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AB MCQ Set 110
42 Questions
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AB MCQ Set 110
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Question 1 of 42
| MCQ
· Level 1
\(\displaystyle\int_{1}^{2} x^{-3} d x =\)
A
\(-\dfrac{7}{8}\)
✕
B
\(-\dfrac{3}{4}\)
✕
C
\(\dfrac{15}{64}\)
✕
D
\(\dfrac{3}{8}\)
✕
E
\(\dfrac{15}{16}\)
✕
Question 2 of 42
| MCQ
· Level 2
If \(f(x) = (2 x + 1)^4\), then the 4th derivative of \(f(x)\) at \(x = 0\) is
A
\(0\)
✕
B
\(24\)
✕
C
\(48\)
✕
D
\(240\)
✕
E
\(384\)
✕
Question 3 of 42
| MCQ
· Level 1
If \(\dfrac{d y}{d x} = \cos(2 x)\), then \(y =\)
A
\(-\dfrac{1}{2} \cos(2 x) + C\)
✕
B
\(-\dfrac{1}{2} \cos^2(2 x) + C\)
✕
C
\(\dfrac{1}{2} \sin(2 x) + C\)
✕
D
\(\dfrac{1}{2} \sin^2(2 x) + C\)
✕
E
\(-\dfrac{1}{2} \sin(2 x) + C\)
✕
Question 4 of 42
| MCQ
· Level 2
\(\operatorname*{lim}\limits_{n \rightarrow \infty} \dfrac{4 n^2}{n^2 + 10000 n}\) is
A
\(0\)
✕
B
\(\dfrac{1}{2500}\)
✕
C
\(1\)
✕
D
\(4\)
✕
E
nonexistent
✕
Question 5 of 42
| MCQ
· Level 1
If \(f(x) = x\), then \(f'(5) =\)
A
\(0\)
✕
B
\(\dfrac{1}{5}\)
✕
C
\(1\)
✕
D
\(5\)
✕
E
\(\dfrac{25}{2}\)
✕
Question 6 of 42
| MCQ
· Level 2
Which of the following is equal to \(\ln 4\)?
A
\(\ln 3 + \ln 1\)
✕
B
\(\dfrac{\ln 8}{\ln 2}\)
✕
C
\(\displaystyle\int_{1}^{4} e^t d t\)
✕
D
\(\displaystyle\int_{1}^{4} \ln x d x\)
✕
E
\(\displaystyle\int_{1}^{4} \dfrac{1}{t} d t\)
✕
Question 7 of 42
| MCQ
· Level 2
The slope of the line tangent to the graph of \(y = \ln\left(\dfrac{x}{2}\right)\) at \(x = 4\) is
A
\(\dfrac{1}{8}\)
✕
B
\(\dfrac{1}{4}\)
✕
C
\(\dfrac{1}{2}\)
✕
D
\(1\)
✕
E
\(4\)
✕
Question 8 of 42
| MCQ
· Level 2
If \(\displaystyle\int_{-1}^1 e^{-x^2} d x = k\), then \(\displaystyle\int_{-1}^0 e^{-x^2} d x =\)
A
\(-2 k\)
✕
B
\(-k\)
✕
C
\(-\dfrac{k}{2}\)
✕
D
\(\dfrac{k}{2}\)
✕
E
\(2 k\)
✕
Question 9 of 42
| MCQ
· Level 3
If \(y = 10^{x^2 - 1}\), then \(\dfrac{d y}{d x} =\)
A
\((\ln 10) 10^{x^2 - 1}\)
✕
B
\((2 x) 10^{x^2 - 1}\)
✕
C
\((x^2 - 1) 10^{x^2 - 2}\)
✕
D
\(2 x (\ln 10) 10^{x^2 - 1}\)
✕
E
\(x^2 (\ln 10) 10^{x^2 - 1}\)
✕
Question 10 of 42
| MCQ
· Level 1
The position of a particle moving along a straight line at any time \(t\) is given by \(s(t) = t^2 + 4 t + 4\). What is the acceleration of the particle when \(t = 4\)?
A
\(0\)
✕
B
\(2\)
✕
C
\(4\)
✕
D
\(8\)
✕
E
\(12\)
✕
Question 11 of 42
| MCQ
· Level 3
If \(f(g(x)) = \ln(x^2 + 4)\), \(f(x) = \ln(x^2)\), and \(g(x) > 0\) for all real \(x\), then \(g(x) =\)
A
\(\dfrac{1}{\sqrt{x^2 + 4}}\)
✕
B
\(\dfrac{1}{x^2 + 4}\)
✕
C
\(\sqrt{x^2 + 4}\)
✕
D
\(x^2 + 4\)
✕
E
\(x + 2\)
✕
Question 12 of 42
| MCQ
· Level 3
If \(x^2 + x y + y^3 = 0\), then \(\dfrac{d y}{d x} =\)
A
\(-\dfrac{2 x + y}{x + 3 y^2}\)
✕
B
\(-\dfrac{x + 3 y^2}{2 x + y}\)
✕
C
\(\dfrac{-2 x}{1 + 3 y^2}\)
✕
D
\(\dfrac{-2 x}{x + 3 y^2}\)
✕
E
\(-\dfrac{2 x + y}{x + 3 y^2 - 1}\)
✕
Question 13 of 42
| MCQ
· Level 2
The velocity of a particle moving on a line at time \(t\) is \(v = 3 t^{\dfrac{1}{2}} + 5 t^{\dfrac{3}{2}}\) m/s. How many meters did it travel from \(t = 0\) to \(t = 4\)?
A
\(32\)
✕
B
\(40\)
✕
C
\(64\)
✕
D
\(80\)
✕
E
\(184\)
✕
Question 14 of 42
| MCQ
· Level 2
The domain of \(f(x) = \ln(x^2 - 4)\) is the set of all real \(x\) such that
A
\(|x| < 2\)
✕
B
\(|x| \leq 2\)
✕
C
\(|x| > 2\)
✕
D
\(|x| \geq 2\)
✕
E
\(x\) is a real number
✕
Question 15 of 42
| MCQ
· Level 2
\(f(x) = x^3 - 3 x^2\) has a relative maximum at \(x =\)
A
\(-2\)
✕
B
\(0\)
✕
C
\(1\)
✕
D
\(2\)
✕
E
\(4\)
✕
Question 16 of 42
| MCQ
· Level 3
\(\displaystyle\int_{0}^{1} x e^{-x} d x =\)
A
\(1 - 2 e\)
✕
B
\(-1\)
✕
C
\(1 - 2 e^{-1}\)
✕
D
\(1\)
✕
E
\(2 e - 1\)
✕
Question 17 of 42
| MCQ
· Level 2
If \(y = \cos^2 x - \sin^2 x\), then \(y' =\)
A
\(-1\)
✕
B
\(0\)
✕
C
\(-2 \sin(2 x)\)
✕
D
\(-2(\cos x + \sin x)\)
✕
E
\(2(\cos x - \sin x)\)
✕
Question 18 of 42
| MCQ
· Level 2
If \(f(x_1) + f(x_2) = f(x_1 + x_2)\) for all real \(x_1, x_2\), which could define \(f\)?
A
\(f(x) = x + 1\)
✕
B
\(f(x) = 2 x\)
✕
C
\(f(x) = \dfrac{1}{x}\)
✕
D
\(f(x) = e^x\)
✕
E
\(f(x) = x^2\)
✕
Question 19 of 42
| MCQ
· Level 3
If \(y = \arctan(\cos x)\), then \(\dfrac{d y}{d x} =\)
A
\(\dfrac{-\sin x}{1 + \cos^2 x}\)
✕
B
\(-(arcsec(\cos x))^2 \sin x\)
✕
C
\((arcsec(\cos x))^2\)
✕
D
\(\dfrac{1}{(\arccos x)^2 + 1}\)
✕
E
\(\dfrac{1}{1 + \cos^2 x}\)
✕
Question 20 of 42
| MCQ
· Level 3
If domain of \(f(x) = 1/(1-x^2)\) is \(\{x: |x| > 1\}\), what is the range of \(f\)?
A
\(\{x: -\infty < x < -1\}\)
✕
B
\(\{x: -\infty < x < 0\}\)
✕
C
\(\{x: -\infty < x < 1\}\)
✕
D
\(\{x: -1 < x < \infty\}\)
✕
E
\(\{x: 0 < x < \infty\}\)
✕
Question 21 of 42
| MCQ
· Level 2
\(\displaystyle\int_{1}^{2} \dfrac{x^2 - 1}{x + 1} d x =\)
A
\(\dfrac{1}{2}\)
✕
B
\(1\)
✕
C
\(2\)
✕
D
\(\dfrac{5}{2}\)
✕
E
\(\ln 3\)
✕
Question 22 of 42
| MCQ
· Level 2
\(\dfrac{d}{d x}\left(\dfrac{1}{x^3} - \dfrac{1}{x} + x^2\right)\) at \(x = -1\) is
A
\(-6\)
✕
B
\(-4\)
✕
C
\(0\)
✕
D
\(2\)
✕
E
\(6\)
✕
Question 23 of 42
| MCQ
· Level 2
If \(\displaystyle\int_{-2}^2 (x^7 + k) d x = 16\), then \(k =\)
The graph of \(y^2 = x^2 + 9\) is symmetric to which of the following? I. x-axis II. y-axis III. origin
A
I only
✕
B
II only
✕
C
III only
✕
D
I and II only
✕
E
I, II, and III
✕
Question 26 of 42
| MCQ
· Level 2
\(\displaystyle\int_{0}^{3} |x - 1| d x =\)
A
\(0\)
✕
B
\(\dfrac{3}{2}\)
✕
C
\(2\)
✕
D
\(\dfrac{5}{2}\)
✕
E
\(6\)
✕
Question 27 of 42
| MCQ
· Level 2
If position is \(-5 t^2\) on \([0, 3]\), average velocity is
A
\(-45\)
✕
B
\(-30\)
✕
C
\(-15\)
✕
D
\(-10\)
✕
E
\(-5\)
✕
Question 28 of 42
| MCQ
· Level 2
Which of the following are continuous for all real \(x\)? I. \(y = x^{\dfrac{2}{3}}\) II. \(y = e^x\) III. \(y = \tan x\)
A
None
✕
B
I only
✕
C
II only
✕
D
I and II
✕
E
I and III
✕
Question 29 of 42
| MCQ
· Level 2
\(\int \tan(2 x) d x =\)
A
\(-2 \ln|\cos(2 x)| + C\)
✕
B
\(-\dfrac{1}{2} \ln|\cos(2 x)| + C\)
✕
C
\(\dfrac{1}{2} \ln|\cos(2 x)| + C\)
✕
D
\(2 \ln|\cos(2 x)| + C\)
✕
E
\(\dfrac{1}{2} \sec(2 x) \tan(2 x) + C\)
✕
Question 30 of 42
| MCQ
· Level 3
Volume of cone \(V = \left(\dfrac{1}{3}\right) \pi r^2 h\). Both \(r\) and \(h\) increase at \(\dfrac{1}{2}\) cm/sec. When \(h = 9\), \(r = 6\), find \(\dfrac{d V}{d t}\).
A
\(\dfrac{\pi}{2}\)
✕
B
\(10 \pi\)
✕
C
\(24 \pi\)
✕
D
\(54 \pi\)
✕
E
\(108 \pi\)
✕
Question 31 of 42
| MCQ
· Level 2
\(\displaystyle\int_{0}^{\dfrac{\pi}{3}} \sin(3 x) d x =\)
A
\(-2\)
✕
B
\(-\dfrac{2}{3}\)
✕
C
\(0\)
✕
D
\(\dfrac{2}{3}\)
✕
E
\(2\)
✕
Question 32 of 42
| MCQ
· Level 3
The area in the first quadrant enclosed by \(y = x^3 + 8\) and \(y = x + 8\) is
A
\(\dfrac{1}{4}\)
✕
B
\(\dfrac{1}{2}\)
✕
C
\(\dfrac{3}{4}\)
✕
D
\(1\)
✕
E
\(\dfrac{65}{4}\)
✕
Question 33 of 42
| MCQ
· Level 3
If max of \(f\) is 5, min is \(-7\), which must be true? I. max of \(f(|x|)\) is 5 II. max of \(|f(x)|\) is 7 III. min of \(f(|x|)\) is 0
A
I only
✕
B
II only
✕
C
I and II only
✕
D
II and III only
✕
E
I, II, and III
✕
Question 34 of 42
| MCQ
· Level 2
\(\operatorname*{lim}\limits_{x \rightarrow 0} (x \csc x)\) is
A
\(-\infty\)
✕
B
\(-1\)
✕
C
\(0\)
✕
D
\(1\)
✕
E
\(\infty\)
✕
Question 35 of 42
| MCQ
· Level 3
If \(f, g\) have continuous first/second derivatives and \(f(x) \leq g(x)\) for all real \(x\), which must be true? I. \(f' \leq g'\) II. \(f'' \leq g''\) III. \(\displaystyle\int_{0}^{1} f \leq \displaystyle\int_{0}^{1} g\)
A
None
✕
B
I only
✕
C
III only
✕
D
I and II only
✕
E
I, II, and III
✕
Question 36 of 42
| MCQ
· Level 3
If \(f(x) = \ln \dfrac{x}{x}\) for \(x > 0\), which is true?
A
\(f\) increasing for all \(x > 0\).
✕
B
\(f\) increasing for \(x > 1\).
✕
C
\(f\) decreasing for \(0 < x < 1\).
✕
D
\(f\) decreasing for \(1 < x < e\).
✕
E
\(f\) decreasing for \(x > e\).
✕
Question 37 of 42
| MCQ
· Level 2
If \(2 \leq f(x) \leq 4\) on \([0, 2]\), max possible \(\displaystyle\int_{0}^{2} f(x) d x\) is
A
\(0\)
✕
B
\(2\)
✕
C
\(4\)
✕
D
\(8\)
✕
E
\(16\)
✕
Question 38 of 42
| MCQ
· Level 2
If \(\operatorname*{lim}\limits_{x\rightarrow a} f(x) = L\), which must be true?
A
\(f'(a)\) exists.
✕
B
\(f\) is continuous at \(a\).
✕
C
\(f(a)\) is defined.
✕
D
\(f(a) = L\)
✕
E
None of the above
✕
Question 39 of 42
| MCQ
· Level 2
\(\dfrac{d}{d x} \displaystyle\int_{2}^{x} \sqrt{1 + t^2} d t =\)
Equation of tangent to \(y = x^3 + 3 x^2 + 2\) at its point of inflection
A
\(y = -6 x - 6\)
✕
B
\(y = -3 x + 1\)
✕
C
\(y = 2 x + 10\)
✕
D
\(y = 3 x - 1\)
✕
E
\(y = 4 x + 1\)
✕
Question 41 of 42
| MCQ
· Level 3
Average value of \(f(x) = x^2 \sqrt{x^3 + 1}\) on \([0, 2]\) is
A
\(\dfrac{26}{9}\)
✕
B
\(\dfrac{13}{3}\)
✕
C
\(\dfrac{26}{3}\)
✕
D
\(13\)
✕
E
\(26\)
✕
Question 42 of 42
| MCQ
· Level 3
Region enclosed by \(y = x^2\), line \(x = 2\), x-axis revolved about y-axis. Volume?
A
\(8 \pi\)
✕
B
\(\dfrac{32 \pi}{5}\)
✕
C
\(\dfrac{16 \pi}{3}\)
✕
D
\(4 \pi\)
✕
E
\(\dfrac{8 \pi}{3}\)
✕
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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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