ADU Depano Math Iecep

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace Transform of a unit step function?

Choices: a. 1b. sc. 1 / sd. u(t)ANSWER:c. 1/sSOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 254

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace transform of t?

Choices: a. 1 / sb.1 / s2

c 1.d. sANSWER:b.1 / s2

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 254

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace transform of eat?

Choices: a. 1 / (s – a)b. 1 / (s + a)c. s + ad. s – aANSWER:a. 1 / (s – a)

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 297

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace transform of teat?

Choices: a. 1 / (s – a)2

b. 1 / (s – a )c. (s + a)2

d. s – aANSWER:a. 1 / (s – a)2

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 15

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace transform of sin (wt)?

Choices: a. 1 / (s2 + w2)b. 1 / (s2 - w2)c. s / (s2 + w2)d. s / (s2 - w2)ANSWER:a. 1 / (s2 + w2)

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 297

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace transform of cos (wt)?

Choices: a. 1 / (s2 + w2)b. 1 / (s2 - w2)c. s / (s2 + w2)d. s / (s2 - w2)ANSWER:c. s / (s2 + w2)

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 297

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace transform of cosh (wt)?

Choices: a. 1 / (s2 + w2)b. 1 / (s2 - w2)c. s / (s2 + w2)d. s / (s2 - w2)ANSWER:d. s / (s2 - w2)SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 297

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:What is the Laplace transform of sinh (wt)?

Choices: a. 1 / (s2 + w2)b. 1 / (s2 - w2)c. s / (s2 + w2)d. s / (s2 - w2)ANSWER:b. 1 / (s2 - w2)

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 297

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given vectors A = i + j + k and B = 2i – 3j + 5k, find A∙B.

Choices: a. 2i -3j + 5kb. 2i + 3j + 5kc. 0d. 4ANSWER:d. 4SOLUTION ( IF PROBLEM -SOLVING)

A∙B = (1)(2) + (1)(-3) + (1) (5)A∙B = 2 – 3 + 5A∙B = 4

Reference: Advanced Engineering MathematicsErwin KreyszigPage 407

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given vectors A = i + 2j and B = 3i – 2j + k, find the angle between them.

Choices: a. 0°b. 36.575°c. 96,865°d. 127.352°ANSWER:c. 96,865°

SOLUTION ( IF PROBLEM -SOLVING)

Φ = cos -1 ( A∙B) / (|A| |B|)A∙ B = (1)(3) + (2)(-2) + (0)(1) = -1|A| = sqrt (12+22) = sqrt(5)|B| = sqrt (32 + (-2)2 + 12) = sqrt (14)Φ = cos -1 ( -1) / (sqrt (5) x sqrt (14) )Φ = 98.865°

Reference: Advanced Engineering MathematicsErwin KreyszigPage 409

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given vectors A = 4i + k and B = -2i + j + 3k, find AxBChoices: a. 0b. -8i + 3kc. -12d. i – 10j + 4kANSWER:d. i – 10j + 4kSOLUTION ( IF PROBLEM -SOLVING)AxB =

AxB = i – 10j + 4k

Reference: Advanced Engineering MathematicsErwin KreyszigPage 416

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given a scalar function f (x, y , z), find the gradient of f.Choices:

a.

b.

c.

d.

ANSWER:

a.

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 446

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given a vector A = axi + ayj + azk, find the divergence of A.Choices:

ANSWER:

a.

b.

c.

d.

SOLUTION ( IF PROBLEM -SOLVING)

b.

Reference: Advanced Engineering MathematicsErwin KreyszigPage 453

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given a scalar function f (x, y , z), find the Laplacian of f.Choices:

a.

b.

c.

d.

ANSWER:

c.

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 454

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department Faculty

Area of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given a scalar function f (x, y , z), find the curl of the gradient of fChoices: a. 1

b. c. inf d. 0 ANSWER:d. 0

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 458

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:It is an equation that contains one or several derivatives of an unknown function called y(x) and which we want to determine from the equation.

Choices: a. homogeneous differential equation b. ordinary differential equationc. partial differential equationd. linear constant coefficient differential equation

ANSWER:b. ordinary differential equation

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 2

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Solve the differential equation y’ = 1 + y2

Choices: a. y = tan -1 (x) + cb. y = tan (x) + cc. y = tan (x + c)d. y = tan (x)ANSWER:c. y = tan (x + c)

SOLUTION ( IF PROBLEM -SOLVING)dy / (1 + y2) = dx

tan -1 (y) = x + c

y = tan (x + c)

Reference: Advanced Engineering MathematicsErwin KreyszigPage 15

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Solve the initial value problem y ‘ = -y / x, where y(1) = 1

Choices: a. y = c / xb. y = x / cc. y = xd. y = 1 / xANSWER:d. y = 1 / x

SOLUTION ( IF PROBLEM -SOLVING)

(dy / y) = - (dx / x)

ln |y| = - ln |x| + c = ln (1 / |x| ) + c

taking the exponentials,

y = c / x

since 1 = c / 1then c = 1

So, y = 1 / x

Reference: Advanced Engineering MathematicsErwin KreyszigPage 15

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:A ______ is a collection of objects, and these objects are called the elements.

Choices: a. setb.subsetc.venn diagramd.unionANSWER:a. set

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Algebra and TrigonometryStewart / Redlin / WatsonPage 15

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:

Solve the equation

Choices: a.1b.-1c.1 / 4d. – 1 / 4ANSWER:d. – 1 / 4

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Algebra and TrigonometryStewart / Redlin / WatsonPage 113

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Find the y-intercept of the graph

Choices: a. 0b. 1.7c.-2d. No answer because only lineaf function have y-interceptANSWER:c.-2

SOLUTION ( IF PROBLEM -SOLVING)

Reference: Algebra and TrigonometryStewart / Redlin / WatsonPage 157

IECEP-Manila Form 1 S.2011 TEST QUESTIONS

PROFILE OF CONTRIBUTORName of School Adamson University

Address 900 San Marcelino Street, Ermita, Manila

Signature over Printed Name , Position Engr. Ernesto Depano Jr.

EcE Department FacultyArea of Specialization Microelectronics, Control Systems, Mathematics

Please indicate the subject:( X) Mathematics( ) General Engineering and Applied Science ( ) Electronics System & TechnologiesQUESTION:Given the equation , find its symmetry.

Choices: a. symmetric with respect to x-axisb. symmetric with respect to y-axisc. symmetric with respect to the origind.all of the aboveANSWER:d. all of the above

SOLUTION ( IF PROBLEM -SOLVING)The equation remains unchanged when x is replaced by –x and y is replaced by –y.

Reference: Algebra and TrigonometryStewart / Redlin / WatsonPage 161