Honors AP Calculus / Mr. Hansen

Name: _______________________________________

9/15/2006

 

 

Warm-Up (not graded) for Monday’s Test

 

 

The test Monday will be mainly multiple-choice, with at least one essay question requiring careful thought and/or explanation.

 

 

1.

Let J(t) be a continuous jerk function. If a(3) is given to have a value of 2.6 m/sec2, find a(4). Hint: Use FTC1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.

State FTC1 and FTC2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.

Why is Boolean algebra considered to be a calculus?

 

(A) It uses derivatives.
(B) It uses integrals.
(C) It uses both derivatives and integrals.
(D) It is a formal (i.e., rule-based) system.
(E) It is geometrical.

 

 

4.

Categorize the following:

 

(A) first-order ODE
(B) second-order ODE
(C) first-order PDE
(D) second-order PDE
(E) linear equation in 3 unknowns

 

 

5.

The easiest types of diffeqs., and in fact the only type that we will learn how to solve exactly, are . . .

 

(A) first- or second-order separable ODEs
(B) first-order ODEs, but not necessarily separable
(C) first-order ODEs and PDEs, but only the separable ones
(D) first-order ODEs and PDEs, both separable and non-separable
(E) separable ODEs and PDEs of all orders

 

 

6.

The inverse operation for indefinite integration (i.e., finding an antiderivative) is . . .

 

(A) derivation
(B) differentiation
(C) diffeq.
(D) dilation
(E) dissipation

 

 

7.

The trapezoid rule approximation for , using 4 subintervals (i.e., 5 mesh points), is . . .

 

(A) 6.000
(B) 6.283
(C) 6.284
(D) 6.285
(E) 6.286

 

 

8.

The correct answer to #7 is
(A) significantly lower than the true integral, since the integrand is an upward-concave function
(B) significantly higher than the true integral, since the integrand is an upward-concave function
(C) significantly lower than the true integral, since the integrand is a downward-concave function
(D) significantly higher than the true integral, since the integrand is a downward-concave function
(E) a correct approximation of the true integral, since the integrand is linear

 

 

9.

Explain what is meant by an initial condition for a diffeq.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10.

A general solution to a diffeq. is a family of relations that satisfy the diffeq. (i.e., a family for which the derivative(s) in the equation can be seen to work correctly as claimed by the equation). We call this “satisfying the equation.” A particular solution, by contrast, is a _________________________ that satisfies not only the _______________ but also one or more _________________________s.