Free Printable AP Calculus AB Full Year Review

1.

Derivative of $y=x^7$

a)

$y'=7x^6$

b)

$y'=x^7\cdot7$

c)

$y'=\frac{1}{8}x^8$

2.

Derivative of $y=\sin x$

a)

$y'=\cos x$

b)

$y'=-\sin x$

c)

$y'=\sec^2x$

d)

$y'=-\cos x$

3.

Derivative of $y=\cos x$

a)

$y'=\sin x$

b)

$y'=-\sin x$

c)

$y'=\sec^2x$

d)

$y'=-\csc^2x$

4.

Derivative of $y=\tan x$

a)

$y'=\sec^2x$

b)

$y'=-\csc^2x$

c)

$y'=\sin x$

d)

$y'=-\cos x$

5.

Derivative of $y=\cot x$

a)

$y'=-\csc^2x$

b)

$y'=\sec^2x$

c)

$y'=\cos x$

d)

$y'=-\sin x$

6.

Derivative of $y=\sec x$

a)

$y'=\sec x\tan x$

b)

$y'=-\csc x\cot x$

c)

$y'=\sec^2x$

d)

$y'=-\csc^2x$

7.

Derivative of $y=\csc x$

a)

$y'=-\csc x\cot x$

b)

$y'=\sec x\tan x$

c)

$y'=\sec^2x$

d)

$y'=-\csc^2x$

8.

Derivative of $y=\ln x$

a)

$y'=\frac{1}{x}$

b)

$y'=e^x$

c)

$y'=\ln x$

d)

$y'=\frac{1}{\ln x}$

9.

Derivative of $y=e^{5x}$

a)

$y'=5e^{5x}$

b)

$y'=5e^{4x}$

c)

$y'=e^{5x}$

d)

$y'=5e^{5x-1}$

10.

Derivative of $y=5^x$

a)

$y'=x5^{x-1}$

b)

$y'=5^x\cdot\ln5$

c)

$y'=\frac{5^x}{\ln5}$

d)

$y'=e^x\cdot\ln5$

11.

Derivative of $y=\sin\left(x^3\right)$

a)

$y'=\sin\left(3x^2\right)$

b)

$y'=\cos\left(3x^2\right)$

c)

$y'=\cos\left(x^3\right)\cdot3x^2$

d)

$y'=\cos\left(x^3\right)$

12.

Derivative of $y=x^3\sin x$

a)

$y'=x^3\cos x+3x^2\sin x$

b)

$y'=3x^2\cos x$

c)

$y'=x^3\cos x-3x^2\sin x$

d)

$y'=x^3\sin x+3x^2\cos x$

13.

Derivative of $y=\frac{f\left(x\right)}{g\left(x\right)}$

a)

$y'=\frac{g\left(x\right)f'\left(x\right)-f\left(x\right)g'\left(x\right)}{\left(g\left(x\right)\right)^2}$

b)

$y'=\frac{f'\left(x\right)}{g'\left(x\right)}$

c)

$y'=\ \frac{f\left(x\right)g'\left(x\right)-g\left(x\right)f'\left(x\right)}{\left(g\left(x\right)\right)^2}$

14.

Fundamental Theorem:
$\int_a^bf'\left(x\right)dx=$

a)

$f\left(a\right)-f\left(b\right)$

b)

$f\left(b\right)-f\left(a\right)$

c)

$f'\left(b\right)-f'\left(a\right)$

d)

$f'\left(a\right)-f'\left(b\right)$

15.

Fundamental Theorem:
$f\left(b\right)=$

a)

$f\left(a\right)+\int_a^bf'\left(x\right)dx$

b)

$f\left(a\right)-\int_a^bf'\left(x\right)dx$

c)

$f\left(a\right)+\int_a^bf\left(x\right)dx$

d)

$f\left(a\right)-\int_a^bf\left(x\right)dx$

16.

Derivative of $f\left(x\right)=\int_4^x\sin\left(t\right)dt$

a)

$f'\left(x\right)=\sin\left(x\right)$

b)

$f'\left(x\right)=\cos\left(x\right)$

c)

$f'\left(x\right)=\sin x-\sin4$

d)

$f'\left(x\right)=-\cos x+\cos4$

17.

Area of a Trapezoid

a)

$A=\frac{1}{2}h\left(b_1+b_2\right)$

b)

$A=2l+2w$

c)

$A=\frac{1}{4}h\left(b_1+b_2\right)$

d)

$A=\frac{1}{2}bh$

18.

Area of a Circle

a)

$A=\pi r^2$

b)

$A=2\pi r$

c)

$A=r^2$

d)

$A=\pi d$

19.

Average rate of change formula

a)

$\frac{f\left(b\right)-f\left(a\right)}{b-a}$

b)

$\frac{1}{b-a}\int_a^bf\left(x\right)dx$

c)

$\frac{f\left(b\right)-f\left(a\right)}{2}$

20.

Average value of a function

a)

$\frac{f\left(b\right)-f\left(a\right)}{b-a}$

b)

$\frac{1}{b-a}\int_a^bf\left(x\right)dx$

c)

$\frac{f\left(b\right)-f\left(a\right)}{2}$

21.

Derivative of Position

a)

velocity

b)

speed

c)

acceleration

d)

displacement

22.

Derivative of Velocity

a)

velocity

b)

speed

c)

acceleration

d)

displacement

23.

Absolute value of Velocity

a)

velocity

b)

speed

c)

acceleration

d)

displacement

24.

Average Velocity

a)

$\frac{\text{final position - initial position}}{\text{change in time}}$

b)

$\frac{\text{final velocity - initial velocity}}{\text{change in time}}$

c)

$\frac{\text{final velocity - initial velocity}}{2}$

25.

Which is best for finding the area under a curve?

a)

Limit

b)

Derivative

c)

Integral

d)

Set equation equal to zero

26.

If we know the rate, how do we find the amount?

a)

Limit

b)

Derivative

c)

Integral

d)

Second Derivative

27.

Which is best for finding the instantaneous rate of change?

a)

Limit

b)

Derivative

c)

Integral

d)

Second Derivative

28.

Which is the best for finding the slope of a tangent line?

a)

Limit

b)

Derivative

c)

Integral

d)

Second Derivative

29.

$\int\sin x\ dx=$

a)

$\cos x+C$

b)

$-\cos x+C$

c)

$\tan x+C$

d)

$\sec^2x+C$

30.

$\int\cos x\ dx=$

a)

$\sin x+C$

b)

$-\sin x+C$

c)

$\sec^2x+C$

d)

$\sec x\tan x+C$

31.

$\int\sec x\tan x\ dx=$

a)

$\sec x+C$

b)

$-\sin x+C$

c)

$\sec^2x+C$

d)

$\sec x\tan x+C$

32.

$\int\csc x\cot x\ dx=$

a)

$-\csc x+C$

b)

$\csc^2x+C$

c)

$\sin x+C$

d)

$-\cos x+C$

33.

$\int\sec^2x\ dx=$

a)

$\tan x+C$

b)

$\frac{1}{3}\sec^3x\ +C$

c)

$2\sec x+C$

d)

$\cot x+C$

34.

$\int\csc^2x\ dx=$

a)

$\frac{1}{3}\csc^3x+C$

b)

$-\cot x+C$

c)

$\tan x+C$

d)

$2\csc x+C$

35.

$\int\frac{1}{x}\ dx=$

a)

$\ln x+C$

b)

$-\frac{1}{x^2}+C$

c)

$x^{-1}+C$

d)

$-1x^{-2}+C$

36.

$\int e^x\ dx=$

a)

$e^x+C$

b)

$\ln\left(x\right)+C$

c)

$\frac{1}{2}e^{2x}+C$

d)

$\frac{1}{x+1}e_{ }^{x+1}\ +C$

37.

$\int e^{4x}\ dx=$

a)

$\frac{1}{4}e^{4x}+C$

b)

$4e^{4x}+C$

c)

$4e^{3x}+C$

d)

$\frac{1}{5}e^{5x}+C$

38.

$\ln e=$

a)

1

b)

0

c)

undefined

39.

$\ln0=$

a)

1

b)

0

c)

undefined

40.

$\ln1=$

a)

1

b)

0

c)

undefined

41.

$\sin\left(0\right)=$

a)

$0$

b)

$1$

c)

$-1$

42.

$\cos\left(0\right)=$

a)

$0$

b)

$1$

c)

$-1$

43.

$\cos\left(\frac{\pi}{2}\right)=$

a)

$0$

b)

$1$

c)

$-1$

44.

$\sin\left(\frac{\pi}{2}\right)=$

a)

$0$

b)

$1$

c)

$-1$

45.

$\sin\left(\pi\right)=$

a)

$0$

b)

$1$

c)

$-1$

46.

$\cos\left(\pi\right)=$

a)

$0$

b)

$1$

c)

$-1$

47.

Which is the best for finding minimums or maximums?

a)

Limit

b)

Derivative

c)

Integral

d)

Second Derivative

48.

Which is the best for finding points of inflection?

a)

Limit

b)

Derivative

c)

Integral

d)

Second Derivative

49.

What equation do we use to find the equation of a tangent line?

a)

$y-y_1=m\left(x-x_1\right)$

b)

$x-x_1=m\left(y-y_1\right)$

c)

$y+y_1=m\left(x+x_1\right)$

d)

$x+x_2=m\left(y+y_1\right)$

50.

Volume of Revolution between two curves

a)

$V=\pi\int_a^b\left[R\left(x\right)-r\left(x\right)\right]^2\ dx$

b)

$V=\pi\int_a^b\left(\left[R\left(x\right)\right]^2-\left[r\left(x\right)\right]^2\right)\ dx$

c)

$V=\pi\int_a^b\left[R\left(x\right)+r\left(x\right)\right]^2\ dx$

d)

$V=\pi\int_a^b\left(\left[R\left(x\right)\right]^2+\left[r\left(x\right)\right]^2\right)\ dx$

AP Calculus AB Full Year Review

Total questions: 50

Worksheet time: 5mins

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