Numerical methods in context Quiz

1. Which equation cannot be solved exactly using A Level algebra?

• A. $x^2-5x+6=0$
• B. $2x+1=7$
• C. $\ln x=2$
• D. $e^x=3x$

2. A root is $2.46$ to 2 d.p. Which pair of values of $f$ proves this?

• A. $f(2.4)$ and $f(2.5)$
• B. $f(2.455)$ and $f(2.465)$
• C. $f(2.46)$ and $f(2.47)$
• D. $f(2)$ and $f(3)$

3. Newton-Raphson is often preferred to bisection because

• A. it converges much faster
• B. it needs no derivative
• C. it never fails
• D. it needs no starting value

4. For $x_{n+1}=g(x_n)$ to converge to $\alpha$ we need

• A. $g(\alpha)=0$
• B. $g'(\alpha)>1$
• C. $|g'(\alpha)|<1$
• D. $g'(\alpha)=0$ only

5. A trapezium rule estimate is not accurate enough. What is the simplest improvement?

• A. Use fewer strips
• B. Round the ordinates more
• C. Change the limits
• D. Use more strips