REM A LEVEL 1, 2, & 3

Question 1

What is/are the conditions for a
function to be continuous on (a,b)?
i. The function is continuous at each
point of (a,b)
ii. The function is right continuous
iii. The function is left continuous

A. i only
B. i and ii
C. i and ii
D. i, ii, and ii
E. i and ii

Answer 1

D. i, ii, and ii

Question 2

The function y=(x-4)/(x+2) is
discontinuous at x equals?

A. 12
B. 2
C. 0
D. -2

Answer 2

D. -2

The given function will have a vertical
asymptote at x =-2. Therefore, the
function is discontinuous at x =-2.

Question 3

A function is invertible if it is

A. Injective
B. Surjective
C. Bijective
D. Surjective

Answer 3

C. Bijective

Question 4

At the maximum point, the second
derivative of the curve is

A. 0
B. Negative
C. Positive
D. 1

Answer 4

B. Negative

Question 5

A curve y = f(x) is concave downward if
the value of y” is

A. zero
B. positive
C. negative

Answer 5

C. negative

At the point of inflection, if y=f(x) is
concaving downward, then y” is
negative. If y=f(x) is concaving upward,
then y” is positive.

Question 6

The partial derivative expression f_xx(x,
y) means

A. a^2y/af^2
B. a^2x/af^2
C. a^2f/ax^2
D. a^2y/af^2
E. a^2f/ay^2

Answer 6

C. a^2f/ax^2

Question 7

The partial derivative expression f_x(x,y)
means

A. ay/af
B. af/ax
C. ax/af
D. af/ay

Answer 7

B. af/ax

Question 8

A curve produced by tracing the path of a chosen point on the circumference of a circle which rolls without slipping around a fixed circle.

A. Hypotrochoid
B. Epicycloid
C. Epitrochoid
D. Hypocyloid

Answer 8

B. Epicycloid

Question 9

The theorem that is defined by:

(REM A L1,2,3 FIGURE)

A. The Integral Prime theorem
B. The Difference theorem
C. The Net Change theorem

Answer 9

C. The Net Change theorem

Question 10

It is a differential equation that can be
written as dy/dx=F(x)G(y) in which the
derivative equals a product of a function
just of x and a function just of y.

A. Homogeneous DE
B. Exact DE
C. Variable Separable DE

Answer 10

C. Variable Separable DE

(REM A L1,2,3 FIGURE)

Question 11

Condition for exactness for differential
equation Mdx+Ndy=0 is

A. aM/ay = aN/ax
B. aM/ax = an/ay
C. M = N
D. Mdx = -Ndy

Answer 11

A. aM/ay = aN/ax

Question 12

A solution which can’t be obtained from
a general solution is called _____ solution

A. Singular
B. None of these choices
C. Particular

Answer 12

A. Singular

A solution is called the singular solution of the differential equation F(x, y, y)=0 if it cannot be obtained from the general solution for any choice of arbitrary constant c, including infinity. In other words, if the initial value problem has at least two solutions, then those of which that is not a member of the general solution is called singular.

Question 13

Laplace transform of the output
response of a linear system is the
system transfer function when the input
is

A. Ramp Signal
B. Impulse Signal
C. Step Signal

Answer 13

B. Impulse Signal

If the input is impulse signal, then the
output is 1. Thus, the Laplace transform
of the output response of a linear
system is equal to the transfer function

Question 14

Denote òu be the partial derivative of a
function u. Given the linear second-
order partial differential equation.Where A, B, C, D, E and F are real constants. If B-4AC< 0, the above equation is:

(REM A L1,2,3 FIGURE)

A. Asymptotic
B. Hyperbolic
C. Elliptic
D. Parabolic

Answer 14

C. Elliptic

If B^2 - 4AC = 0, it is parabolic
If B^2 - 4AC< 0, it is elliptic
If B^2 - 4AC > 0, it is hyperbolic

Question 15

A fractional integral of order 1/2.

A. Inverse integral
B. Anti integral
C. Sub integral

Answer 15

B. Anti integral

Question 16

A curve generated by the trace of a fixed point on a small circle that rolls withn a large circle.

A. Epitrochoid
B. Epicycloid
C. Hypocycloid
D. Hypotrochoid

Answer 16

C. Hypocycloid

Question 17

Determine the type of the given
Differential Equation: dy/dx + 3xy = xy^2

A. Bernoulli’s DE
B. Homogeneous DE
C. Linear DE
D. Variable Separable DE

Answer 17

A. Bernoulli’s DE

Question 18

The equation

(REM A L1,2,3 FIGURE)

A. Heat Equation
B. Wave Equation
C. Oscillation Equation
D. Heat Equation

Answer 18

B. Wave Equation

Question 19

Denote òu be the partial derivative of a
function u. Given the linear second-
order partial differential equation

(REM A L1,2,3 GIGURE)

Where A, B, C, D, E and F are real constants.
If B²-4AC> 0, the above equation is

A. Hyperbolic
B. Parabolic
C. Asymptotic
D. Elliptic

Answer 19

A. Hyperbolic

If B-4AC> 0, the PDE is hyperbolic.
If B-4AC< 0, the PDE is elliptic.
If B-4AC= 0, the PDE is parabolic.

Question 20

In Advanced Mathematics, it is an
integral transform that converts a
function of a real variable t to a complex
variable s.

A. Laplace Transform
B. Fourier Transform
C. Borel Transform
D. Fourier Transform

Answer 20

A. Laplace Transform

Question 21

What is the domain of a function?

A. the maximal set of numbers for which a
function is defined
B. the maximal set of numbers which a
function can take values
C. it is a set of natural numbers for which a
function is defined

Answer 21

A. the maximal set of numbers for which a
function is defined

Question 22

If A and B are constants, the secondorder differential equation xy”+ Axy’+By = 0 is called _____

A. Bernoulli’s DE
B. Riccati DE
C. Euler’s DE

Answer 22

C. Euler’s DE

Question 23

Determine the differential equation of the family of lines passing through the origin.

A. xdy - ydx = 0
B. xdx - ydy = 0
C. xdx + ydy = 0
D. xdy + ydx = 0

Answer 23

A. xdy - ydx = 0

Let the equation of lines be y = mx, where m is a slope
Differentiating the equation: dy/dx = m, m = y/x
Thus, dy/dx = y/x - xdy-ydx = 0

Question 24

The kernel of Laplace Transform is:

A. e^(-st)
B. z^(-n)
C. e^(-jw)
D. e^(-n)

Answer 24

A. e^(-st)