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AB MCQ Set 150 (1998 Official AP)
38 Questions
Question 1 of 38
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AB MCQ Set 150 (1998 Official AP) 0/38
Question 1 of 38   |  MCQ  · 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   |  MCQ  · Level 1
\(\displaystyle\int_{1}^{2} \left(\dfrac{1}{x}^2\right) dx =\)
A
\(-\dfrac{1}{2}\)
✕
B
\(\dfrac{7}{24}\)
✕
C
\(\dfrac{1}{2}\)
✕
D
\(1\)
✕
E
\(2 \ln 2\)
✕
Question 3 of 38   |  MCQ  · 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
\(\displaystyle\int_{a}^{b} f dx\) exists
✕
Question 4 of 38   |  MCQ  · Level 1
\(\displaystyle\int_{0}^{x} \sin t dt =\)
A
\(\sin x\)
✕
B
\(-\cos x\)
✕
C
\(\cos x\)
✕
D
\(\cos x - 1\)
✕
E
\(1 - \cos x\)
✕
Question 5 of 38   |  MCQ  · 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   |  MCQ  · Level 2
\(\displaystyle\int_{1}^{e} ((x^2 - 1)/x) dx =\)
A
\(e - \dfrac{1}{e}\)
✕
B
\(e^2 - e\)
✕
C
\(e^\dfrac{2}{2} - e + \dfrac{1}{2}\)
✕
D
\(e^2 - 2\)
✕
E
\(e^\dfrac{2}{2} - \dfrac{3}{2}\)
✕
Question 7 of 38   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · Level 1
\(f\) linear, \(0 < a < b\). \(\displaystyle\int_{a}^{b} f''(x) dx =\)
A
\(0\)
✕
B
\(1\)
✕
C
\(\dfrac{ab}{2}\)
✕
D
\(b - a\)
✕
E
\((b^2 - a^2)/2\)
✕
Question 10 of 38   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · Level 2
\(F(x) = \displaystyle\int_{0}^{x} \sqrt{t^3 + 1} dt\), \(F'(2) =\)
A
\(-3\)
✕
B
\(-2\)
✕
C
\(2\)
✕
D
\(3\)
✕
E
\(18\)
✕
Question 13 of 38   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · Level 1
\(\displaystyle\int_{-3}^k x^2 dx = 0\). \(k =\)
A
\(-3\)
✕
B
\(0\)
✕
C
\(3\)
✕
D
\(-3\) and \(3\)
✕
E
\(-3, 0\), and \(3\)
✕
Question 17 of 38   |  MCQ  · 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   |  MCQ  · Level 2
\(f(x) = x^4 + x^2 - 2\) increasing on
A
\((-1/\sqrt{2}, \infty)\)
✕
B
\((-1/\sqrt{2}, 1/\sqrt{2})\)
✕
C
\((0, \infty)\)
✕
D
\((-\infty, 0)\)
✕
E
\((-\infty, -1/\sqrt{2})\)
✕
Question 19 of 38   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · Level 3
[Calc] Radius decreasing 0.1 cm/s. In terms of circumference \(C\), \(\dfrac{dA}{dt} =\)
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   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · Level 3
\(F'(x) = f(x)\), \(\displaystyle\int_{1}^{3} f(2 x) dx =\)
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   |  MCQ  · Level 2
\(\operatorname*{lim}\limits_{x \rightarrow a}\dfrac{x^2 - a^2}{x^4 - a^4}\)
A
\(\dfrac{1}{a}^2\)
✕
B
\(1/(2 a^2)\)
✕
C
\(1/(6 a^2)\)
✕
D
\(0\)
✕
E
nonexistent
✕
Question 30 of 38   |  MCQ  · Level 3
[Calc] \(\dfrac{dy}{dt} = k y\), doubles every 10 years. \(k =\)
A
\(0.069\)
✕
B
\(0.200\)
✕
C
\(0.301\)
✕
D
\(3.322\)
✕
E
\(5.000\)
✕
Question 31 of 38   |  MCQ  · Level 2
[Calc] \(f(2)=10, f(5)=30, f(7)=40, f(8)=20\). Trapezoidal \(\displaystyle\int_{2}^{8} f dx\)
A
\(110\)
✕
B
\(130\)
✕
C
\(160\)
✕
D
\(190\)
✕
E
\(210\)
✕
Question 32 of 38   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · Level 3
[Calc] \(F\) antiderivative of \((\ln x)^\dfrac{3}{x}\), \(F(1) = 0\). \(F(9) =\)
A
\(0.048\)
✕
B
\(0.144\)
✕
C
\(5.827\)
✕
D
\(23.308\)
✕
E
\(1640.250\)
✕
Question 35 of 38   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · 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   |  MCQ  · 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
\(0.436\)
✕

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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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