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AB MCQ Set 170 (41-problem AI-solved)
35 Questions
Question 1 of 35
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AB MCQ Set 170 (41-problem AI-solved) 0/35
Question 1 of 35   |  MCQ  · Level 1
If \(f(x) = \dfrac{x^2 - 9}{x + 3}\) is continuous at \(x = -3\), then \(f(-3) =\)
A
\(3\)
✕
B
\(-3\)
✕
C
\(0\)
✕
D
\(6\)
✕
E
\(-6\)
✕
Question 2 of 35   |  MCQ  · Level 2
\(y = 3 x^2 - x^3\) has a relative maximum at
A
\((0, 0)\) only
✕
B
\((2, 2)\) only
✕
C
\((2, 4)\) only
✕
D
\((4, -16)\) only
✕
E
\((0, 0)\) and \((2, 4)\)
✕
Question 3 of 35   |  MCQ  · Level 2
\(\operatorname*{lim}\limits_{x \rightarrow \infty} \dfrac{10^8 x^5 + 10^6 x^4 + 10^4 x^2}{10^9 x^6 + 10^7 x^5 + 10^6 x^4} =\)
A
\(0\)
✕
B
\(1\)
✕
C
\(-1\)
✕
D
\(\dfrac{1}{10}\)
✕
E
\(-\dfrac{1}{10}\)
✕
Question 4 of 35   |  MCQ  · Level 2
\(f(x) = \sqrt{4 \sin x + 2}\), \(f'(0) =\)
A
\(-2\)
✕
B
\(0\)
✕
C
\(\sqrt{2}\)
✕
D
\(\sqrt{2}/2\)
✕
E
\(1\)
✕
Question 5 of 35   |  MCQ  · Level 3
Tangent to \(x^2 + y^2 = 169\) at \((5, -12)\)
A
\(5 y - 12 x = -120\)
✕
B
\(5 x - 12 y = 119\)
✕
C
\(5 x - 12 y = 169\)
✕
D
\(12 x + 5 y = 0\)
✕
E
\(12 x + 5 y = 169\)
✕
Question 6 of 35   |  MCQ  · Level 3
\(f(x) = 2 x^2 + \dfrac{k}{x}\) has inflection at \(x = -1\). \(k =\)
A
\(1\)
✕
B
\(-1\)
✕
C
\(2\)
✕
D
\(-2\)
✕
E
\(0\)
✕
Question 7 of 35   |  MCQ  · Level 3
Tangent line to \(x = 3 e^{-t}\), \(y = 6 e^t\) at \(t = 0\)
A
\(2 x + y - 12 = 0\)
✕
B
\(-2 x + y - 12 = 0\)
✕
C
\(2 x + y - 6 = 0\)
✕
D
\(-2 x + y - 6 = 0\)
✕
E
\(2 x + y = 0\)
✕
Question 8 of 35   |  MCQ  · Level 3
\(x = \sin t\), \(y = \cos^2 t\). \(d^2 \dfrac{y}{d} x^2\) at \(t = \dfrac{\pi}{2}\)
A
\(0\)
✕
B
\(\dfrac{1}{4}\)
✕
C
\(-\dfrac{1}{4}\)
✕
D
\(-2\)
✕
E
\(2\)
✕
Question 9 of 35   |  MCQ  · Level 2
\(y = x(\ln x)^2\), \(\dfrac{dy}{dx} =\)
A
\(3(\ln x)^2\)
✕
B
\((\ln x)(2 x + \ln x)\)
✕
C
\((\ln x)(2 + \ln x)\)
✕
D
\((\ln x)(2 + x \ln x)\)
✕
E
\((\ln x)(1 + \ln x)\)
✕
Question 10 of 35   |  MCQ  · Level 2
Particle on x-axis: \(v(t) = \sin 2 t\), \(x(0) = 0\). Find \(x(t)\)
A
\(\cos 2 t + \dfrac{1}{2}\)
✕
B
\(-\left(\dfrac{1}{2}\right) \sin 2 t + \dfrac{1}{2}\)
✕
C
\(-\left(\dfrac{1}{2}\right) \cos 2 t\)
✕
D
\(-\left(\dfrac{1}{2}\right) \cos 2 t + \dfrac{1}{2}\)
✕
E
\(-\left(\dfrac{1}{2}\right) \cos 2 t - \dfrac{1}{2}\)
✕
Question 11 of 35   |  MCQ  · Level 2
Max of \(f(x) = 2 x^3 - 9 x^2 + 12 x - 1\) on \([-1, 2]\)
A
\(0\)
✕
B
\(1\)
✕
C
\(2\)
✕
D
\(3\)
✕
E
\(4\)
✕
Question 12 of 35   |  MCQ  · Level 3
\(f(x) = x^4 - 8 x^2\), rel min at
A
\(0\) and \(-2\) only
✕
B
\(0\) and \(2\) only
✕
C
\(0\) only
✕
D
\(-2\) and \(2\) only
✕
E
\(-2, 0\), and \(2\)
✕
Question 13 of 35   |  MCQ  · Level 4
\(y = x^4 + b x^2 + 8 x + 1\) has horizontal tangent and inflection at same \(x\). \(b =\)
A
\(-1\)
✕
B
\(4\)
✕
C
\(1\)
✕
D
\(6\)
✕
E
\(-6\)
✕
Question 14 of 35   |  MCQ  · Level 3
\(\operatorname*{lim}\limits_{x \rightarrow 2} \dfrac{2^{\dfrac{x}{2}} - 2}{2^x - 4}\)
A
\(0\)
✕
B
\(\dfrac{1}{4}\)
✕
C
\(\dfrac{1}{2}\)
✕
D
\(\ln 2\)
✕
E
nonexistent
✕
Question 15 of 35   |  MCQ  · Level 3
\(x + y = x y\), \(\dfrac{dy}{dx} =\)
A
\(1/(x-1)\)
✕
B
\(\dfrac{y-1}{x-1}\)
✕
C
\(\dfrac{1-y}{x-1}\)
✕
D
\(x + y - 1\)
✕
E
\((2 - x y)/y\)
✕
Question 16 of 35   |  MCQ  · Level 2
For \(x < 1\), derivative of \(y = \ln \sqrt{1 - x^2}\)
A
\(x/(1 - x^2)\)
✕
B
\(x/(x^2 - 1)\)
✕
C
\(-x/(x^2 - 1)\)
✕
D
\(1/(2(1 - x^2))\)
✕
E
\(1/\sqrt{1 - x^2}\)
✕
Question 17 of 35   |  MCQ  · Level 2
\(y = x^3 - 6 x^2\) concave down for
A
\(0 < x < 4\)
✕
B
\(x > 2\)
✕
C
\(x < 2\)
✕
D
\(x < 0\)
✕
E
\(x > 4\)
✕
Question 18 of 35   |  MCQ  · Level 3
Normal line to \(y = \sqrt[3]{x^2 - 1}\) at \(x = 3\)
A
\(y + 12 x = 38\)
✕
B
\(y - 4 x = 10\)
✕
C
\(y + 2 x = 4\)
✕
D
\(y + 2 x = 8\)
✕
E
\(y - 2 x = -4\)
✕
Question 19 of 35   |  MCQ  · Level 3
\(\displaystyle\int_{0}^{6} (x^2 - 2 x + 2) dx\) approximated by 3 inscribed rectangles, equal width
A
\(24\)
✕
B
\(26\)
✕
C
\(28\)
✕
D
\(48\)
✕
E
\(76\)
✕
Question 20 of 35   |  MCQ  · Level 3
\(\operatorname*{lim}\limits_{x \rightarrow -3} (x^2 + 3 x)/\sqrt{x^2 + 6 x + 9}\)
A
\(-3\)
✕
B
\(-1\)
✕
C
\(1\)
✕
D
\(3\)
✕
E
nonexistent
✕
Question 21 of 35   |  MCQ  · Level 3
\(C(x) = 20000 + 5(x - 60)^2\), \(R(x) = 15000 + 130 x\). Revenue exceeds cost when
A
\(0 < x < 46\)
✕
B
\(x > 46\)
✕
C
\(x < 100\)
✕
D
\(46 < x < 100\)
✕
E
\(x > 100\)
✕
Question 22 of 35   |  MCQ  · Level 3
Trapezoidal approx of \(\displaystyle\int_{0}^{10} f(x) dx\) where \(f\) values: \(f(0)=20, f(1)=19.5, f(2)=18, f(3)=15.5, f(4)=12, f(5)=7.5, f(6)=2, f(7)=-4.5, f(8)=-12, f(9)=-20.5, f(10)=-30\)
A
\(30.825\)
✕
B
\(32.500\)
✕
C
\(33.325\)
✕
D
\(33.333\)
✕
E
\(35.825\)
✕
Question 23 of 35   |  MCQ  · Level 2
For which pair \(f, g\) is \(lim \dfrac{f}{g} = 0\)?
A
\(e^x, x^2\)
✕
B
\(e^x, \ln x\)
✕
C
\(\ln x, e^x\)
✕
D
\(x, \ln x\)
✕
E
\(3^x, 2^x\)
✕
Question 24 of 35   |  MCQ  · Level 3
Table near \(x=0\): \(f(x)\) approaches 2, \(g\) jumps from 1 (left) to 2 (right), \(h\) approaches 2 from both sides. For which functions does limit at 0 equal 2?
A
\(f\) only
✕
B
\(g\) only
✕
C
\(h\) only
✕
D
\(f\) and \(h\) only
✕
E
\(f, g\), and \(h\)
✕
Question 25 of 35   |  MCQ  · Level 4
\(f(x) = |(x^2 - 12)(x^2 + 4)|\) on \(-2 < x < 3\). How many \(c\) satisfy MVT conclusion?
A
None
✕
B
One
✕
C
Two
✕
D
Three
✕
E
Four
✕
Question 26 of 35   |  MCQ  · Level 3
\(A(t) = 4000 + 48(t - 3) - 4(t - 3)^3\). Production rate is increasing most rapidly at
A
8:00 am
✕
B
10:00 am
✕
C
11:00 am
✕
D
12:00 am
✕
E
1:00 pm
✕
Question 27 of 35   |  MCQ  · Level 4
\(y = 4 x^5 - 3 x^4 + 15 x^2 + 6\). How many points \(a\) on the curve have tangent through origin?
A
One
✕
B
Two
✕
C
Three
✕
D
Four
✕
E
Five
✕
Question 28 of 35   |  MCQ  · Level 4
[Calc] \(P(t) = 6000 - 5500 e^{-0.159 t}\) for \(t \geq 0\). During which year does \(P\) reach half its limiting value?
A
Second
✕
B
Third
✕
C
Fourth
✕
D
Eighth
✕
E
Twenty-ninth
✕
Question 29 of 35   |  MCQ  · Level 3
Which value is NOT in domain of \(f(x) = (\cos x)^x\)?
A
\(1\)
✕
B
\(\dfrac{\pi}{2}\)
✕
C
\(4 \dfrac{\pi}{3}\)
✕
D
\(4\)
✕
E
\(2 \pi\)
✕
Question 30 of 35   |  MCQ  · Level 2
\(f\) everywhere differentiable. \(f'\) values: \(f'(-10)=-2\), \(f'(-5)=-1\), \(f'(0)=0\), \(f'(5)=1\), \(f'(10)=2\). \(f'\) always increasing. Which must be true?
A
\(f\) has rel min at \(x = 0\)
✕
B
\(f\) concave down for all \(x\)
✕
C
\(f\) has inflection at \((0, f(0))\)
✕
D
\(f\) passes through origin
✕
E
\(f\) is odd
✕
Question 31 of 35   |  MCQ  · Level 4
[Calc] \(f'(x) = e^x(-x^3 + 3 x) - 3\) for \(0 \leq x \leq 5\). At what value of \(x\) is \(f\) absolute minimum?
A
For no value
✕
B
\(0\)
✕
C
\(0.618\)
✕
D
\(1.623\)
✕
E
\(5\)
✕
Question 32 of 35   |  MCQ  · Level 2
[Calc] Table: \(f(3.998)=1.15315\), \(f(3.999)=1.15548\), \(f(4)=1.15782\), \(f(4.001)=1.16016\), \(f(4.002)=1.16250\). Approximate \(f'(4)\)
A
\(0.00234\)
✕
B
\(0.289\)
✕
C
\(0.427\)
✕
D
\(2.340\)
✕
E
Cannot be determined
✕
Question 33 of 35   |  MCQ  · Level 2
If \(y = 7\) is horizontal asymptote of rational \(f\), which must be true?
A
\(\operatorname*{lim}\limits_{x \rightarrow 7} f(x) = \infty\)
✕
B
\(\operatorname*{lim}\limits_{x \rightarrow \infty} f(x) = 7\)
✕
C
\(\operatorname*{lim}\limits_{x \rightarrow 0} f(x) = \infty\)
✕
D
\(\operatorname*{lim}\limits_{x \rightarrow 7} f(x) = 0\)
✕
E
\(\operatorname*{lim}\limits_{x \rightarrow -\infty} f(x) = -7\)
✕
Question 34 of 35   |  MCQ  · Level 2
[Calc] Midpoint Riemann sum for \(\displaystyle\int_{0}^{6} f(x) dx\) with 3 intervals of width 2, table \(f(0)=0, f(1)=0.25, f(2)=0.48, f(3)=0.68, f(4)=0.84, f(5)=0.95, f(6)=1\)
A
\(2.64\)
✕
B
\(3.64\)
✕
C
\(3.72\)
✕
D
\(3.76\)
✕
E
\(4.64\)
✕
Question 35 of 35   |  MCQ  · Level 3
Tangent to \(y = e^{2-x}\) at \((1, e)\) intersects axes. Triangle area?
A
\(2 e\)
✕
B
\(e^2 - 1\)
✕
C
\(e^2\)
✕
D
\(2 e \sqrt{e}\)
✕
E
\(4 e\)
✕

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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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