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2020 AP Calculus AB Practice Exam, Exams of Calculus

Stanford UniversityCalculus

2020 AP Calculus AB Practice Exam. By: Patrick Cox. Original non-secure materials written based on previous secure multiple choice and FRQ.

Typology: Exams

2022/2023

Uploaded on 03/01/2023

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2020 AP Calculus AB Practice Exam
By: Patrick Cox
Original non-secure materials written based on previous secure multiple choice and FRQ
questions from the past three years. I wrote this as a way for my students to have access to
multiple choice and FRQ since secure materials can’t be used outside of class.
Feel free to use in your class, post to the internet/classroom, you will find the answer key
to the multiple choice and FRQ at the end. Below, you can find which problems can be
answered after each unit in the CED (although questions definitely can span across
multiple units in the CED). I do not work for Collegeboard so these categorizations are to
the best of my knowledge using the public CED.
Pages 2-15 Non-Calculator MC
Pages 16-23 Calculator MC
Pages 24-27 Calculator FRQ
Pages 28-34 Non-Calculator FRQ
Pages 36-42 Solutions
Questions By Unit in CED:
Unit 1: 21, 24, 76, 90, FRQ 1(a), FRQ 5 (d)
Unit 2: 6, 8, 25, 28, 80, FRQ 5 (c), FRQ 6 (a)
Unit 3: 14, 16, 81, FRQ 4 (c), FRQ 6 (b)
Unit 4: 5, 10, 12, 18, 23, 87, 88, FRQ 1(d), FRQ 2 (b) (c), FRQ 5 (b) (c), FRQ 6 (d)
Unit 5: 9, 13, 15, 82, 83, 84, 85, FRQ 3 (b) (c)
Unit 6: 3, 4, 11, 19, 20, 22, 29, 78, 79, 86, FRQ 3 (a) (d), FRQ 5 (a) (b), FRQ 6 (c)
Unit 7: 2, 7, 27, FRQ 4 (a) (b)
Unit: 8: 1, 17, 26, 30, 77, 89, FRQ 1 (b) (c), FRQ 2 (a) (d)
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2020 AP Calculus AB Practice Exam

By: Patrick Cox Original non-secure materials written based on previous secure multiple choice and FRQ questions from the past three years. I wrote this as a way for my students to have access to multiple choice and FRQ since secure materials can’t be used outside of class. Feel free to use in your class, post to the internet/classroom, you will find the answer key to the multiple choice and FRQ at the end. Below, you can find which problems can be answered after each unit in the CED (although questions definitely can span across multiple units in the CED). I do not work for Collegeboard so these categorizations are to the best of my knowledge using the public CED. Pages 2-15 Non-Calculator MC Pages 16-23 Calculator MC Pages 24-27 Calculator FRQ Pages 28-34 Non-Calculator FRQ Pages 36-42 Solutions Questions By Unit in CED: Unit 1: 21, 24, 76, 90, FRQ 1(a), FRQ 5 (d) Unit 2: 6, 8, 25, 28, 80, FRQ 5 (c), FRQ 6 (a) Unit 3: 14, 16, 81, FRQ 4 (c), FRQ 6 (b) Unit 4: 5, 10, 12, 18, 23, 87, 88, FRQ 1(d), FRQ 2 (b) (c), FRQ 5 (b) (c), FRQ 6 (d) Unit 5: 9, 13, 15, 82, 83, 84, 85, FRQ 3 (b) (c) Unit 6: 3, 4, 11, 19, 20, 22, 29, 78, 79, 86, FRQ 3 (a) (d), FRQ 5 (a) (b), FRQ 6 (c) Unit 7: 2, 7, 27, FRQ 4 (a) (b) Unit: 8: 1, 17, 26, 30, 77, 89, FRQ 1 (b) (c), FRQ 2 (a) (d)

Non-Calculator Multiple Choice

  1. A particle moves along a straight line so that at time t ≥ 0 its acceleration is given by the function a ( t ) = 4 t. At time t = 0, the velocity of the particle is 4 and the position of the particle is 1. Which of the following is an expression for the position of the particle at time t ≥ 0? (a) 23 t t 3
  • 4 + 1 (b) 2 t t 3
  • 4 + 1 (c) 13 t t 3
  • 4 + 1 (d) 32 t 3
  • 4

Shown above is a slope field for which of the following differential equations?

(a) dx

dy

x

y (b)^ dx y

dy

= x (c) dx

dy

= x + y (d) dx

dy

= x − y

is (a) (^2) e^ (b) 1 (c) 0 (d) nonexistent

  1. Let f be the function defined above. Which of the following statements about f is true? (a) f is continuous and differentiable at x = -2. (b) f is continuous but not differentiable at x = -2. (c) f is differentiable but not continuous at x = -2. (d) f is defined but is neither continuous nor differentiable at x = -2.
  2. The equation y = e^2 x is a particular solution to which of the following differential equations? (a) dx dy = 1 (b) dx dy = y (c) dx dy = y + 1 (d) dx dy = y − 1
  1. For any real number x, lim h → h cos (( x + h ) )− cos ( x ) (^2 ) = (a) cos ( x^2 ) (b) 2 xcos ( x^2 ) (c) − sin ( x^2 )^ (d) − 2 xsin ( x^2 )
  2. What is the value of x at which the maximum value of occurs on the closed interval [0, 4]? (a) 0 (b) 23 (c) 25 (d) 4
  1. A particle moves along the x-axis so that at time t ≥ 0 its velocity is given by v ( t ) = et −1^ − 3 sin ( t − 1 ). Which of the following statements describes the motion of the particle at time t = 1? (a) The particle is speeding up at t = 1. (b) The particle is slowing down at t = 1. (c) The particle is neither speeding up nor slowing down at t = 1. (d) The particle is at rest at t = 1.

x 0 2 4 6 8 f ( x ) 1 -1 -5 7 5 The table above gives selected values for the twice-differentiable function f. In which of the following intervals must there be a number c such that (a) (0, 2 ) (b) (2, 4 ) (c) (4, 6 ) (d) (6, 8 )

  1. (^) dxd ( tan ( ln ( x ))) = (a) x tan ( ln ( x )) (b) sec^2 ( ln ( x )) (c) x sec^2 ( ln ( x )) (d) tan ( ) x^1
  2. The function f is given by f ( x ) = x x. On what interval(s) is f(x) 3 − 2 2 concave down? (a) (0, 3 ) 4 (b) (− ∞, 0) and ( 3 , ) (c) ) (d) 4 ∞ (− ∞, (^3) 2 ( 3 , ) 2 ∞
  3. If what is (^) dx at the point (4,0)? dy (a) − 161 (b) 161 (c) − 41 (d) 41
  1. Let g be the function given by f ( x ) = (^) ∫(3 t t ) dt .What is the x-coordinate x 1

2 of the point of inflection of the graph of f? (a) − (^4) 1 (b) (^4) 1 (c) 0 (d) (^2) 1

  1. (^) ∫ sin (3 x ) dx = (a) 3 cos (3 x )+ C (b) 31 cos (3 x )+ C (c) − 3 cos (3 x )+ C (d) − 31 cos (3 x )+ C
  2. How many removable discontinuities does the graph of have? (a) one (b) two (c) three (d) four
  1. If (^) ∫ ( x ) dx and then what is the value of 6 4 f = (^5) ∫ ( x ) dx 4 10 f = (^8) ∫(4 f ( x ) 0) dx 10 6

(a) − 12 (b) 12 (c) 52 (d) 62

  1. What is the equation of the line tangent to the graph y = e^2 x^ at x = 1? (a) y + 2 e ( x ) 2 = e^2 − 1 (b) y + e^2 = 2 e^2 ( x − 1 ) (c) y − 2 e ( x ) 2 = e 2 − 1 (d) y − e^2 = 2 e^2 ( x − 1 )
  1. A region R is the base of a solid where f ( x ) ≥ g ( x )for all x a ≤ x ≤ b. For this solid, each cross section perpendicular to the x-axis are rectangles with height 5 times the base. Which of the following integrals gives the volume of this solid? (a) 2 5 ( (^) ∫ g ( x ) ( x )) dx b a − f 2 (b) (^5) ∫( g ( x ) ( x )) dx b a − f (c) (^5) ∫( f ( x ) ( x )) dx b a − g (d) (^5) ∫( f ( x ) ( x )) dx b a − g 2
  2. If and if y = 4 when x = 2, then y = (a)

21 x^^4 2

  • 1 (b) (^) √ 2 x 2
  • 8 (c) (^) √ x^2 + 6 (d) (^) √ x^2 + 12
  1. If then f ′( x )= (a) (b) (c) (d)
  2. (^) ∫(2 x + 3 )( x^2 + 3 x ) dx 4 = (a) 5 ( x x ) 1 2
  • 3 5
  • C (b) 101 ( x^2 + 3 x ) 5
  • C (c) ( x^2 + 3 x ) 5
  • C (d) 5 ( x x ) 2
  • 3 5
  • C

Calculator Active Multiple Choice

  1. Let f be the function defined above, where k is a constant. For what value of k, is f(x) continuous at x = 1? (a) − 92 (b) -4 (c) 4 (d) 29
  2. At time t, 0 < t < 2, the velocity of a particle moving along the x-axis is given by v ( t ) = et. What is the total distance traveled by the particle 2 − 2 during the time interval 0 < t < 2? a) 1 2.453 (b) 1 3.368 (c) 5 1.598 (d) 5 3.
  1. Let f be a continuous function such that (^) ∫ ( x ) dx and 5 2 f = − (^4) ∫ ( x ) dx 3 5 8 f = then (^) ∫ ( x ) dx 2 8 f = (a) − 7 (b) -1 (c) 1 (d) 7
  2. Let f be a twice-differentiable function defined by the differentiable function g such that f ( x ) = (^) ∫ ( x ) dx. It is also known that g(x) is always x − g concave up, decreasing, and positive for all real numbers. Which of the following could be false about f(x)? (a) f(x) is concave down for all x (b) f(x) is increasing for all x (c) f(x) is negative for all x (d) f(x) = 0 for some x in the real numbers
  1. The graph of y = f ( x )is shown above. Which of the following could be the graph of y = f ′( x )? (a) (b) (c) (d)

x -5 0 3 f(x) 6 4 -

  1. The table above gives values of a differentiable function f(x) at selected x values. Based on the table, which of the following statements about f(x) could be false? (A) There exists a value c, where -5 < c < 3 such that f(c) = 1 (B) There exists a value c, where -5 < c < 3 such that f’(c) = 1 (C) There exists a value c, where -5 < c < 3 such that f(c) = - (D) There exists a value c, where -5 < c < 3 such that f’(c) = -
  2. The function f is the antiderivative of the function g defined by g ( x ) = e n ( x ) x. Which of the following is the x-coordinate of location x − l − 2 2 of a relative maximum for the graph of y = f(x). (a) 1 .312 (b) 2 .242 (c) 2 .851 (d) 2.