BitWithBite
Mathematics Worksheet
🔢 Numerical Methods
SCORE___ / 20
NameClassDate
After this worksheet you can
Apply the bisection method.Apply one step of Newton's method.Compare convergence speeds.Understand approximation error.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1A root lies between x = 2 and x = 6. The first bisection midpoint is:
2Newton's method on f(x) = x2 − 9 from x₀ = 4 gives x₁ =:
3Newton's method converges faster because it uses the:
4As a converging method iterates, the error:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5The bisection midpoint of [2, 6] is .
6Bisection requires a change between endpoints.
7A root lies between x = 2 and x = 6. Find the first bisection midpoint.
8Apply one step of Newton's method to f(x) = x2 − 9, starting at x₀ = 4.
9Why does Newton's method typically converge faster than bisection?
🚀 Section C · Challenge ● CHALLENGE 5
10What happens to the error as a converging method iterates?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
Teacher's Signature
Parent's Signature
✂ answer key — fold or cut before handing out
1-A 2-A 3-B 4-C | 5 4 6 sign 7 = 4 8 = x₁ = 4 − 7/8 = 3.125 9 = It uses the slope to make smarter jumps toward the root | 10 = It gets smaller, approaching zero