CAE Exam 1 Questions with Correct Answers Latest Update 2025/2026
accuracy - Answers how close the value is compared to the true value
precision - Answers how close the value is to the previous value
inaccuracy - Answers the deviation from the actual value (bias)
imprecision - Answers the magnitude of the scatter (uncertainty)
round off errors - Answers came from computers having a fixed number of sig figs during
calculations. computers used a base-2 representation so they can represent base-10 numbers
like pi or exp
subtractive cancellation - Answers happens when subtracting two nearly equal numbers. comes
from round off error. avoid by multiplying by the conjugate over the conjugate.
stability - Answers applies to algorithms and is unstable if the uncertainty of the input values is
greatly magnified by the numerical method. stable algorithm computes nearly the right answer
or nearly the right question
condition number - Answers applies to problems and relates to a problem's sensitivity to
changes in the input. all small deviations of a system have small effects. ill-conditioned
problems mean some small deviations of a system will have large effects. if k = 0 then well-
conditioned otherwise ill-conditioned
bracketing method pros - Answers fast to execute, roots will always be found as long as the
initial two guesses bracket the root.
bracketing method cons - Answers unable to tell if there are multiple roots, takes many
iterations if guesses are far from the root
bisection pros - Answers easy, always finds the root, number of iterations required to attain an
absolute error can be computed a priori
bisection cons - Answers slow, need to make good initial estimates, problematic with multiple
roots
false position pros - Answers faster than bisection and it always converges for a single root
false position cons - Answers requires interpolation and the interval definitions can get stuck
bracketing methods - Answers bisection, false position
open methods - Answers fixed point iteration, Newton Raphson, secant, mueller's method
fixed point iteration pros - Answers fast and only requires one initial guess
accuracy - Answers how close the value is compared to the true value
precision - Answers how close the value is to the previous value
inaccuracy - Answers the deviation from the actual value (bias)
imprecision - Answers the magnitude of the scatter (uncertainty)
round off errors - Answers came from computers having a fixed number of sig figs during
calculations. computers used a base-2 representation so they can represent base-10 numbers
like pi or exp
subtractive cancellation - Answers happens when subtracting two nearly equal numbers. comes
from round off error. avoid by multiplying by the conjugate over the conjugate.
stability - Answers applies to algorithms and is unstable if the uncertainty of the input values is
greatly magnified by the numerical method. stable algorithm computes nearly the right answer
or nearly the right question
condition number - Answers applies to problems and relates to a problem's sensitivity to
changes in the input. all small deviations of a system have small effects. ill-conditioned
problems mean some small deviations of a system will have large effects. if k = 0 then well-
conditioned otherwise ill-conditioned
bracketing method pros - Answers fast to execute, roots will always be found as long as the
initial two guesses bracket the root.
bracketing method cons - Answers unable to tell if there are multiple roots, takes many
iterations if guesses are far from the root
bisection pros - Answers easy, always finds the root, number of iterations required to attain an
absolute error can be computed a priori
bisection cons - Answers slow, need to make good initial estimates, problematic with multiple
roots
false position pros - Answers faster than bisection and it always converges for a single root
false position cons - Answers requires interpolation and the interval definitions can get stuck
bracketing methods - Answers bisection, false position
open methods - Answers fixed point iteration, Newton Raphson, secant, mueller's method
fixed point iteration pros - Answers fast and only requires one initial guess
