Free Free AB Calculus Test Practice Questions with Answers - Sample 1



A set of AB calculus questions, with answers, similar to the questions in the AP calculus test are presented. The answers to the suggested questions are at the bottom of the page. Detailed solutions and explanations are also included.

  1. AB test sample 1, problem 1 =

    A) e

    B) 1

    C) eh

    D) e4

    E) 4e

  2. The graph of function g defined by

    AB test sample 1, problem 2

    will have vertical asymptotes at

    A)x = 1 , -3

    B) x = 0

    C) x = 1

    D) x = -3

    E) Fundtion g has no vertical asymptotes


  3. Given that

    AB test sample 1, problem 3-1

    find

    AB test sample 1, problem 3-2

    A) 2/3

    B) 4/3

    C) 1/3

    D) 2

    E) Does not exist

  4. Function f is defined by

    AB test sample 1, problem 4.

    Find df(x) / dx.

    A) 6x2 sin(x) - (1/x2)tan(x) + sec(x)

    B) 6x2 sin(x) + 2x3 cos(x) - (1/x2)tan(x) + (1/x) sec2(x)) + sec(x) + x sin(x) sec2(x)

    C) 2x3 cos(x) + 1/x sec2(x)) + x sin(x) sec2(x)

    D) 6x2 cos(x) - (1/x2 sec2(x)) + sec2(x)

    E) 6x2 sin(x) + 2x3 cos(x) - (1/x2)tan(x) + (1/x sec2(x)) + sec(x) + x sin(x) sec2(x) + 2

  5. Curve C is described by the equation 0.25x2 + y2 = 9. Determine the y coordinates of the points on curve C whose tangent lines have slope equal to 1.

    A) -3 sqrt(5) / 5 , 3 sqrt(5) / 5

    B) - sqrt(35) / 2 , sqrt(35) / 2

    C) -3 , 3

    D) - sqrt(2) / 2 , sqrt(2) / 2

    E) -3 sqrt(2) , 3 sqrt(2)

  6. Find the solution to the differential equation dy/dx = cos(x) / y2 , where y(π/2) = 0.

    A) y = (3 sin(x) - 3)

    B) y = sin(x) - 1

    C) y = (3 sin(x) - 3)1/3

    D) y = (3 sin(x) - 3)3

    E) y = (3 sin(x) - 3)-1/3

  7. AB test sample 1, problem 7

    A) cos5(x) + C

    B) -(1/5)sin5(x) + C

    C) sin5(x) + C

    D) -(1/5)cos5(x) + C

    E) -5cos5(x) + C

  8. AB test sample 1, problem 8

    A) 2sin(4x2 + 1)

    B) 2sin(x2 + 1)

    C) sin(x2 + 1)

    D) 2sin(4x2 + 1) - 2sin(32 + 1)

    E) 2sin(4x2)


  9. AB test sample 1, problem 9

    A) 100

    B) 108

    C) 110

    D) 112

    E) 114

  10. Evaluate the integral

    AB test sample 1, problem 10

    A) (5 + x3/4)10

    B) (x3/4)10

    C) (1/10)(5 + x3/4)10

    D) (1/10)(5 + x3/4)10 / x1/4

    E) (2/15)(5 + x3/4)10

  11. Given that function h is defined by

    AB test sample 1, problem 11

    find h'(x).

    A) (3x2 / (x6 + 2x3 + 2) + 2)

    B) 4 (arctan(x3 + 1) + 2x)3 (3x2 / (x6 + 2x3 + 2) )

    C) 4 (arctan(x3 + 1) + 2x)3

    D) 4 (3x2 / (x6 + 2x3 + 2) + 2)

    E) (1/4)(arctan(x3 + 1) + 2x)3

  12. The graph of function h is shown below. How many zeros does the first derivative h' of h have?

    AB test sample 1, problem 12

    A) 1

    B) 2

    C) 3

    D) 4

    E) 5

  13. The graph of a polynomial f is shown below. If f' is the first derivative of f, then the remainder of the division of f'(x) by x - b is more likely to be equal to

    AB test sample 1, problem 13

    A) f(b)

    B) 1

    C) 0

    D) 2

    E) -1

  14. The set of all points (ln(t - 2) , 3t), where t is a real number greater than 2, is the graph of

    A) y = ln(x/3 - 2)

    B) y = 3x

    C) x = ln(y - 2)

    D) y = 3(ex + 2)

    E) y = ln(x)

  15. Let P(x) = 2 x3 + K x + 1. Find K if the remainder of the division of P(x) by x - 2 is equal to 10.

    A) -7/2

    B) 2/7

    C) 7/2

    D) -2/7

    E) K cannot be determined

  16. Function f is defined by

    AB test sample 1, problem 16
    .

    where C is a constant. What must the value of C be equal to for function f to be continuous at x = 0?

    A) 0

    B) 1/4

    C) 1/8

    D) 1

    E) Any real number

  17. f and g are functions such that f'(x) = g(x) and g'(x) = f(x). The second derivative of (f . g)(x) is equal to

    A) f"(x) g"(x)

    B) g'(x) g(x) + f(x) f'(x)

    C) 4 g(x) f(x)

    D) 2 g(x) f(x)

    E) g(x) f(x)

  18. The average rate of change of the function f defined by f(x) = sin(x) + x on the closed interval [0 , pi] is equal to

    A) 0

    B) 2 pi

    C) pi

    D) 2

    E) 1

  19. The figure shows the graphs of y = sin(x) over half a period and the line y = 1/2. Find area of the shaded region.

    AB test sample 1, problem 19
    .

    A) 1

    B) 0.5

    C) 2 + π/3

    D) 2 + π/3 - √3

    E) 2 + π/3 + √3

  20. Functions f, g and h are defined as follow: g(x) = f(x2), f(x) = h(x3 + 1) and h'(x) = 2x + 1. g'(x) =

    A) 2 x3

    B) 12 x9 + 18 x3

    C) 2 x11 + 3 x5

    D) 2 x9 + 3 x3

    E) 12 x11 + 18 x5

Answers to the Above Questions
  1. D
  2. E
  3. A
  4. B
  5. A

  6. C
  7. D
  8. A
  9. B
  10. E

  11. B
  12. E
  13. C
  14. D
  15. A

  16. B
  17. C
  18. E
  19. D
  20. E



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Updated: 2 April 2013

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