⌛ 5 minutes remaining. The timer is now always visible.
AB MCQ Set 120
43 Questions
Question 1 of 43
--:--
AB MCQ Set 120 0/43
Question 1 of 43   |  MCQ  · Level 1
If \(y = x^2 e^x\), then \(\dfrac{d y}{d x} =\)
A
\(2 x e^x\)
✕
B
\(x(x + 2 e^x)\)
✕
C
\(x e^x (x + 2)\)
✕
D
\(2 x + e^x\)
✕
E
\(2 x + e\)
✕
Question 2 of 43   |  MCQ  · Level 2
What is the domain of \(f(x) = \dfrac{\sqrt{x^2 - 4}}{x - 3}\)?
A
\(\{x: x \neq 3\}\)
✕
B
\(\{x: |x| \leq 2\}\)
✕
C
\(\{x: |x| \geq 2\}\)
✕
D
\(\{x: |x| \geq 2\) and \(x \neq 3\}\)
✕
E
\(\{x: x \geq 2\) and \(x \neq 3\}\)
✕
Question 3 of 43   |  MCQ  · Level 1
Particle velocity \(v(t) = e^t\). Distance from \(t = 0\) to \(t = 2\)?
A
\(e^2 - 1\)
✕
B
\(e - 1\)
✕
C
\(2 e\)
✕
D
\(e^2\)
✕
E
\(\dfrac{e^3}{3}\)
✕
Question 4 of 43   |  MCQ  · Level 2
\(y = -5/(x - 2)\) is concave downward for what \(x\)?
A
\(x < 0\)
✕
B
\(x < 2\)
✕
C
\(x < 5\)
✕
D
\(x > 0\)
✕
E
\(x > 2\)
✕
Question 5 of 43   |  MCQ  · Level 1
\(\int \sec^2 x d x =\)
A
\(\tan x + C\)
✕
B
\(\csc^2 x + C\)
✕
C
\(\cos^2 x + C\)
✕
D
\(\dfrac{\sec^3 x}{3} + C\)
✕
E
\(2 \sec^2 x \tan x + C\)
✕
Question 6 of 43   |  MCQ  · Level 2
If \(y = \ln \dfrac{x}{x}\), then \(\dfrac{d y}{d x} =\)
A
\(\dfrac{1}{x}\)
✕
B
\(\dfrac{1}{x^2}\)
✕
C
\(\dfrac{\ln x - 1}{x^2}\)
✕
D
\(\dfrac{1 - \ln x}{x^2}\)
✕
E
\(\dfrac{1 + \ln x}{x^2}\)
✕
Question 7 of 43   |  MCQ  · Level 2
\(\int \dfrac{x d x}{\sqrt{3 x^2 + 5}} =\)
A
\(\dfrac{1}{9}(3 x^2 + 5)^{\dfrac{3}{2}} + C\)
✕
B
\(\dfrac{1}{4}(3 x^2 + 5)^{\dfrac{3}{2}} + C\)
✕
C
\(\dfrac{1}{12}(3 x^2 + 5)^{\dfrac{1}{2}} + C\)
✕
D
\(\dfrac{1}{3}(3 x^2 + 5)^{\dfrac{1}{2}} + C\)
✕
E
\(\dfrac{3}{2}(3 x^2 + 5)^{\dfrac{1}{2}} + C\)
✕
Question 8 of 43   |  MCQ  · Level 3
If \(x + 2 x y - y^2 = 2\), then at \((1, 1)\), \(\dfrac{d y}{d x} =\)
A
\(\dfrac{3}{2}\)
✕
B
\(\dfrac{1}{2}\)
✕
C
\(0\)
✕
D
\(-\dfrac{3}{2}\)
✕
E
nonexistent
✕
Question 9 of 43   |  MCQ  · Level 2
If \(\displaystyle\int_{0}^{k} (2 k x - x^2) d x = 18\), then \(k =\)
A
\(-9\)
✕
B
\(-3\)
✕
C
\(3\)
✕
D
\(9\)
✕
E
\(18\)
✕
Question 10 of 43   |  MCQ  · Level 2
Equation of tangent to \(f(x) = x(1 - 2 x)^3\) at \((1, -1)\)
A
\(y = -7 x + 6\)
✕
B
\(y = -6 x + 5\)
✕
C
\(y = -2 x + 1\)
✕
D
\(y = 2 x - 3\)
✕
E
\(y = 7 x - 8\)
✕
Question 11 of 43   |  MCQ  · Level 1
If \(f(x) = \sin x\), then \(f'\left(\dfrac{\pi}{3}\right) =\)
A
\(-\dfrac{1}{2}\)
✕
B
\(\dfrac{1}{2}\)
✕
C
\(\dfrac{\sqrt{2}}{2}\)
✕
D
\(\dfrac{\sqrt{3}}{2}\)
✕
E
\(\sqrt{3}\)
✕
Question 12 of 43   |  MCQ  · Level 1
\(\displaystyle\int_{0}^{c} f'(x) d x\) where \(f\) has continuous derivative
A
\(f(c) - f(0)\)
✕
B
\(|f(c) - f(0)|\)
✕
C
\(f(c)\)
✕
D
\(f(x) + c\)
✕
E
\(f''(c) - f''(0)\)
✕
Question 13 of 43   |  MCQ  · Level 3
\(\displaystyle\int_{0}^{\dfrac{\pi}{2}} \dfrac{\cos \theta}{\sqrt{1 + \sin \theta}} d \theta =\)
A
\(-2(\sqrt{2} - 1)\)
✕
B
\(-2 \sqrt{2}\)
✕
C
\(2 \sqrt{2}\)
✕
D
\(2(\sqrt{2} - 1)\)
✕
E
\(2(\sqrt{2} + 1)\)
✕
Question 14 of 43   |  MCQ  · Level 1
If \(f(x) = \sqrt{2 x}\), then \(f'(2) =\)
A
\(\dfrac{1}{4}\)
✕
B
\(\dfrac{1}{2}\)
✕
C
\(\dfrac{\sqrt{2}}{2}\)
✕
D
\(1\)
✕
E
\(\sqrt{2}\)
✕
Question 15 of 43   |  MCQ  · Level 2
\(x(t) = t^3 - 3 t^2 - 9 t + 1\). Particle at rest when?
A
No values
✕
B
\(1\) only
✕
C
\(3\) only
✕
D
\(5\) only
✕
E
\(1\) and \(3\)
✕
Question 16 of 43   |  MCQ  · Level 2
\(\displaystyle\int_{0}^{1} (3 x - 2)^2 d x =\)
A
\(-\dfrac{7}{3}\)
✕
B
\(-\dfrac{7}{9}\)
✕
C
\(\dfrac{1}{9}\)
✕
D
\(1\)
✕
E
\(3\)
✕
Question 17 of 43   |  MCQ  · Level 2
If \(y = 2 \cos\left(\dfrac{x}{2}\right)\), then \(\dfrac{d^2 y}{d x^2} =\)
A
\(-8 \cos\left(\dfrac{x}{2}\right)\)
✕
B
\(-2 \cos\left(\dfrac{x}{2}\right)\)
✕
C
\(-\sin\left(\dfrac{x}{2}\right)\)
✕
D
\(-\cos\left(\dfrac{x}{2}\right)\)
✕
E
\(-\left(\dfrac{1}{2}\right) \cos\left(\dfrac{x}{2}\right)\)
✕
Question 18 of 43   |  MCQ  · Level 2
\(\displaystyle\int_{2}^{3} \dfrac{x}{x^2 + 1} d x =\)
A
\(\dfrac{1}{2} \ln \dfrac{3}{2}\)
✕
B
\(\dfrac{1}{2} \ln 2\)
✕
C
\(\ln 2\)
✕
D
\(2 \ln 2\)
✕
E
\(\dfrac{1}{2} \ln 5\)
✕
Question 19 of 43   |  MCQ  · Level 3
Polynomial degree > 2, \(a \neq b\), \(f(a)=f(b)=1\). Which must be true between \(a\) and \(b\)?
I. \(f=0\)
II. \(f'=0\)
III. \(f''=0\)
A
None
✕
B
I only
✕
C
II only
✕
D
I and II only
✕
E
I, II, and III
✕
Question 20 of 43   |  MCQ  · Level 2
Area enclosed by \(y = x\) and \(y = x^2 - 3 x + 3\)
A
\(\dfrac{2}{3}\)
✕
B
\(1\)
✕
C
\(\dfrac{4}{3}\)
✕
D
\(2\)
✕
E
\(\dfrac{14}{3}\)
✕
Question 21 of 43   |  MCQ  · Level 2
If \(\ln x - \ln\left(\dfrac{1}{x}\right) = 2\), then \(x =\)
A
\(1/e^2\)
✕
B
\(\dfrac{1}{e}\)
✕
C
\(e\)
✕
D
\(2 e\)
✕
E
\(e^2\)
✕
Question 22 of 43   |  MCQ  · Level 3
\(f'(x) = \cos x\), \(g'(x) = 1\), \(f(0) = g(0) = 0\). \(\operatorname*{lim}\limits_{x\rightarrow 0} f(x)/g(x) =\)
A
\(\dfrac{\pi}{2}\)
✕
B
\(1\)
✕
C
\(0\)
✕
D
\(-1\)
✕
E
nonexistent
✕
Question 23 of 43   |  MCQ  · Level 4
\(\dfrac{d}{d x} (x^{\ln x}) =\)
A
\(x^{\ln x}\)
✕
B
\((\ln x)^x\)
✕
C
\(\left(\dfrac{2}{x}\right)(\ln x)(x^{\ln x})\)
✕
D
\((\ln x)(x^{\ln x - 1})\)
✕
E
\(2(\ln x)(x^{\ln x})\)
✕
Question 24 of 43   |  MCQ  · Level 1
For \(x > 1\), \(f(x) = \displaystyle\int_{1}^{x} d \dfrac{t}{t}\), then \(f'(x) =\)
A
\(1\)
✕
B
\(\dfrac{1}{x}\)
✕
C
\(\ln x - 1\)
✕
D
\(\ln x\)
✕
E
\(e^x\)
✕
Question 25 of 43   |  MCQ  · Level 2
\(\displaystyle\int_{0}^{\dfrac{\pi}{2}} x \cos x d x =\)
A
\(-\dfrac{\pi}{2}\)
✕
B
\(-1\)
✕
C
\(1 - \dfrac{\pi}{2}\)
✕
D
\(1\)
✕
E
\(\dfrac{\pi}{2} - 1\)
✕
Question 26 of 43   |  MCQ  · Level 2
At \(x = 3\), \(f(x) = x^2\) for \(x<3\), \(f(x) = 6x - 9\) for \(x \geq 3\)
A
undefined
✕
B
continuous but not differentiable
✕
C
differentiable but not continuous
✕
D
neither continuous nor differentiable
✕
E
both continuous and differentiable
✕
Question 27 of 43   |  MCQ  · Level 2
\(\displaystyle\int_{1}^{4} |x - 3| d x =\)
A
\(-\dfrac{3}{2}\)
✕
B
\(\dfrac{3}{2}\)
✕
C
\(\dfrac{5}{2}\)
✕
D
\(\dfrac{9}{2}\)
✕
E
\(5\)
✕
Question 28 of 43   |  MCQ  · Level 2
\(\operatorname*{lim}\limits_{h \rightarrow 0} \dfrac{\tan(3(x+h)) - \tan(3x)}{h}\)
A
\(0\)
✕
B
\(3 \sec^2(3x)\)
✕
C
\(\sec^2(3 x)\)
✕
D
\(3 \cot(3 x)\)
✕
E
nonexistent
✕
Question 29 of 43   |  MCQ  · Level 3
Region in Q1 enclosed by \(y = e^{2x}\), \(x = 1\), axes. Rotated about y-axis. Volume?
A
\(2 \pi \displaystyle\int_{0}^{1} x e^{2x} d x\)
✕
B
\(2 \pi \displaystyle\int_{0}^{1} e^{2x} d x\)
✕
C
\(\pi \displaystyle\int_{0}^{1} e^{4x} d x\)
✕
D
\(\pi \displaystyle\int_{0}^{e} y \ln y d y\)
✕
E
\(\left(\dfrac{\pi}{4}\right) \displaystyle\int_{0}^{e} \ln^2 y d y\)
✕
Question 30 of 43   |  MCQ  · Level 2
If \(f(x) = x/(x+1)\), find \(f^{-1}(x)\)
A
\(\dfrac{x - 1}{x}\)
✕
B
\(\dfrac{x + 1}{x}\)
✕
C
\(\dfrac{x}{1 - x}\)
✕
D
\(\dfrac{x}{x + 1}\)
✕
E
\(x\)
✕
Question 31 of 43   |  MCQ  · Level 2
Which does NOT have period \(\pi\)?
A
\(\sin\left(\dfrac{x}{2}\right)\)
✕
B
\(|\sin x|\)
✕
C
\(\sin^2 x\)
✕
D
\(\tan x\)
✕
E
\(\tan^2 x\)
✕
Question 32 of 43   |  MCQ  · Level 3
Absolute max of \(f(x) = x^3 - 3 x^2 + 12\) on \([-2, 4]\) at \(x =\)
A
\(4\)
✕
B
\(2\)
✕
C
\(1\)
✕
D
\(0\)
✕
E
\(-2\)
✕
Question 33 of 43   |  MCQ  · Level 2
\(4 \cos\left(x + \dfrac{\pi}{3}\right) =\)
A
\(2 \sqrt{3} \cos x - 2 \sin x\)
✕
B
\(2 \cos x - 2 \sqrt{3} \sin x\)
✕
C
\(2 \cos x + 2 \sqrt{3} \sin x\)
✕
D
\(2 \sqrt{3} \cos x + 2 \sin x\)
✕
E
\(4 \cos x + 2\)
✕
Question 34 of 43   |  MCQ  · Level 3
Average value of \(y\) for \(y = 3 x - x^2\) in first quadrant
A
\(-6\)
✕
B
\(-2\)
✕
C
\(\dfrac{3}{2}\)
✕
D
\(\dfrac{9}{4}\)
✕
E
\(\dfrac{9}{2}\)
✕
Question 35 of 43   |  MCQ  · Level 3
If \(f(x) = e^x \sin x\), number of zeros on \([0, 2\pi]\) is
A
\(0\)
✕
B
\(1\)
✕
C
\(2\)
✕
D
\(3\)
✕
E
\(4\)
✕
Question 36 of 43   |  MCQ  · Level 3
For \(x > 0\), \(\int \left(\dfrac{1}{x}\right) \displaystyle\int_{1}^{x} d \dfrac{u}{u} d x =\)
A
\(1/x^3 + C\)
✕
B
\(8/x^4 - 2/x^2 + C\)
✕
C
\(\ln(\ln x) + C\)
✕
D
\(\ln(x^2)/2 + C\)
✕
E
\((\ln x)^2/2 + C\)
✕
Question 37 of 43   |  MCQ  · Level 1
\(\displaystyle\int_{1}^{10} f d x = 4\), \(\displaystyle\int_{10}^3 f d x = 7\), then \(\displaystyle\int_{1}^{3} f d x =\)
A
\(-3\)
✕
B
\(0\)
✕
C
\(3\)
✕
D
\(10\)
✕
E
\(11\)
✕
Question 38 of 43   |  MCQ  · Level 3
Rectangle: \(\dfrac{d z}{d t} = 1\), \(\dfrac{d x}{d t} = 3 \dfrac{d y}{d t}\). At \(x=4, y=3\), find \(\dfrac{d x}{d t}\).
A
\(\dfrac{1}{3}\)
✕
B
\(1\)
✕
C
\(2\)
✕
D
\(\sqrt{5}\)
✕
E
\(5\)
✕
Question 39 of 43   |  MCQ  · Level 2
\(\operatorname*{lim}\limits_{x \rightarrow 3} f(x) = 7\), which must be true?
I. continuous at 3
II. differentiable at 3
III. \(f(3) = 7\)
A
None
✕
B
II only
✕
C
III only
✕
D
I and III only
✕
E
I, II, and III
✕
Question 40 of 43   |  MCQ  · Level 2
Which has \(y = 1\) as asymptote?
A
\(y = \ln x\)
✕
B
\(y = \sin x\)
✕
C
\(y = x/(x+1)\)
✕
D
\(y = x^2/(x-1)\)
✕
E
\(y = e^{-x}\)
✕
Question 41 of 43   |  MCQ  · Level 3
Ellipse \(x^2 + 9 y^2 = 9\) revolved about x-axis. Volume?
A
\(2 \pi\)
✕
B
\(4 \pi\)
✕
C
\(6 \pi\)
✕
D
\(9 \pi\)
✕
E
\(12 \pi\)
✕
Question 42 of 43   |  MCQ  · Level 3
\(f, g\) odd. Which must be odd?
I. \(f(g(x))\)
II. \(f+g\)
III. \(fg\)
A
I only
✕
B
II only
✕
C
I and II only
✕
D
II and III only
✕
E
I, II, and III
✕
Question 43 of 43   |  MCQ  · Level 3
Cylinder volume \(16 \pi\), minimize tin (surface area). Height?
A
\(2 \sqrt[3]{2}\)
✕
B
\(2 \sqrt{2}\)
✕
C
\(2 \sqrt[3]{4}\)
✕
D
\(4\)
✕
E
\(8\)
✕

Review Your Answers

Check your work before submitting. You can return to any question.

Answered: 0 Unanswered: 0 Flagged: 0
—

Report an issue with this question

Question ID: —
Questions
Answered Unanswered ⚑ Flagged
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 $2\pi$.

Submit Exam?

Answered: 0 / 43

Exam Paused

Your timer is paused. Click Resume to continue from where you left off — your answers and current position are saved.

Time is up

This exam was already started and the time limit has passed. Submit your answers as they are, or open the review panel to inspect them before submitting.