Numerical methods worksheet with answers

Free printable Numerical methods worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
x11.522.533.5y1.09861.25281.38631.50411.60941.7047

Use linear interpolation in the table to estimate y at x = 3.125.

x = 3.125
y =
2.Easy
xya = 1b = 2

Use the bisection method on f(x) = ln x + x − 2 with the starting interval [1, 2]. Find the midpoint c3 of step 3.

f(x) = ln x + x − 2[a, b] = [1, 2]n = 3
c3 =
3.Medium
t (s)024681012v (m/s)64911151715

A vehicle's speed is measured every 2 s (table). Estimate the distance s travelled from t = 0 to t = 12 s with Simpson's rule.

h = 2 sn = 6
s = m
4.Medium
xy00.751.52.253

Approximate ∫03 √x·e−x dx with Simpson's rule using n = 4 strips. Give S.

f(x) = √x·e−x[a, b] = [0, 3]n = 4
S =
5.Hard
00.050.10.150.200.10.2ty(0, 0)

Use Heun's method (improved Euler) with h = 0.1 for y′ = e−ty, y(0) = 0 to estimate y2 ≈ y(0.2).

y′ = e−tyy(0) = 0h = 0.1
y2 =
6.Hard
00.10.20.322.5ty(0, 2)

Use Heun's method (improved Euler) with h = 0.1 for y′ = y − t², y(0) = 2 to estimate y3 ≈ y(0.3).

y′ = y − t²y(0) = 2h = 0.1
y3 =

Answer key

  1. 1. y = 1.633
  2. 2. c3 = 1.625
  3. 3. s = 131.3 m
  4. 4. S = 0.7254
  5. 5. y2 = 0.1971
  6. 6. y3 = 2.688

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