⌛ 5 minutes remaining. The timer is now always visible.
AB MCQ Set 150
38 Questions
Question 1 of 38
AB MCQ Set 150 0/38
Question 1 of 38   |  Analytical Applications of Differentiation  · Level 2
What is the x-coordinate of the point of inflection on \(y = \left(\dfrac{1}{3}\right) x^3 + 5 x^2 + 24\)?
A
\(5\)
✕
B
\(0\)
✕
C
\(-\dfrac{10}{3}\)
✕
D
\(-5\)
✕
E
\(-10\)
✕
Question 2 of 38   |  Integration and Accumulation of Change  · Level 1
\(\displaystyle\int_{1}^{2} (1/x^2) d x =\)
A
\(-\dfrac{1}{2}\)
✕
B
\(\dfrac{7}{24}\)
✕
C
\(\dfrac{1}{2}\)
✕
D
\(1\)
✕
E
\(2 \ln 2\)
✕
Question 3 of 38   |  Analytical Applications of Differentiation  · Level 2
\(f\) continuous on \([a,b]\), differentiable on \((a,b)\). Which COULD be false?
A
\(f'(c) = \dfrac{f(b)-f(a)}{b-a}\) for some \(c\)
✕
B
\(f'(c) = 0\) for some \(c\)
✕
C
\(f\) has min on \([a,b]\)
✕
D
\(f\) has max on \([a,b]\)
✕
E
\(\displaystyle\int_{a}^{b} f d x\) exists
✕
Question 4 of 38   |  Integration and Accumulation of Change  · Level 1
\(\displaystyle\int_{0}^{x} \sin t d t =\)
A
\(\sin x\)
✕
B
\(-\cos x\)
✕
C
\(\cos x\)
✕
D
\(\cos x - 1\)
✕
E
\(1 - \cos x\)
✕
Question 5 of 38   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
\(x^2 + xy = 10\), at \(x=2\), \(\dfrac{dy}{dx} =\)
A
\(-\dfrac{7}{2}\)
✕
B
\(-2\)
✕
C
\(\dfrac{2}{7}\)
✕
D
\(\dfrac{3}{2}\)
✕
E
\(\dfrac{7}{2}\)
✕
Question 6 of 38   |  Integration and Accumulation of Change  · Level 2
\(\displaystyle\int_{1}^{e} ((x^2 - 1)/x) d x =\)
A
\(e - \dfrac{1}{e}\)
✕
B
\(e^2 - e\)
✕
C
\(e^2/2 - e + \dfrac{1}{2}\)
✕
D
\(e^2 - 2\)
✕
E
\(e^2/2 - \dfrac{3}{2}\)
✕
Question 7 of 38   |  Differentiation: Definition and Fundamental Properties  · Level 3
\(g(x) > 0\), \(f(0) = 1\), \(h = fg\), \(h' = f g'\). Then \(f(x) =\)
A
\(f'(x)\)
✕
B
\(g(x)\)
✕
C
\(e^x\)
✕
D
\(0\)
✕
E
\(1\)
✕
Question 8 of 38   |  Differentiation: Definition and Fundamental Properties  · Level 2
Instantaneous rate of \(f(x) = \dfrac{x^2 - 2}{x - 1}\) at \(x = 2\)
A
\(-2\)
✕
B
\(\dfrac{1}{6}\)
✕
C
\(\dfrac{1}{2}\)
✕
D
\(2\)
✕
E
\(6\)
✕
Question 9 of 38   |  Integration and Accumulation of Change  · Level 1
\(f\) linear, \(0 < a < b\). \(\displaystyle\int_{a}^{b} f''(x) d x =\)
A
\(0\)
✕
B
\(1\)
✕
C
\(\dfrac{ab}{2}\)
✕
D
\(b - a\)
✕
E
\((b^2 - a^2)/2\)
✕
Question 10 of 38   |  Limits and Continuity  · Level 2
\(f(x) = \ln x\) for \(0 < x \leq 2\), \(x^2 \ln 2\) for \(2 < x \leq 4\). \(\operatorname*{lim}\limits_{x\rightarrow 2} f(x) =\)
A
\(\ln 2\)
✕
B
\(\ln 8\)
✕
C
\(\ln 16\)
✕
D
\(4\)
✕
E
nonexistent
✕
Question 11 of 38   |  Contextual Applications of Differentiation  · Level 1
\(x(t) = t^2 - 6 t + 5\). \(v = 0\) when \(t =\)
A
\(1\)
✕
B
\(2\)
✕
C
\(3\)
✕
D
\(4\)
✕
E
\(5\)
✕
Question 12 of 38   |  Integration and Accumulation of Change  · Level 2
\(F(x) = \displaystyle\int_{0}^{x} \sqrt{t^3 + 1} d t\), \(F'(2) =\)
A
\(-3\)
✕
B
\(-2\)
✕
C
\(2\)
✕
D
\(3\)
✕
E
\(18\)
✕
Question 13 of 38   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
\(f(x) = \sin(e^{-x})\), \(f'(x) =\)
A
\(-\cos(e^{-x})\)
✕
B
\(\cos(e^{-x}) + e^{-x}\)
✕
C
\(\cos(e^{-x}) - e^{-x}\)
✕
D
\(e^{-x} \cos(e^{-x})\)
✕
E
\(-e^{-x} \cos(e^{-x})\)
✕
Question 14 of 38   |  Differentiation: Definition and Fundamental Properties  · Level 1
Tangent to \(y = x + \cos x\) at \((0, 1)\)
A
\(y = 2 x + 1\)
✕
B
\(y = x + 1\)
✕
C
\(y = x\)
✕
D
\(y = x - 1\)
✕
E
\(y = 0\)
✕
Question 15 of 38   |  Analytical Applications of Differentiation  · Level 3
\(f''(x) = x(x+1)(x-2)^2\). Inflection points at \(x =\)
A
\(-1\) only
✕
B
\(2\) only
✕
C
\(-1\) and \(0\) only
✕
D
\(-1\) and \(2\) only
✕
E
\(-1, 0\), and \(2\) only
✕
Question 16 of 38   |  Integration and Accumulation of Change  · Level 1
\(\displaystyle\int_{-3}^k x^2 d x = 0\). \(k =\)
A
\(-3\)
✕
B
\(0\)
✕
C
\(3\)
✕
D
\(-3\) and \(3\)
✕
E
\(-3, 0\), and \(3\)
✕
Question 17 of 38   |  Differential Equations  · Level 1
\(\dfrac{dy}{dt} = ky\), \(k\) nonzero. \(y\) could be
A
\(2 e^{kty}\)
✕
B
\(2 e^{kt}\)
✕
C
\(e^{kt} + 3\)
✕
D
\(kty + 5\)
✕
E
\(\left(\dfrac{1}{2}\right) k y^2 + \left(\dfrac{1}{2}\right)\)
✕
Question 18 of 38   |  Analytical Applications of Differentiation  · Level 2
\(f(x) = x^4 + x^2 - 2\) increasing on
A
\(\left(-\dfrac{1}{\sqrt{2}}, \infty\right)\)
✕
B
\(\left(-\dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}\right)\)
✕
C
\((0, \infty)\)
✕
D
\((-\infty, 0)\)
✕
E
\(\left(-\infty, -\dfrac{1}{\sqrt{2}}\right)\)
✕
Question 19 of 38   |  Analytical Applications of Differentiation  · Level 3
Max accel of \(v(t) = t^3 - 3 t^2 + 12 t + 4\) on \([0, 3]\)
A
\(9\)
✕
B
\(12\)
✕
C
\(14\)
✕
D
\(21\)
✕
E
\(40\)
✕
Question 20 of 38   |  Applications of Integration  · Level 2
Area between \(y = x^2\) and \(y = -x\) from \(0\) to \(2\)
A
\(\dfrac{2}{3}\)
✕
B
\(\dfrac{8}{3}\)
✕
C
\(4\)
✕
D
\(\dfrac{14}{3}\)
✕
E
\(\dfrac{16}{3}\)
✕
Question 21 of 38   |  Limits and Continuity  · Level 3
\(f\) continuous, \(f(0)=1\), \(f(1)=k\), \(f(2)=2\). \(f(x) = \dfrac{1}{2}\) has at least 2 solutions in \([0,2]\) if \(k =\)
A
\(0\)
✕
B
\(\dfrac{1}{2}\)
✕
C
\(1\)
✕
D
\(2\)
✕
E
\(3\)
✕
Question 22 of 38   |  Applications of Integration  · Level 3
Average value of \(y = x^2 \sqrt{x^3 + 1}\) on \([0, 2]\)
A
\(\dfrac{26}{9}\)
✕
B
\(\dfrac{52}{9}\)
✕
C
\(\dfrac{26}{3}\)
✕
D
\(\dfrac{52}{3}\)
✕
E
\(24\)
✕
Question 23 of 38   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
\(f(x) = \tan(2 x)\), \(f'\left(\dfrac{\pi}{6}\right) =\)
A
\(\sqrt{3}\)
✕
B
\(2 \sqrt{3}\)
✕
C
\(4\)
✕
D
\(4 \sqrt{3}\)
✕
E
\(8\)
✕
Question 24 of 38   |  MCQ  · Level 3
[Calc] \(f(x) = 3 e^{2 x}\) and \(g(x) = 6 x^3\) have parallel tangent lines at \(x =\)
A
\(-0.701\)
✕
B
\(-0.567\)
✕
C
\(-0.391\)
✕
D
\(-0.302\)
✕
E
\(-0.258\)
✕
Question 25 of 38   |  Contextual Applications of Differentiation  · Level 3
[Calc] Radius decreasing 0.1 cm/s. In terms of circumference \(C\), \(\dfrac{d A}{d t} =\)
A
\(-(0.2) \pi C\)
✕
B
\(-(0.1) C\)
✕
C
\(-(0.1) C/(2 \pi)\)
✕
D
\((0.1)^2 C\)
✕
E
\((0.1)^2 \pi C\)
✕
Question 26 of 38   |  Analytical Applications of Differentiation  · Level 3
[Calc] \(f'(x) = \cos^2 \dfrac{x}{x} - \dfrac{1}{5}\). Critical values on \((0, 10)\)
A
One
✕
B
Three
✕
C
Four
✕
D
Five
✕
E
Seven
✕
Question 27 of 38   |  Differentiation: Definition and Fundamental Properties  · Level 2
\(f(x) = |x|\). Which true?
I. continuous at 0
II. differentiable at 0
III. abs min at 0
A
I only
✕
B
II only
✕
C
III only
✕
D
I and III only
✕
E
II and III only
✕
Question 28 of 38   |  Integration and Accumulation of Change  · Level 3
\(F'(x) = f(x)\), \(\displaystyle\int_{1}^{3} f(2 x) d x =\)
A
\(2 F(3) - 2 F(1)\)
✕
B
\(\left(\dfrac{1}{2}\right) F(3) - \left(\dfrac{1}{2}\right) F(1)\)
✕
C
\(2 F(6) - 2 F(2)\)
✕
D
\(F(6) - F(2)\)
✕
E
\(\left(\dfrac{1}{2}\right) F(6) - \left(\dfrac{1}{2}\right) F(2)\)
✕
Question 29 of 38   |  Limits and Continuity  · Level 2
\(\operatorname*{lim}\limits_{x \rightarrow a}\dfrac{x^2 - a^2}{x^4 - a^4}\)
A
\(1/a^2\)
✕
B
\(1/(2 a^2)\)
✕
C
\(1/(6 a^2)\)
✕
D
\(0\)
✕
E
nonexistent
✕
Question 30 of 38   |  Differential Equations  · Level 3
[Calc] \(\dfrac{d y}{d t} = k y\), doubles every 10 years. \(k =\)
A
\(0.069\)
✕
B
\(0.200\)
✕
C
\(0.301\)
✕
D
\(3.322\)
✕
E
\(5.000\)
✕
Question 31 of 38   |  Integration and Accumulation of Change  · Level 2
[Calc] \(f(2)=10, f(5)=30, f(7)=40, f(8)=20\). Trapezoidal \(\displaystyle\int_{2}^{8} f d x\)
A
\(110\)
✕
B
\(130\)
✕
C
\(160\)
✕
D
\(190\)
✕
E
\(210\)
✕
Question 32 of 38   |  Applications of Integration  · Level 3
[Calc] Base in Q1 by \(x+2y=8\) and axes. Cross-sections perp to x-axis are semicircles. Volume?
A
\(12.566\)
✕
B
\(14.661\)
✕
C
\(16.755\)
✕
D
\(67.021\)
✕
E
\(134.041\)
✕
Question 33 of 38   |  Differentiation: Definition and Fundamental Properties  · Level 3
[Calc] \(f(x) = x^4 + 2 x^2\). Tangent where \(f'(x) = 1\)
A
\(y = 8 x - 5\)
✕
B
\(y = x + 7\)
✕
C
\(y = x + 0.763\)
✕
D
\(y = x - 0.122\)
✕
E
\(y = x - 2.146\)
✕
Question 34 of 38   |  Integration and Accumulation of Change  · Level 3
[Calc] \(F\) antiderivative of \((\ln x)^3/x\), \(F(1) = 0\). \(F(9) =\)
A
\(0.048\)
✕
B
\(0.144\)
✕
C
\(5.827\)
✕
D
\(23.308\)
✕
E
\(1640.250\)
✕
Question 35 of 38   |  Analytical Applications of Differentiation  · Level 3
\(g(x) < 0\). \(f'(x) = (x^2 - 4) g(x)\). Which true?
A
max at \(-2\), min at \(2\)
✕
B
min at \(-2\), max at \(2\)
✕
C
minima at \(-2\) and \(2\)
✕
D
maxima at \(-2\) and \(2\)
✕
E
Cannot be determined
✕
Question 36 of 38   |  Contextual Applications of Differentiation  · Level 3
Triangle base \(b\) inc 3 in/min, height \(h\) dec 3 in/min. Area \(A\):
A
\(A\) always increasing
✕
B
\(A\) always decreasing
✕
C
\(A\) decreasing only when \(b < h\)
✕
D
\(A\) decreasing only when \(b > h\)
✕
E
\(A\) remains constant
✕
Question 37 of 38   |  Analytical Applications of Differentiation  · Level 3
\(f\) diff on \((1, 10)\), \(f(2)=-5\), \(f(5)=5\), \(f(9)=-5\). Which true?
I. at least 2 zeros
II. horizontal tangent
III. \(f(c) = 3\) for \(c\) in \((2, 5)\)
A
None
✕
B
I only
✕
C
I and II only
✕
D
I and III only
✕
E
I, II, and III
✕
Question 38 of 38   |  Integration and Accumulation of Change  · Level 3
[Calc] Area under \(y = \cos x\) from \(k\) to \(\dfrac{\pi}{2}\) is 0.1, find \(k\)
A
\(1.471\)
✕
B
\(1.414\)
✕
C
\(1.277\)
✕
D
\(1.120\)
✕
E
\(0.436\)
✕

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 / 38

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.