AP Calculus AB Multiple Choice

There are 25 multiple choice questions and few short free responses to be finished. Please highlight the correct answer in yellow. There is only one answer to each question. Please read the questions carefully.

1.  Which one of the following does not find the value of f ‘(5) for f(x) = 3x2 – 2x – 4? (4 points)
 
All of these find the value for f ‘(5).

 

2.  Use your graphing calculator to find the value of f ‘(1) for f(x) = x2 + Ln(x). (4 points)
 
1
3
2
0

 

3.  How do Curves A and B compare to each other with respect to f and f ′?

(4 points)

 
The answer cannot be determined.
f: Curve A, f ′: Curve B, f ′′: Curve C
Neither Curve A or Curve B are derivatives of each other.
f: Curve A, f ′: Curve B

 

4.  Find the equation of the line tangent to y = 2x2 – x + 4 at x = 3. (4 points)
 
y = 11x – 14
y = 4x + 14
y = 4x + 3
y = 11x + 3

 

5.  If f(x) = 3a|4x – 4| – ax, where a is some constant not equal to zero, find f ‘(1). (4 points)
 
0
DNE
not enough information
1
1.  Find f'(x) for f(x) = -8x2 – 5x – 4. (4 points)
 
-16x – 5
-16x – 4
16x + 5
None of these

 

2.  Find f ‘(-3), if f(x) = (2x2 – 7x)(-x2 – 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative values. (4 points)
 

 

3.  Find the derivative  for  . (4 points)
 

 

4.  If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f ‘(3) = -5, f ‘(1) = -4, g ‘(1) = -3, g ‘(3) = 2, then find h ‘(1) if h(x) = f(x) g(x). (4 points)
 
-9
-24
0
24

 

5.  Find the coefficient of the squared term in the simplified form for the second derivative, f “(x) for f(x) = (x3 + 2x + 3)(3x3 – 6x2 – 8x + 1). Use the hyphen symbol, -, for negative values. (4 points)

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1.  If f(x) = (5x3 – 4)4, then what is f ‘(x)? (4 points)
 
20x2(x3 – 4)3
20x8
4(5x3 – 4)3(15x2)
4(2x3 – 4)4

 

2.  Find f ‘(x) for  . (4 points)
 
f'(x) = sin(8x)

 

3.  Is the following true or false?

(4 points)

 
True
False

 

4.  Find  of  . (4 points)
 

 

5.  Differentiate y = sin2x – cos2x. (4 points)
 
2sin(x) – 2cos(x)
2sin(x) + 2cos(x)
4sin(x)cos(x)
0
1.  If f(x) = 5x4 tan-1x, find f ‘(x). (4 points)
 
20x3tan-1x – 5x4tan-2x
20x3tan-1x + 5x4
20x3tan-1x – 5x4
20x3tan-1x + 5x4

 

2.  Find the derivative of e6x. (4 points)
 
e6x
6xe6x
6e6x
6ex

 

3.  If f(x) = ln(1 – x), then find f ‘(x). (4 points)
 
(1 – x)2

 

4.  Find  . (4 points)
 
7e7lnx
7x6
x7

 

5.  For f(x) = ecos(x) use your graphing calculator to find the number of zeros for f ‘(x) on the closed interval [0, 2π]. (4 points)
 
1
2
3
4
1.  Find y’ if x = cos(y). (4 points)
 
-sin2(y)
sec2(y)
-tan2(y)
-csc(y)

 

2.  Find  for x2 – y2 = xy. (4 points)
 
2x – 2y
0

 

3.  If 3x2 + y2 = 7 then evaluate  when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -, for negative values. (4 points)
 

 

4.  Find  if f(x) = (x + 8)3x. (4 points)
 
3xln(x + 8)
3x(x + 8)(3x – 1)

 

5.  Find the slope of the graph of the relation y3 – xy = -6 at the point (7, 2). (4 points)
 

 

 

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