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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

1. Vectors

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

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

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2. Analytic Geometry

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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3. Roots of Equations

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

A quadratic equation has ______ root(s) 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 one two three cannot be determined

Equation such as tan (x)=x has __ root(s) zero one two infinite

A polynomial of order n has zeros

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 = 0.1823 s 0.3979 s 0.9162 s 1.609 s

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4. Numerical Methods

The number of significant digits in 2.30500 is 4 5 6

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5. Ordinary Differential Equations

In the differential equation the variable x is the variable Independent Dependent

In the differential equation the variable y is the variable Independent Dependent

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

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

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

Classify the differential equation linear nonlinear undeterminable to be linear or nonlinear

Classify the differential equation linear nonlinear linear with fixed constants undeterminable to be linear or nonlinear

Classify the differential equation linear nonlinear linear 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

The form of the exact solution to is

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6. Matrices

The size of matrix is

The c32 entity of the matrix 6.3 does not exist

Given then if [C]=[A]+[B], c12= 6 12

Given then if [C]=[A]-[B], c23= -3 3 9

A square matrix [A] is lower triangular if

A square matrix [A] is upper triangular if

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

Given then if [C]=[A][B], then c31= . -57 -45 57 Does not exist

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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7. Differential Calculus

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

The definition of the derivative of a function f (x) is

The exact derivative of f (x)=x 3 at x=5 is most nearly 25.00 75.00 106.25 125.00

Given y=sin (2x), dy/dx at x=3 0.9600 0.9945 1.920 1.989

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8. Integral Calculus

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

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

The value of the integral x3 x3 +C x3/3 x3/3 +C 2x

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

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

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

9. Partial Differential Equations

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

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