CALCULUS BC EXAM QUESTIONS WITH
CORRECT ANSWERS
Which of the following is the interval of convergence for the series
E (x+2)^n/2^n - ANSWER--4<x<0
∫0 5 √((5-x)/5) - ANSWER-10/3
Which of the following are equal to -1?
I. lim x->0- [x]/x
II. lim x->3 (x^2-7x+12)/(3-x)
III. lim x->infinite (1-x)/(1+x) - ANSWER-I and III only
Let f be the function given by f(x)=2cosx+1.
What is the approximation for f(1.5) found by using the
line tangent to the graph of f at x=π/2? - ANSWER-π-2
A particle moves in the xy-plane so that its position for t>= is given by the parametric
equations x=ln(t+1) and y=kt^2, where k is a positive constant. The line tangent to the
particle's path at the point where t=3 has slope 8.
What is the value of k? - ANSWER-1/3
The table above(#21) gives the level of a person's cholesterol at different times during a
10-week treatment period.
What is the average level over this 10-week period obtained by using a trapezoidal
approximation with the subintervals [0,2] [2,6] [6,10]? - ANSWER-193
∫(x/2)(e^-3x/4) - ANSWER-((-2x/3)e^-3x/4) + ((3/8)e^-3x/4) + c
If f(x)= E x^2n/n!
f'(x)= - ANSWER-2x + 2x^3 + x^5 + x^7/3 + ... + 2nx^2n-1/n!
If the average value of a continuous function f on the interval [-2,4] is 12
, what is ∫-2 4 f(x)/8 - ANSWER-9
What is the radius of convergence of the Maclaurin series for 2x/1+x^2? - ANSWER-
infinite
Let f be the function with f(0)=1/pi^2, f(2)=1/pi^2, and derivative given by
f'(x)=(x+1)cos(pix).
How many values of x in the open interval (0,2) satisfy the condition of the MVT for the
function f on the closed interval [0,2]? - ANSWER-two
The number of students in a cafeteria is modeled by the function P that satisfies the
logistic differential equation dP/dt= 1/2000P(200-P), where t is the time in seconds and
P(0)=25.
What is the greatest rate of change, in students per second, of the number of students
in the cafeteria? - ANSWER-5
A cube with edges of length x centimeters has volume V(x)=x^3 cubic centimeters. The
volume is increasing at a constant rate of 40 cubic centimeters per minute.
At the instant when x=2, what is the rate of change of x, in centimeters per minute, with
respect to time? - ANSWER-10/3
Which of the following is a power series expansion of
e^x+e^-x/2? - ANSWER-1 - x^2/2! + x^4/4! - x^6/6! + ... + ((-1)^n x^2n)/(2n!)
Which of the following statement about the series
E 1/2^n-n is true? - ANSWER-The series converges by the limit comparison to the
geometric series
E 1/2^n
Let f be a twice-differentiable function for all real numbers x.
Which of the following additional properties guarantees that f has a relative minimum at
x=c? - ANSWER-f'(c)=0 and f"(c)>0
Let H(x) be an antiderivative of
x^3+sinx / x^2+2
If H(5)=π
CORRECT ANSWERS
Which of the following is the interval of convergence for the series
E (x+2)^n/2^n - ANSWER--4<x<0
∫0 5 √((5-x)/5) - ANSWER-10/3
Which of the following are equal to -1?
I. lim x->0- [x]/x
II. lim x->3 (x^2-7x+12)/(3-x)
III. lim x->infinite (1-x)/(1+x) - ANSWER-I and III only
Let f be the function given by f(x)=2cosx+1.
What is the approximation for f(1.5) found by using the
line tangent to the graph of f at x=π/2? - ANSWER-π-2
A particle moves in the xy-plane so that its position for t>= is given by the parametric
equations x=ln(t+1) and y=kt^2, where k is a positive constant. The line tangent to the
particle's path at the point where t=3 has slope 8.
What is the value of k? - ANSWER-1/3
The table above(#21) gives the level of a person's cholesterol at different times during a
10-week treatment period.
What is the average level over this 10-week period obtained by using a trapezoidal
approximation with the subintervals [0,2] [2,6] [6,10]? - ANSWER-193
∫(x/2)(e^-3x/4) - ANSWER-((-2x/3)e^-3x/4) + ((3/8)e^-3x/4) + c
If f(x)= E x^2n/n!
f'(x)= - ANSWER-2x + 2x^3 + x^5 + x^7/3 + ... + 2nx^2n-1/n!
If the average value of a continuous function f on the interval [-2,4] is 12
, what is ∫-2 4 f(x)/8 - ANSWER-9
What is the radius of convergence of the Maclaurin series for 2x/1+x^2? - ANSWER-
infinite
Let f be the function with f(0)=1/pi^2, f(2)=1/pi^2, and derivative given by
f'(x)=(x+1)cos(pix).
How many values of x in the open interval (0,2) satisfy the condition of the MVT for the
function f on the closed interval [0,2]? - ANSWER-two
The number of students in a cafeteria is modeled by the function P that satisfies the
logistic differential equation dP/dt= 1/2000P(200-P), where t is the time in seconds and
P(0)=25.
What is the greatest rate of change, in students per second, of the number of students
in the cafeteria? - ANSWER-5
A cube with edges of length x centimeters has volume V(x)=x^3 cubic centimeters. The
volume is increasing at a constant rate of 40 cubic centimeters per minute.
At the instant when x=2, what is the rate of change of x, in centimeters per minute, with
respect to time? - ANSWER-10/3
Which of the following is a power series expansion of
e^x+e^-x/2? - ANSWER-1 - x^2/2! + x^4/4! - x^6/6! + ... + ((-1)^n x^2n)/(2n!)
Which of the following statement about the series
E 1/2^n-n is true? - ANSWER-The series converges by the limit comparison to the
geometric series
E 1/2^n
Let f be a twice-differentiable function for all real numbers x.
Which of the following additional properties guarantees that f has a relative minimum at
x=c? - ANSWER-f'(c)=0 and f"(c)>0
Let H(x) be an antiderivative of
x^3+sinx / x^2+2
If H(5)=π
