Unit 5: Calculus
Topic 5.16: Euler's method (1st order) (HL only) Questions
Practice 12 exam-style questions for IB Math AI SL Topic 5.16. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
The Euler recurrence for dy/dx = f(x, y) is:
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2026
To go from x = 0 to x = 1.5 with a step length of h = 0.3, the number of Euler steps is:
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2026
A cup of tea cools so that dT/dt = −0.5(T − 20), where t is in minutes and T in °C. At t = 0 the tea is at 80 °C. Use Euler's method with h = 0.5 to estimate T at t = 1.5 minutes.
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2026
For dy/dx = x·y with y(1) = 2 and h = 0.1, the first Euler estimate y₁ (at x = 1.1) is:
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2026
An Euler estimate gives 7.8 while the exact solution is 8.0. The percentage error is:
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2026
For dy/dx = y² with y = 1 when x = 0, use Euler's method with step length h = 0.2 to estimate y when x = 0.6. The exact solution is y = 1/(1 − x). Find the percentage error of your estimate.
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2026
A tank drains so that the depth d (cm) satisfies dd/dt = −0.2√d, where t is in seconds. At t = 0 the depth is d = 16 cm. Use Euler's method with h = 1 to estimate the depth at t = 3 seconds.
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2026
For dy/dx = 2x − y with y = 3 when x = 1, use Euler's method with step length h = 0.5 to estimate y when x = 2.5.
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2026
A capacitor charges so that dQ/dt = (10 − Q)/4, with Q = 0 at t = 0 (Q in coulombs, t in seconds). (a) Use Euler's method with h = 1 to estimate Q at t = 3. (b) State, with a reason, whether your estimate is likely to be too high or too low.
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2026
For dy/dx = x + y with y = 1 when x = 0, use Euler's method with step length h = 0.25 to estimate y when x = 1.
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