfrac{d r}{d t} = 0.5 \dfrac{\text{ft}}{\text{s}}\). (Recall that the volume of a sphere is given by \(V = \dfrac{4}{3} \pi r^3\).)
A
\(\dfrac{16 \pi}{3} \dfrac{\text{ft}^3}{\text{s}}\)
✕
B
\(\dfrac{32 \pi}{3} \dfrac{\text{ft}^3}{\text{s}}\)
✕
C
\(8 \pi \dfrac{\text{ft}^3}{\text{s}}\)
✕
D
\(4 \pi \dfrac{\text{ft}^3}{\text{s}}\)
✕
E
\(2 \pi \dfrac{\text{ft}^3}{\text{s}}\)
✕
Question 12 of 20   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
Find \(\dfrac{d y}{d x}\) if \(y = \ln(4 x^2)\).
A
\(\dfrac{1}{x}\)
✕
B
\(\dfrac{2}{x^2}\)
✕
C
\(\dfrac{1}{2 x^2}\)
✕
D
\(\dfrac{1}{x^2}\)
✕
E
\(\dfrac{2}{x}\)
✕
Question 13 of 20   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 3
Find \(\dfrac{d y}{d x}\) if \(x^3 + 3 y^2 = 9\).
A
\(\dfrac{9 - 3 x^2}{6 y}\)
✕
B
\(-\dfrac{x^2}{2 y}\)
✕
C
\(\dfrac{x^2}{2 y}\)
✕
D
\(\dfrac{9 + 3 x^2}{6 y}\)
✕
E
\(3 x^2\)
✕
Question 14 of 20   |  MCQ  · Level 2
\(\operatorname*{lim}\limits_{x \rightarrow +\infty} \dfrac{\ln x}{e^x} =\)
A
\(0\)
✕
B
\(+\infty\)
✕
C
\(-\infty\)
✕
D
\(1\)
✕
E
\(-1\)
✕
Question 15 of 20   |  Analytical Applications of Differentiation  · Level 2
The largest interval on which \(f(x) = x^2 + 4 x + 2\) is increasing is
A
\([0, +\infty)\)
✕
B
\((-\infty, 0]\)
✕
C
\([-2, +\infty)\)
✕
D
\((-\infty, -2]\)
✕
E
\((-\infty, +\infty)\)
✕
Question 16 of 20   |  Analytical Applications of Differentiation  · Level 3
TRUE or FALSE: The function \(f(x) = \sqrt{x - 6}\) is concave down on its entire domain.
A
TRUE
✕
B
FALSE
✕
Question 17 of 20   |  Analytical Applications of Differentiation  · Level 2
Where is the function \(f(x) = \cos x\) increasing on the interval \([0, 2 \pi]\)?
A
\([0, \pi]\)
✕
B
\([\pi, 2 \pi]\)
✕
C
\([\dfrac{\pi}{2}, \dfrac{3 \pi}{2}]\)
✕
D
\([0, \dfrac{\pi}{2}] \cup [\dfrac{3 \pi}{2}, 2 \pi]\)
✕
E
\([0, 2 \pi]\)
✕
Question 18 of 20   |  Analytical Applications of Differentiation  · Level 2
The weekly profit function for a certain company is \(P(x) = -\dfrac{1}{10} x^2 + 30 x - 500\) where \(x\) is the number of the company's product made and sold. How many individual items of the product must the company make and sell weekly in order to maximize its profit?
A
\(300\)
✕
B
\(50\)
✕
C
\(500\)
✕
D
\(150\)
✕
E
\(200\)
✕
Question 19 of 20   |  Analytical Applications of Differentiation  · Level 2
The function \(f(x) = \dfrac{1}{x}\) has an absolute maximum on the interval \([1, 3]\) of
A
\(1\)
✕
B
\(\dfrac{1}{9}\)
✕
C
\(9\)
✕
D
\(\dfrac{1}{3}\)
✕
E
No absolute maximum exists
✕
Question 20 of 20   |  Analytical Applications of Differentiation  · Level 3
TRUE or FALSE: The hypotheses of the Mean Value Theorem are satisfied for the function \(f(x) = \dfrac{1}{x^8} - 1\) on the interval \([-1, 1]\).
A
TRUE
✕
B
FALSE
✕

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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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