⌛ 5 minutes remaining. The timer is now always visible.
AB MCQ Set 170
35 Questions
Question 1 of 35
--:--
AB MCQ Set 170 0/35
Question 1 of 35   |  Limits and Continuity  · 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   |  Analytical Applications of Differentiation  · 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   |  Limits and Continuity  · 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   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
\(f(x) = \sqrt{4 \sin x + 2}\), \(f'(0) =\)
A
\(-2\)
✕
B
\(0\)
✕
C
\(\sqrt{2}\)
✕
D
\(\dfrac{\sqrt{2}}{2}\)
✕
E
\(1\)
✕
Question 5 of 35   |  Differentiation: Composite, Implicit, and Inverse Functions  · 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   |  Analytical Applications of Differentiation  · 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   |  Parametric Equations, Polar Coordinates, and Vector-Valued Functions  · 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   |  Parametric Equations, Polar Coordinates, and Vector-Valued Functions  · 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   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 2
\(y = x(\ln x)^2\), \(\dfrac{d y}{d x} =\)
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   |  Analytical Applications of Differentiation  · 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   |  Analytical Applications of Differentiation  · 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   |  Analytical Applications of Differentiation  · 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   |  Limits and Continuity  · 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   |  Differentiation: Composite, Implicit, and Inverse Functions  · Level 3
\(x + y = x y\), \(\dfrac{d y}{d x} =\)
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   |  Differentiation: Composite, Implicit, and Inverse Functions  · 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
\(\dfrac{1}{\sqrt{1 - x^2}}\)
✕
Question 17 of 35   |  Analytical Applications of Differentiation  · 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   |  Integration and Accumulation of Change  · Level 3
\(\displaystyle\int_{0}^{6} (x^2 - 2 x + 2) d x\) approximated by 3 inscribed rectangles, equal width
A
\(24\)
✕
B
\(26\)
✕
C
\(28\)
✕
D
\(48\)
✕
E
\(76\)
✕
Question 20 of 35   |  Limits and Continuity  · Level 3
\(\operatorname*{lim}\limits_{x \rightarrow -3} \dfrac{x^2 + 3 x}{\sqrt{x^2 + 6 x + 9}}\)
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   |  Integration and Accumulation of Change  · Level 3
Trapezoidal approx of \(\displaystyle\int_{0}^{10} f(x) d x\) 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   |  Limits and Continuity  · 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   |  Limits and Continuity  · 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   |  Analytical Applications of Differentiation  · 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   |  Contextual Applications of Differentiation  · 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   |  Differentiation: Definition and Fundamental Properties  · 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   |  Differential Equations  · 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   |  Limits and Continuity  · 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   |  Analytical Applications of Differentiation  · 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   |  Analytical Applications of Differentiation  · 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   |  Differentiation: Definition and Fundamental Properties  · 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   |  Limits and Continuity  · 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   |  Integration and Accumulation of Change  · Level 2
[Calc] Midpoint Riemann sum for \(\displaystyle\int_{0}^{6} f(x) d x\) 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   |  Differentiation: Definition and Fundamental Properties  · 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
\(4 e\)
✕

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 / 35

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.