FE Exam Tutorial http fe eng usf edu

FE Exam Tutorial http: //fe. eng. usf. edu

Math syllabus Chem ical Civil Analytic Geometry x x Roots of Equations x Calculus x Differential Equations x x Roots of Equations x Vector Analysis x Elect rical & Com puter Mech anical Environ mental Indus trial x x x Complex Numbers x Discrete Math x Linear Algebra x Matrix Operations x x x Algebra and Trigonometry Numerical Methods General x x x x x

1. Vectors

What can you say about two vectors whose dot product is negative? 1. 2. 3. The vectors are orthogonal Angle between vectors is <90 o Angle between vectors is >90 o

If two vectors u and v are orthogonal to each other, then u. v= 1. 2. 3. -1 0 1

END

2. Analytic Geometry

Two straight lines are perpendicular to each other. The product of the slope of the two lines is 1. 2. 3. 4. -1 0 1 Cannot be determined

END

3. Roots of Equations

The value of x that satisfies f (x)=0 is called the 1. 2. 3. 4. root of equation f (x)=0 root of function f (x) zero of equation f (x)=0 none of the above

A quadratic equation has ______ root(s) 1. 2. 3. 4. one two three cannot be determined

For a certain cubic equation, at least one of the roots is known to be a complex root. The total number of complex roots the cubic equation has is 1. 2. 3. 4. one two three cannot be determined

Equation such as tan (x)=x has __ root(s) 1. 2. 3. 4. zero one two infinite

A polynomial of order n has zeros 1. 2. 3. 4. n -1 n n +1 n +2

The velocity of a body is given by v (t)=5 e-t+4, where t is in seconds and v is in m/s. The velocity of the body is 6 m/s at t = 1. 2. 3. 4. 0. 1823 s 0. 3979 s 0. 9162 s 1. 609 s

END

4. Numerical Methods

The number of significant digits in 2. 30500 is A. B. C. D. 3 4 5 6

END

5. Ordinary Differential Equations

In the differential equation the variable x is the A. Independent B. Dependent variable

In the differential equation the variable y is the A. Independent B. Dependent variable

Ordinary differential equations can have these many dependent variables. A. one B. two C. any positive integer

Ordinary differential equations can have these many independent variables. A. one B. two C. any positive integer

A differential equation is considered to be ordinary if it has A. B. C. D. one dependent variable more than one dependent variable one independent variable more than one independent variable

Classify the differential equation A. B. C. linear nonlinear undeterminable to be linear or nonlinear

Classify the differential equation A. B. C. D. linear nonlinear with fixed constants undeterminable to be linear or nonlinear

Classify the differential equation A. B. C. D. linear nonlinear with fixed constants undeterminable to be linear or nonlinear

The velocity of a body is given by Then the distance covered by the body from t=0 to t=10 can be calculated by solving the differential equation for x(10) for A. B. C. D.

The form of the exact solution to A. B. C. D. is

END

6. Matrices

The size of matrix A. B. C. is

The c 32 entity of the matrix 1. 2. 3. 4. 2 3 6. 3 does not exist

Given then if [C]=[A]+[B], c 12= 1. 0 2. 6 3. 12

Given then if [C]=[A]-[B], c 23= 1. 2. 3. -3 3 9

A square matrix [A] is lower triangular if 1. 2. 3. 4.

A square matrix [A] is upper triangular if 1. 2. 3. 4.

An identity matrix [I] needs to satisfy the following 1. 2. matrix is square all of the above 3.

Given then if [C]=[A][B], then c 31= 1. 2. 3. 4. -57 -45 57 Does not exist .

The following system of equations x + y=2 6 x + 6 y=12 has solution(s). 1. 2. 3. 4. no one more than one but finite number of infinite

END

7. Differential Calculus

To find velocity from the location vs time data of the body, the mathematical procedure used is A. Differentiation B. Integration

The definition of the derivative of a function f (x) is 1. 2. 3. 4.

The exact derivative of f (x)=x at x=5 is most nearly 1. 2. 3. 4. 25. 00 75. 00 106. 25 125. 00 3

Given y=sin (2 x), dy/dx at x=3 1. 2. 3. 4. 0. 9600 0. 9945 1. 920 1. 989

END

8. Integral Calculus

To find the velocity from acceleration vs time data, the mathematical procedure used is A. Differentiation B. Integration

Physically, integrating A. B. C. D. Area means finding the under the curve from a to b to the left of point a to the right of point b above the curve from a to b

The value of the integral A. x 3 B. x 3 +C C. x 3/3 D. x 3/3 +C E. 2 x

Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of A. B. C. D. 5 12 14 Cannot be determined y 5 a b 7 2 c x

Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of A. B. C. D. -7 -2 7 12 y 5 a b 7 2 c x

Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of A. B. C. D. -7 -2 12 Cannot be determined y 5 a b 7 2 c x

9. Partial Differential Equations

The number of independent variable(s) for partial differential equations is more than or equal to _____. A. B. C. D. one two three four

END