Multiple Choice Practice and Examination Practice – for TEST 1
Section A - Don’t use a calculator.
1.
Find the slope of the tangent line to the graph of f at x = 4, given that 4√
a) -8
2.
Determine: lim
a) ∞
3.
4.
b) -10
c) -9
e) -7
d) 3/10
e) 1
b) 0
c) ½
Given that: 5x3 – 4 xy – 2y2 = 1 determine the change in y with respect to x.
a)
b)
d)
e)
c)
Compute the derivative of: - 4 sec(x) + 2csc(x)
a) - 4sec(x) tan(x) – 2csc(x) cot(x)
c) – 4(sec(x))2 – 2(csc(x))2
e) – 4(tan(x))2 – 2(cot(x))2
5.
d) -5
b) - 4csc(x) – 2sec(x)
d) – 4 sec(x)tan(x) + 2csc(x) cot(x)
Determine
a)
b)
d)
e)
AP Calculus – Horton High School
c)
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Multiple Choice Practice and Examination Practice – for TEST 1
6.
Give the equation of the normal line to the graph of
at the point ( 0 , 2 ).
a)
b)
d)
e)
7.
Determine the concavity of the graph of
a) 8
8.
b) -10
at x =
c) 4
d) - 8
.
e) - 6
Give the value of x where the function f(x) = x3 – 9 x2 + 24x + 4 has a local maximum.
a) 4
9.
c)
b) - 2
c) 2
d) - 4
e) 3
The slope of the tangent line to the graph of 4x2 + cx – 2ey = - 2 at x = 0 is 4.
Give the value of c. [Note the derivative of ex is itself]
a) - 2
b) 4
c) 8
d) - 4
e) – 8
10. What is the average value of the function g(x) = (2x + 3)2 on the interval from x = -3
to x = -1?
a) 7/3
b) - 4
c) 5
d) 14/3
e) 3
11. Find the instantaneous rate of change of 2 3 4√ 3 4 at t = 0.
a) - 3
b) – 3/4
c) 0
d) - 4
12. Determine the derivative of f(x) = (cos (2x - 4))3
e) -5/4
at x =
/2.
a) – 6 (cos (π – 4 ))2
b) – 6 cos ( π – 4 )2 sin(π – 4)
c) – 6 (cos (π – 4))2 sin(π – 4)
d) 18 ( cos (π – 4))2 sin ( π – 4)
e) 18 (cos (π – 4))2
AP Calculus – Horton High School
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Multiple Choice Practice and Examination Practice – for TEST 1
Section B – You may use a calculator
1.
The derivative of f is graphed to the right.
Give a value of x where f has a local maximum.
a) - 4
c) - 5/2
e) 1
b) - 1
d) There is no such value of x.
2. Let
Which of the following is (are) true?
1) f is continuous at x = -2.
2) f is differentiable at x = 1.
3) f has a local minimum at x = 0.
4) f has an absolute maximum at x = -2.
a) 2 and 4
b) 3 only
c) 2 only
d) 1 and 3
e) 1 and 4
3. At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the
instant when the surface area is 5 square meters and the radius is increasing at the rate of 1/3
meters per minute?
a) 5.271
4.
b) 1.700
The function
a) - 9
5.
c) 1.667
d) 1.080
e) 2.714
is differentiable everywhere. What is n?
b) 13
c) - 17
d) - 11
e) - 14
d) - 2
e) undefined
Compute
a) ∞
b) 0
c) – 5/2
AP Calculus – Horton High School
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Multiple Choice Practice and Examination Practice – for TEST 1
Some partial questions from 2010 and 2011 College Board Examinations:
these questions should be done without a calculator.
1.
Consider a differentiable function f having domain all positive real numbers, and for which
it is known that ′ 4 for x > 0.
(a) Find the x-coordinate of the critical point of f. Determine whether the point is a relative
maximum, a relative minimum, or neither for the function f. Justify your answer.
(b) Find all intervals on which the graph of f is concave down. Justify your answer.
2.
Two particles move along the x-axis. For 0 ≤ t ≤ 6,
the position of particle P at time t is given by: 2cos .
while the position of particle R at time t is given by: ! 6 9 3
(a) For 0 ≤ t ≤ 6, find all times t during which particle R is moving to the right.
(b) For 0 ≤ t ≤ 6, find all times t during which the two particles travel in opposite directions
(c) Find the acceleration of particle P at time t = 3. Is particle P speeding up, slowing down,
or doing neither at time t = 3 ? Explain your reasoning.
AP Calculus – Horton High School
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