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FE Exam Tutorial
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Math syllabus Analytic Geometry x Roots of Equations Calculus
Chemical Civil Electrical & Computer Mechanical Environmental Industrial General Analytic Geometry x Roots of Equations Calculus Differential Equations Vector Analysis Algebra and Trigonometry Complex Numbers Discrete Math Linear Algebra Numerical Methods Matrix Operations
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1. Vectors
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What can you say about two vectors whose dot product is negative?
The vectors are orthogonal Angle between vectors is <90o Angle between vectors is >90o
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If two vectors u and v are orthogonal to each other, then u.v=
-1 1
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2. Analytic Geometry
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Two straight lines are perpendicular to each other
Two straight lines are perpendicular to each other. The product of the slope of the two lines is -1 1 Cannot be determined
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END
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3. Roots of Equations
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The value of x that satisfies f (x)=0 is called the
root of equation f (x)=0 root of function f (x) zero of equation f (x)=0 none of the above
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A quadratic equation has ______ root(s)
one two three cannot be determined
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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 one two three cannot be determined
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Equation such as tan (x)=x has __ root(s)
zero one two infinite
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A polynomial of order n has zeros
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The velocity of a body is given by v (t)=5e-t+4, where t is in seconds and v is in m/s. The velocity of the body is 6 m/s at t = s s s 1.609 s
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4. Numerical Methods
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The number of significant digits in 2.30500 is
4 5 6
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END
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5. Ordinary Differential Equations
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In the differential equation
the variable x is the variable Independent Dependent
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In the differential equation
the variable y is the variable Independent Dependent
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Ordinary differential equations can have these many dependent variables.
one two any positive integer
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Ordinary differential equations can have these many independent variables.
one two any positive integer
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A differential equation is considered to be ordinary if it has
one dependent variable more than one dependent variable one independent variable more than one independent variable
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Classify the differential equation
linear nonlinear undeterminable to be linear or nonlinear
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Classify the differential equation
linear nonlinear linear with fixed constants undeterminable to be linear or nonlinear
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Classify the differential equation
linear nonlinear linear with fixed constants undeterminable to be linear or nonlinear
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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
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The form of the exact solution to
is
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END
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6. Matrices
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The size of matrix is
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The c32 entity of the matrix
6.3 does not exist
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Given then if [C]=[A]+[B], c12= 6 12
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Given then if [C]=[A]-[B], c23= -3 3 9
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A square matrix [A] is lower triangular if
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A square matrix [A] is upper triangular if
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An identity matrix [I] needs to satisfy the following
matrix is square all of the above
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Given then if [C]=[A][B], then c31= -57 -45 57 Does not exist
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The following system of equations x + y=2 6x + 6y=12 has solution(s).
no one more than one but finite number of infinite
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END
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7. Differential Calculus
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To find velocity from the location vs time data of the body, the mathematical procedure used is
Differentiation Integration
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The definition of the derivative of a function f (x) is
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The exact derivative of f (x)=x 3 at x=5 is most nearly
25.00 75.00 106.25 125.00
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Given y=sin (2x), dy/dx at x=3
0.9600 0.9945 1.920 1.989
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END
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8. Integral Calculus
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To find the velocity from acceleration vs time data, the mathematical procedure used is
Differentiation Integration
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Physically, integrating
means finding the Area under the curve from a to b Area to the left of point a Area to the right of point b Area above the curve from a to b
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The value of the integral
x3 x3 +C x3/3 x3/3 +C 2x
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Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of
y x a 5 7 2 b c 5 12 14 Cannot be determined
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Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of
y x a 5 7 2 b c -7 -2 7 12
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Given the f(x) vs x curve, and the magnitude of the areas as shown, the value of
y x a 5 7 2 b c -7 -2 12 Cannot be determined
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9. Partial Differential Equations
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The number of independent variable(s) for partial differential equations is more than or equal to _____. one two three four
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