AP Calculus BC Unit 1 - 9 Review

Authored by Eric Eshleman

Mathematics

9th - 12th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Evaluate the indefinite integral.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is the solution to the differential equation $\frac{dy}{dx}=\frac{x^2}{y}$ with the initial condition y(3) = -2?

$y=-2e^{\left(-9+\frac{x^3}{3}\right)}$

$y=\sqrt{\frac{2x^3}{3}}$

$y=\sqrt{\frac{2x^3}{3}-14}$

$y=-\sqrt{\frac{2x^3}{3}-14}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

OPEN ENDED QUESTION

30 sec • 1 pt

$\frac{dy}{dx}=x-y$ and $f(3)=1$ Use Euler’s method with two steps of equal size to approximate $f(6)$

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OPEN ENDED QUESTION

30 sec • 1 pt

$\frac{dy}{dx}=2x+y$ and $y(1)=k$ Using Euler’s method, starting at $x=1$ with a step-size of 0.5, gives the approximation $y(1.5)\approx4$ . Find k.

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10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Evaluate the limit.

$\lim_{x\rightarrow2}\ \frac{x^3-8}{x^2-4}$

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AP Calculus BC Unit 1 - 9 Review

Evaluate the indefinite integral.

Which of the following is the solution to the differential equation dydx=x2y\frac{dy}{dx}=\frac{x^2}{y}dxdy​=yx2​ with the initial condition y(3) = -2?

dydx=x−y\frac{dy}{dx}=x-ydxdy​=x−y and f(3)=1f(3)=1f(3)=1 Use Euler’s method with two steps of equal size to approximate f(6)f(6)f(6)

dydx=2x+y\frac{dy}{dx}=2x+ydxdy​=2x+y and y(1)=ky(1)=ky(1)=k Using Euler’s method, starting at x=1x=1x=1 with a step-size of 0.5, gives the approximation y(1.5)≈4y(1.5)\approx4y(1.5)≈4 . Find k.

Use the function values in the following table and the Trapezoidal Rule with n=6 to approximate the integral from x=0 to x=12.x: 0 2 4 6 8 10 12 f(x): 7 11 20 25 18 14 9

Evaluate the limit. lim⁡x→2 x3−8x2−4\lim_{x\rightarrow2}\ \frac{x^3-8}{x^2-4}x→2lim​ x2−4x3−8​

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Which of the following is the solution to the differential equation $\frac{dy}{dx}=\frac{x^2}{y}$ with the initial condition y(3) = -2?

$\frac{dy}{dx}=x-y$ and $f(3)=1$ Use Euler’s method with two steps of equal size to approximate $f(6)$

$\frac{dy}{dx}=2x+y$ and $y(1)=k$ Using Euler’s method, starting at $x=1$ with a step-size of 0.5, gives the approximation $y(1.5)\approx4$ . Find k.

Use the function values in the following table and the Trapezoidal Rule with n=6 to approximate the integral from x=0 to x=12.
x: 0 2 4 6 8 10 12
f(x): 7 11 20 25 18 14 9

Evaluate the limit.

$\lim_{x\rightarrow2}\ \frac{x^3-8}{x^2-4}$