Numerical Methods — Engineering Board Exam Practice Questions

8 free engineering board exam reviewer questions on Numerical Methods (Advanced Engineering Mathematics), each with the correct answer and a worked solution.

1. Use the secant method on f(x)=x2-2 with x0=1 and x1=2. Find the third approximation x3.
2. Use one step of the fourth-order Runge-Kutta method with h=0.2 to estimate y(0.2) for y'=x+y, y(0)=1.
3. Use Simpson's 13 rule with n=4 to approximate 0π x,dx.
4. Use Euler's method with h=0.1 to estimate y(0.2) for y'=x+y, y(0)=1.
5. Use the bisection method on f(x)=x3-x-1 with the starting interval [1,2]. What is the third midpoint computed?
6. Apply one Newton-Raphson iteration to f(x)=x3-2x-5 starting from x0=2.
7. Apply one Newton-Raphson iteration to f(x)=x2-5 starting from x0=2.
8. Use the trapezoidal rule with n=2 subintervals to approximate 02x2,dx.