Taylor Series Quizzes

Begin with a polynomial chosen to match a function’s value and derivatives at a center point. Compare increasingly higher-degree approximations with the original function on a graph, then connect the coefficients to f⁽ⁿ⁾(a)/n! before introducing full Taylor series notation.

Use a sequence of problems that asks students to: build expansions from derivatives, transform familiar series through substitution or differentiation, and find intervals of convergence with endpoint checks. Approximation problems involving functions such as eˣ, sin x, and ln(1+x) give the algebra a clear purpose.

Common errors include omitting n!, using xⁿ instead of (x−a)ⁿ for a nonzero center, losing alternating signs, and stopping after the ratio test without checking convergence at both endpoints. A quick substitution of x=a can catch several coefficient and centering errors.

Assign the quiz as a digital quiz on Wayground or use the printable PDF for paper practice. Every quiz includes a complete answer key, and paper submissions can be scanned or captured for grading with the Wayground for Teachers app.

Have students compare the polynomial and function at several values near the expansion center, then calculate the absolute error. They should observe that accuracy usually improves with more terms and worsens as the input moves farther from the center; remainder estimates can then provide a formal error bound.

Give students who need more processing time an extended-time digital assignment, and use reduced answer choices when the main goal is identifying the correct expansion or convergence interval. Alternate quiz versions can also use larger text or wider spacing to make dense factorial and summation notation easier to track.