EIT Computer Science and Numerical Methods 3

Question 1

Gaussian elimination is a direct method for solving:

Accepted Answer

Systems of linear algebraic equations

Answer

Nonlinear transcendental equations

Answer

Ordinary differential equations

Answer

Polynomial root-finding problems

Question 2

Using 8-bit two's complement representation, the range of signed integers is:

Accepted Answer

-128 to 127

Answer

-127 to 127

Answer

-128 to 128

Answer

-256 to 255

Question 3

The central difference approximation for the second derivative f''(x) is:

Accepted Answer

[f(x+h) - 2f(x) + f(x-h)] / h²

Answer

[f(x+h) - f(x-h)] / (2h)

Answer

[f(x+h) + f(x-h)] / h²

Answer

[f(x+2h) - 2f(x+h) + f(x)] / h²

Question 4

For the bisection method to guarantee finding a root on interval [a, b], which condition must hold?

Accepted Answer

f(a) · f(b) < 0 (the function changes sign over the interval)

Answer

f(a) and f(b) must both be positive

Answer

f'(a) and f'(b) must have opposite signs

Answer

The function must be differentiable at every point in [a, b]

Question 5

In object-oriented programming, inheritance primarily allows:

Accepted Answer

A subclass to acquire the methods and attributes of a parent class

Answer

A class to conceal its internal implementation details from outside code

Answer

Multiple independent instances of a class to coexist in memory

Answer

An object to respond differently to the same method call based on type

Question 6

The condition number of a matrix is used to measure:

Accepted Answer

The sensitivity of the linear system solution to small perturbations in inputs

Answer

The total number of non-zero elements in the matrix

Answer

The number of linearly independent rows (matrix rank)

Answer

The computational cost of performing Gaussian elimination

Question 7

The IEEE 754 standard specifies:

Accepted Answer

Binary floating-point number representation and arithmetic rules

Answer

Integer binary arithmetic and overflow behavior

Answer

Character encoding schemes for programming languages

Answer

Network packet data transmission protocols