Numerical Methods for Engineers
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1. Numerical methods are primarily used to:
A. Replace all analytical mathematics
B. Eliminate the need for computers
C. Obtain approximate solutions to mathematical problems
D. Increase measurement errors
Answer: C. Obtain approximate solutions to mathematical problems
Rationale: Numerical methods provide approximate solutions when exact
analytical solutions are difficult, impossible, or inefficient to obtain.
2. The difference between the exact value and the approximate value is called:
A. Relative error
B. Truncation error
C. Absolute error
D. Round-off error
Answer: C. Absolute error
Rationale: Absolute error is calculated as the magnitude of the difference between
the true value and the approximate value.
,3. Relative error is calculated by:
A. Multiplying true value by approximate value
B. Dividing absolute error by the true value
C. Adding absolute and percentage errors
D. Dividing approximate value by zero
Answer: B. Dividing absolute error by the true value
Rationale: Relative error normalizes the absolute error by comparing it to the
actual value.
4. Round-off error occurs because:
A. Equations are nonlinear
B. Computers store numbers with limited precision
C. Derivatives are difficult to calculate
D. Matrices cannot be inverted
Answer: B. Computers store numbers with limited precision
Rationale: Digital computers represent numbers with a finite number of digits,
causing small approximation errors.
5. Truncation error is caused by:
A. Hardware failure
B. Measurement mistakes
C. Approximating an infinite process with a finite one
D. Incorrect unit conversion
Answer: C. Approximating an infinite process with a finite one
Rationale: Truncation error results when mathematical procedures such as series
expansions are stopped after a limited number of terms.
6. Significant figures indicate:
,A. Number of equations solved
B. Precision of a numerical value
C. Computer processing speed
D. Matrix size
Answer: B. Precision of a numerical value
Rationale: Significant figures represent the meaningful digits in a measured or
calculated value.
7. The condition number of a problem indicates:
A. Number of variables
B. Sensitivity of the solution to input errors
C. Number of iterations required
D. Matrix dimensions only
Answer: B. Sensitivity of the solution to input errors
Rationale: A high condition number indicates that small changes in input values
may create large changes in results.
8. A well-conditioned problem:
A. Amplifies small errors significantly
B. Cannot be solved numerically
C. Has low sensitivity to input changes
D. Always requires iteration
Answer: C. Has low sensitivity to input changes
Rationale: Well-conditioned problems produce stable solutions when small
numerical changes occur.
9. The bisection method is used to find:
, A. Matrix determinants
B. Roots of nonlinear equations
C. Numerical integrals only
D. Eigenvectors only
Answer: B. Roots of nonlinear equations
Rationale: The bisection method finds values where a function equals zero by
repeatedly dividing an interval.
10. The bisection method requires:
A. A derivative function
B. A matrix inverse
C. An interval containing a sign change
D. A random initial guess
Answer: C. An interval containing a sign change
Rationale: Bisection requires the function values at the interval endpoints to have
opposite signs.
11. The main advantage of the bisection method is:
A. It never requires iterations
B. It guarantees convergence when conditions are satisfied
C. It always converges faster than Newton’s method
D. It requires no function evaluation
Answer: B. It guarantees convergence when conditions are satisfied
Rationale: If the initial interval brackets a root, bisection will converge reliably.
12. Newton-Raphson method uses:
A. Matrix multiplication only
B. Function values and derivatives
Practice Exam Questions And Correct
Answers (Verified Answers) Plus
Rationales 2026 Q&A | Instant
Download Pdf
1. Numerical methods are primarily used to:
A. Replace all analytical mathematics
B. Eliminate the need for computers
C. Obtain approximate solutions to mathematical problems
D. Increase measurement errors
Answer: C. Obtain approximate solutions to mathematical problems
Rationale: Numerical methods provide approximate solutions when exact
analytical solutions are difficult, impossible, or inefficient to obtain.
2. The difference between the exact value and the approximate value is called:
A. Relative error
B. Truncation error
C. Absolute error
D. Round-off error
Answer: C. Absolute error
Rationale: Absolute error is calculated as the magnitude of the difference between
the true value and the approximate value.
,3. Relative error is calculated by:
A. Multiplying true value by approximate value
B. Dividing absolute error by the true value
C. Adding absolute and percentage errors
D. Dividing approximate value by zero
Answer: B. Dividing absolute error by the true value
Rationale: Relative error normalizes the absolute error by comparing it to the
actual value.
4. Round-off error occurs because:
A. Equations are nonlinear
B. Computers store numbers with limited precision
C. Derivatives are difficult to calculate
D. Matrices cannot be inverted
Answer: B. Computers store numbers with limited precision
Rationale: Digital computers represent numbers with a finite number of digits,
causing small approximation errors.
5. Truncation error is caused by:
A. Hardware failure
B. Measurement mistakes
C. Approximating an infinite process with a finite one
D. Incorrect unit conversion
Answer: C. Approximating an infinite process with a finite one
Rationale: Truncation error results when mathematical procedures such as series
expansions are stopped after a limited number of terms.
6. Significant figures indicate:
,A. Number of equations solved
B. Precision of a numerical value
C. Computer processing speed
D. Matrix size
Answer: B. Precision of a numerical value
Rationale: Significant figures represent the meaningful digits in a measured or
calculated value.
7. The condition number of a problem indicates:
A. Number of variables
B. Sensitivity of the solution to input errors
C. Number of iterations required
D. Matrix dimensions only
Answer: B. Sensitivity of the solution to input errors
Rationale: A high condition number indicates that small changes in input values
may create large changes in results.
8. A well-conditioned problem:
A. Amplifies small errors significantly
B. Cannot be solved numerically
C. Has low sensitivity to input changes
D. Always requires iteration
Answer: C. Has low sensitivity to input changes
Rationale: Well-conditioned problems produce stable solutions when small
numerical changes occur.
9. The bisection method is used to find:
, A. Matrix determinants
B. Roots of nonlinear equations
C. Numerical integrals only
D. Eigenvectors only
Answer: B. Roots of nonlinear equations
Rationale: The bisection method finds values where a function equals zero by
repeatedly dividing an interval.
10. The bisection method requires:
A. A derivative function
B. A matrix inverse
C. An interval containing a sign change
D. A random initial guess
Answer: C. An interval containing a sign change
Rationale: Bisection requires the function values at the interval endpoints to have
opposite signs.
11. The main advantage of the bisection method is:
A. It never requires iterations
B. It guarantees convergence when conditions are satisfied
C. It always converges faster than Newton’s method
D. It requires no function evaluation
Answer: B. It guarantees convergence when conditions are satisfied
Rationale: If the initial interval brackets a root, bisection will converge reliably.
12. Newton-Raphson method uses:
A. Matrix multiplication only
B. Function values and derivatives
