MATH 6

Which numerical integration method approximates the area under a curve by dividing it into trapezoids?

• Trapezoidal Rule

• Gaussian Quadrature

• Midpoint Rule

• Simpson's 1/3 Rule

Which of the following methods is a direct method for solving systems of linear equations?

• Gauss-Seidel Method

• Jacobi iteration

• Successive Over-Relaxation (SOR)

• LU Decomposition

What refers to a locus of a point which move so that it is always equidistant from a fixed point (focus) and from a fixed straight line (directrix)?

• Circle

• Ellipse

• Parabola

• Hyperbola

Which of the following statements is FALSE for identity matrix, I?

• All nonzero entries are equal to 1

• AI = A^(-1)

• I is a square matrix.

• All entries in I are zero, except the entries whose row and column numbers are equal.

Which of the following is an iterative method used to find the roots of a non-linear equation?

• Cramer's Rule

• Newton-Raphson Method

• LU Decomposition

• Gauss Elimination Method

The general solution of the differential equation x dy - y dx is a family of _____

• circles

• parabolas

• straight lines passing through the origin

• ellipses

The general solution of the differential equation dy/dx = (1 - 2x)/y is a family of _____

• ellipses

• straight lines passing through the origin

• parabolas

• circles

If the equation is unchanged by the substitution of -x for x and -y for y simultaneously, its curve is symmetric with respect to the:

• origin

• x-axis

• line 45° with the axes

• y-axis

Identify what type of conic section is r = 5/(4 - 8 sinθ).

• Parabola

• Circle

• Ellipse

• Hyperbola

The equation |z + 1 - i| = |z - 1 + i| represents a _____

• parabola

• circle

• straight line

• hyperbola