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AB MCQ Set 140
34 Questions
Question 1 of 34
AB MCQ Set 140 0/34
Question 1 of 34   |  Integration and Accumulation of Change  · Level 1
\(\displaystyle\int_{1}^{2} (4 x^3 - 6 x) d x =\)
A
\(2\)
✕
B
\(4\)
✕
C
\(6\)
✕
D
\(36\)
✕
E
\(42\)
✕
Question 2 of 34   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
If \(f(x) = x \sqrt{2 x - 3}\), then \(f'(x) =\)
A
\(\dfrac{3 x - 3}{\sqrt{2 x - 3}}\)
✕
B
\(\dfrac{x}{\sqrt{2 x - 3}}\)
✕
C
\(\dfrac{1}{\sqrt{2 x - 3}}\)
✕
D
\(\dfrac{-x + 3}{\sqrt{2 x - 3}}\)
✕
E
\(\dfrac{5 x - 6}{2 \sqrt{2 x - 3}}\)
✕
Question 3 of 34   |  Integration and Accumulation of Change  · Level 1
\(\displaystyle\int_{a}^{b} f d x = a + 2 b\), then \(\displaystyle\int_{a}^{b} (f + 5) d x =\)
A
\(a + 2b + 5\)
✕
B
\(5b - 5a\)
✕
C
\(7b - 4a\)
✕
D
\(7b - 5a\)
✕
E
\(7b - 6a\)
✕
Question 4 of 34   |  Differentiation: Definition and Fundamental Properties  · Level 2
\(f(x) = -x^3 + x + \dfrac{1}{x}\), \(f'(-1) =\)
A
\(3\)
✕
B
\(1\)
✕
C
\(-1\)
✕
D
\(-3\)
✕
E
\(-5\)
✕
Question 5 of 34   |  Analytical Applications of Differentiation  · Level 3
\(y = 3 x^4 - 16 x^3 + 24 x^2 + 48\) concave down for
A
\(x < 0\)
✕
B
\(x > 0\)
✕
C
\(x < -2\) or \(x > -\dfrac{2}{3}\)
✕
D
\(x < \dfrac{2}{3}\) or \(x > 2\)
✕
E
\(\dfrac{2}{3} < x < 2\)
✕
Question 6 of 34   |  Integration and Accumulation of Change  · Level 1
\(\left(\dfrac{1}{2}\right) \int e^{\dfrac{t}{2}} d t =\)
A
\(e^{-t} + C\)
✕
B
\(e^{-\dfrac{t}{2}} + C\)
✕
C
\(e^{\dfrac{t}{2}} + C\)
✕
D
\(2 e^{\dfrac{t}{2}} + C\)
✕
E
\(e^t + C\)
✕
Question 7 of 34   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
\(\dfrac{d}{d x} \cos^2(x^3) =\)
A
\(6 x^2 \sin(x^3) \cos(x^3)\)
✕
B
\(6 x^2 \cos(x^3)\)
✕
C
\(\sin^2(x^3)\)
✕
D
\(-6 x^2 \sin(x^3) \cos(x^3)\)
✕
E
\(-2 \sin(x^3) \cos(x^3)\)
✕
Question 8 of 34   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
Tangent to \(y = \cos(2 x)\) at \(x = \dfrac{\pi}{4}\)
A
\(y - 1 = -\left(x - \dfrac{\pi}{4}\right)\)
✕
B
\(y - 1 = -2\left(x - \dfrac{\pi}{4}\right)\)
✕
C
\(y = 2\left(x - \dfrac{\pi}{4}\right)\)
✕
D
\(y = -\left(x - \dfrac{\pi}{4}\right)\)
✕
E
\(y = -2\left(x - \dfrac{\pi}{4}\right)\)
✕
Question 9 of 34   |  Differentiation: Definition and Fundamental Properties  · Level 3
Point on \(y = \left(\dfrac{1}{2}\right) x^2\) where tangent parallel to \(2 x - 4 y = 3\)
A
\(\left(\dfrac{1}{2}, -\dfrac{1}{2}\right)\)
✕
B
\(\left(\dfrac{1}{2}, \dfrac{1}{8}\right)\)
✕
C
\(\left(1, -\dfrac{1}{4}\right)\)
✕
D
\(\left(1, \dfrac{1}{2}\right)\)
✕
E
\((2, 2)\)
✕
Question 10 of 34   |  Analytical Applications of Differentiation  · Level 3
\(f'(x) = |4 - x^2|/(x - 2)\). \(f\) decreasing on
A
\((-\infty, 2)\)
✕
B
\((-\infty, \infty)\)
✕
C
\((-2, 4)\)
✕
D
\((-2, \infty)\)
✕
E
\((2, \infty)\)
✕
Question 11 of 34   |  Contextual Applications of Differentiation  · Level 3
\(f(3) = 2\), \(f'(3) = 5\). Tangent line approx to zero of \(f\)
A
\(0.4\)
✕
B
\(0.5\)
✕
C
\(2.6\)
✕
D
\(3.4\)
✕
E
\(5.5\)
✕
Question 12 of 34   |  Applications of Integration  · Level 3
Area enclosed by \(y = x^2 + 1\) and \(y = 5\)
A
\(\dfrac{14}{3}\)
✕
B
\(\dfrac{16}{3}\)
✕
C
\(\dfrac{28}{3}\)
✕
D
\(\dfrac{32}{3}\)
✕
E
\(8 \pi\)
✕
Question 13 of 34   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 3
\(x^2 + y^2 = 25\), \(\dfrac{d^2 y}{d x^2}\) at \((4, 3)\)
A
\(-\dfrac{25}{27}\)
✕
B
\(-\dfrac{7}{27}\)
✕
C
\(\dfrac{7}{27}\)
✕
D
\(\dfrac{3}{4}\)
✕
E
\(\dfrac{25}{27}\)
✕
Question 14 of 34   |  Integration and Accumulation of Change  · Level 3
\(\displaystyle\int_{0}^{\dfrac{\pi}{4}} e^{\tan x}/\cos^2 x d x\)
A
\(0\)
✕
B
\(1\)
✕
C
\(e - 1\)
✕
D
\(e\)
✕
E
\(e + 1\)
✕
Question 15 of 34   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
\(f(x) = \ln|x^2 - 1|\), \(f'(x) =\)
A
\(|2 x/(x^2-1)|\)
✕
B
\(2 x/|x^2-1|\)
✕
C
\(2 |x|/(x^2-1)\)
✕
D
\(2 x/(x^2-1)\)
✕
E
\(1/(x^2-1)\)
✕
Question 16 of 34   |  Applications of Integration  · Level 2
Average of \(\cos x\) on \([-3, 5]\)
A
\((\sin 5 - \sin 3)/8\)
✕
B
\((\sin 5 - \sin 3)/2\)
✕
C
\((\sin 3 - \sin 5)/2\)
✕
D
\((\sin 3 + \sin 5)/2\)
✕
E
\((\sin 3 + \sin 5)/8\)
✕
Question 17 of 34   |  Limits and Continuity  · Level 2
\(\operatorname*{lim}\limits_{x \rightarrow 1} \dfrac{x}{\ln} x\) is
A
\(0\)
✕
B
\(\dfrac{1}{e}\)
✕
C
\(1\)
✕
D
\(e\)
✕
E
nonexistent
✕
Question 18 of 34   |  Analytical Applications of Differentiation  · Level 3
\(f(x) = (x^2 - 3) e^{-x}\) increasing on
A
No values
✕
B
\(x < -1\) and \(x > 3\)
✕
C
\(-3 < x < 1\)
✕
D
\(-1 < x < 3\)
✕
E
All values
✕
Question 19 of 34   |  Applications of Integration  · Level 3
Region enclosed by y-axis, \(y=2\), \(y=\sqrt{x}\) revolved about y-axis
A
\(32 \dfrac{\pi}{5}\)
✕
B
\(16 \dfrac{\pi}{3}\)
✕
C
\(16 \dfrac{\pi}{5}\)
✕
D
\(8 \dfrac{\pi}{3}\)
✕
E
\(\pi\)
✕
Question 20 of 34   |  Integration and Accumulation of Change  · Level 3
\(\left(\dfrac{1}{50}\right)\left(\sqrt{\dfrac{1}{50}} + \sqrt{\dfrac{2}{50}} + ... + \sqrt{\dfrac{50}{50}}\right)\) as Riemann sum
A
\(\displaystyle\int_{0}^{1} \sqrt{\dfrac{x}{50}} d x\)
✕
B
\(\displaystyle\int_{0}^{1} \sqrt{x} d x\)
✕
C
\(\left(\dfrac{1}{50}\right) \displaystyle\int_{0}^{1} \sqrt{\dfrac{x}{50}} d x\)
✕
D
\(\left(\dfrac{1}{50}\right) \displaystyle\int_{0}^{1} \sqrt{x} d x\)
✕
E
\(\left(\dfrac{1}{50}\right) \displaystyle\int_{0}^{50} \sqrt{x} d x\)
✕
Question 21 of 34   |  Integration and Accumulation of Change  · Level 3
\(\int x \sin(2 x) d x =\)
A
\(-\left(\dfrac{x}{2}\right) \cos(2x) + \left(\dfrac{1}{4}\right) \sin(2x) + C\)
✕
B
\(-\left(\dfrac{x}{2}\right) \cos(2x) - \left(\dfrac{1}{4}\right) \sin(2x) + C\)
✕
C
\(\left(\dfrac{x}{2}\right) \cos(2x) - \left(\dfrac{1}{4}\right) \sin(2x) + C\)
✕
D
\(-2 x \cos(2x) + \sin(2x) + C\)
✕
E
\(-2 x \cos(2x) - 4 \sin(2x) + C\)
✕
Question 22 of 34   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
[Calc] \(f(x) = e^{2x}/(2 x)\), \(f'(x) =\)
A
\(1\)
✕
B
\(\dfrac{e^{2x}(1 - 2x)}{2 x^2}\)
✕
C
\(e^{2x}\)
✕
D
\(\dfrac{e^{2x}(2 x + 1)}{x^2}\)
✕
E
\(\dfrac{e^{2x}(2 x - 1)}{2 x^2}\)
✕
Question 23 of 34   |  Analytical Applications of Differentiation  · Level 3
[Calc] \(y = x^3 + 6 x^2 + 7 x - 2 \cos x\) changes concavity at \(x =\)
A
\(-1.58\)
✕
B
\(-1.63\)
✕
C
\(-1.67\)
✕
D
\(-1.89\)
✕
E
\(-2.33\)
✕
Question 24 of 34   |  Differentiation: Definition and Fundamental Properties  · Level 3
[Calc] \(\operatorname*{lim}\limits_{h\rightarrow 0}(f(2+h)-f(2))/h = 5\). Which must be true?
I. \(f\) continuous at 2
II. \(f\) differentiable at 2
III. \(f'\) continuous at 2
A
I only
✕
B
II only
✕
C
I and II only
✕
D
I and III only
✕
E
II and III only
✕
Question 25 of 34   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 3
[Calc] \(f(x) = 2 e^{4 x^2}\). \(f'(x) = 3\) at?
A
\(0.168\)
✕
B
\(0.276\)
✕
C
\(0.318\)
✕
D
\(0.342\)
✕
E
\(0.551\)
✕
Question 26 of 34   |  Contextual Applications of Differentiation  · Level 3
[Calc] Train moving 60 m/s east. Observer 70 m south. After 4 sec, train moves at how many m/s away?
A
\(57.60\)
✕
B
\(57.88\)
✕
C
\(59.20\)
✕
D
\(60.00\)
✕
E
\(67.40\)
✕
Question 27 of 34   |  Analytical Applications of Differentiation  · Level 2
[Calc] \(y = 2 x - 8\), min of \(xy\)
A
\(-16\)
✕
B
\(-8\)
✕
C
\(-4\)
✕
D
\(0\)
✕
E
\(2\)
✕
Question 28 of 34   |  Applications of Integration  · Level 3
[Calc] Area in Q1 enclosed by \(y = \cos x\), \(y = x\), y-axis
A
\(0.127\)
✕
B
\(0.385\)
✕
C
\(0.400\)
✕
D
\(0.600\)
✕
E
\(0.947\)
✕
Question 29 of 34   |  Applications of Integration  · Level 3
[Calc] Base of solid: \(y = \sqrt{\ln x}\), \(x = e\), x-axis. Square cross-sections perp to x-axis. Volume?
A
\(\dfrac{1}{2}\)
✕
B
\(\dfrac{2}{3}\)
✕
C
\(1\)
✕
D
\(2\)
✕
E
\(\left(\dfrac{1}{3}\right)(e^3 - 1)\)
✕
Question 30 of 34   |  Analytical Applications of Differentiation  · Level 3
[Calc] \(f'(x) = e^x - 3 x^2\). \(f\) has rel max at?
A
\(-0.46\)
✕
B
\(0.20\)
✕
C
\(0.91\)
✕
D
\(0.95\)
✕
E
\(3.73\)
✕
Question 31 of 34   |  MCQ  · Level 3
[Calc] \(f(x) = \sqrt{x}\). Rate at \(c\) twice rate at \(x=1\). \(c=\)
A
\(\dfrac{1}{4}\)
✕
B
\(1\)
✕
C
\(4\)
✕
D
\(\dfrac{1}{\sqrt{2}}\)
✕
E
\(1/(2 \sqrt{2})\)
✕
Question 32 of 34   |  Applications of Integration  · Level 3
[Calc] \(a(t) = t + \sin t\), \(v(0) = -2\). \(v(t) = 0\) when?
A
\(1.02\)
✕
B
\(1.48\)
✕
C
\(1.85\)
✕
D
\(2.81\)
✕
E
\(3.14\)
✕
Question 33 of 34   |  Integration and Accumulation of Change  · Level 2
[Calc] \(f(0)=3, f(0.5)=3, f(1)=5, f(1.5)=8, f(2)=13\). Trapezoidal with 4 subintervals on \([0,2]\)
A
\(8\)
✕
B
\(12\)
✕
C
\(16\)
✕
D
\(24\)
✕
E
\(32\)
✕
Question 34 of 34   |  Integration and Accumulation of Change  · Level 2
[Calc] Antiderivatives of \(\sin x \cos x\).
I. \(\sin^2 \dfrac{x}{2}\)
II. \(\cos^2 \dfrac{x}{2}\)
III. \(-\cos(2x)/4\)
A
I only
✕
B
II only
✕
C
III only
✕
D
I and III only
✕
E
II and III only
✕

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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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