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Practice mode gives one hint and a worked explanation after every question. Test mode mixes all 7 units, holds the explanations until you submit, and then reports which units need another pass. The 8 questions printed further down this page are fixed, so you can read them and their worked answers without starting a set.
Building your Numerical Methods question set. This can take a few seconds while the questions are matched to this course and its units.
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Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.
This page follows the Numerical Methods syllabus unit by unit. For shorter mixed retrieval outside the course sequence, use calculus practice questions with answers.
Choose a computational method, track approximation error and stability, and compare the output with a known bound or independent estimate.
Goal: recognise a floating-point error problem from its wording, carry out the governing method, and check that the result is reasonable.
Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.
Goal: recognise a root finding problem from its wording, carry out the governing method, and check that the result is reasonable.
Choose a computational method, track approximation error and stability, and compare the output with a known bound or independent estimate.
Goal: recognise a interpolation problem from its wording, carry out the governing method, and check that the result is reasonable.
Relate local change to slope, apply the appropriate derivative rule, and use sign, units, and graph behavior to interpret the result.
Goal: recognise a numerical differentiation problem from its wording, carry out the governing method, and check that the result is reasonable.
Represent accumulated change, choose bounds and technique carefully, and check the result with units, area, or differentiation.
Goal: recognise a numerical integration problem from its wording, carry out the governing method, and check that the result is reasonable.
Represent the constraints symbolically, choose an equivalence-preserving solution method, and verify the result in every original relationship.
Goal: recognise a linear systems problem from its wording, carry out the governing method, and check that the result is reasonable.
Define the central objects, connect at least two representations, solve direct and unfamiliar applications, and explain how the result can be checked.
Goal: recognise a ode solvers problem from its wording, carry out the governing method, and check that the result is reasonable.
These 8 questions are printed in full on this page and are drawn across all 7 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.
Answer: absolute 0.00172, relative about 0.063%
Answer: [1.5, 2]
Answer: 3.16667
Answer: 9.5
Answer: 12.01
Answer: 2.75
Answer: x = 2.25, y = 1.9167
Answer: 2.25
Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.
| Question | Unit | What it asks | Answer |
|---|---|---|---|
| 1 | Floating-point error | The value 2.71828 is approximated by 2.72. What are the absolute and relative errors? | absolute 0.00172, relative about 0.063% |
| 2 | Root finding | Bisection is applied to f(x) = x^3 - x - 2 on [1, 2]. What is the interval after the first step? | [1.5, 2] |
| 3 | Root finding | Apply one Newton step to f(x) = x^2 - 10 starting at x0 = 3. What is x1, to five decimal places? | 3.16667 |
| 4 | Interpolation | Linear interpolation uses the points (2, 5) and (6, 17). What value does it predict at x = 3.5? | 9.5 |
| 5 | Numerical differentiation | Use the central difference with h = 0.1 to estimate the derivative of f(x) = x^3 at x = 2. | 12.01 |
| 6 | Numerical integration | Use the trapezoid rule with 4 equal strips to estimate the integral of x^2 from 0 to 2. | 2.75 |
| 7 | Linear systems | Apply one Gauss-Seidel sweep to 4x + y = 9 and x + 3y = 8, starting from x = 0 and y = 0. | x = 2.25, y = 1.9167 |
| 8 | ODE solvers | Use Euler's method with h = 0.5 on y' = y, y(0) = 1, for two steps. What is the estimate of y(1)? | 2.25 |
The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.
It covers all 7 Numerical Methods units listed above. Choose one unit for focused work, or mixed review to test method selection, and switch to test mode when you want all units mixed under time.
The 8 printed questions on this page keep their worked answers behind a toggle, so you can check any one of them straight away. In the generator above, practice mode explains each question as soon as you answer it, while test mode holds every explanation until you submit.
Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.