These descriptions explain mistakes Keiko's questions were written to distinguish. The counts describe this bank's authored distractors. They do not measure student performance or prescribe how to divide your study time. Independent specialist and outcome validation remain pending.
GRE Math
653 items in this bank carry named causes on their wrong answers, covering 2,256 wrong answers between them and drawing on 42 of the 84 named errors. 29 of those errors appear nowhere else: they are the ones that are about math rather than about reading a question. They are set out below, grouped by the content area each one turns up in most. The other 13 are the cross-exam errors listed under errors that are not about the subject.
formula_variant_misrememberedThe chosen expression is a corrupted variant of the standard formula for this quantity: a real formula, but not the one this situation calls for.
Rederive the formula from a case you can check rather than recalling it under time pressure. A near-miss variant looks exactly as convincing as the real one.
61 wrong answers written to catch it, 28 of them in calculus · concept gap
convergence_test_misappliedA convergence test or comparison was invoked in a direction that gives no conclusion for this series or integral, or was dismissed where it does decide.
Check that the test's hypotheses hold here and that its conclusion answers the question. A test that gives no conclusion is not evidence either way.
40 wrong answers written to catch it, 28 of them in calculus · wrong method
derivative_rule_misappliedA differentiation or antidifferentiation rule was used where a different one governs this expression.
Name the structure of the expression — product, quotient, composition — before reaching for a rule. The rule follows from the structure, not from what the terms look like.
29 wrong answers written to catch it, 21 of them in calculus · wrong method
limit_taken_by_naive_substitutionThe point was substituted into an indeterminate or discontinuous expression and the resulting symbol was reported, instead of resolving the form first.
Resolve the form first — factor, expand, or apply a limit theorem — and substitute only once the expression is defined at the point.
26 wrong answers written to catch it, 20 of them in calculus · wrong method
symmetry_argument_missedThe odd or even symmetry of the integrand over a symmetric interval was not used, so a cancellation was computed away or invented.
Check whether the integrand is odd or even over a symmetric interval before you integrate anything. Symmetry often replaces the whole calculation.
18 wrong answers written to catch it · concept gap
integration_differentiation_swappedThe chosen expression is what differentiating produces where the problem asks you to antidifferentiate, or the reverse.
Check whether you are being asked to differentiate or to antidifferentiate, then verify by running the opposite operation on your answer.
18 wrong answers written to catch it, 14 of them in calculus · wrong method
chain_rule_factor_omittedThe outer rule was carried out correctly, but the derivative of the inner function was never multiplied in — or it was placed inside the outer function instead of alongside it.
Name the inside function explicitly, then multiply by its derivative as a separate factor sitting alongside the outer result.
14 wrong answers written to catch it, 13 of them in calculus · wrong method
normalization_step_omittedThe numerator was built correctly but was never divided by the interval length, the squared norm, or the count that the definition divides by.
Finish the definition. The interval length, the squared norm, or the count the formula divides by is part of the answer, not decoration.
22 wrong answers written to catch it, 12 of them in calculus · calculation or execution error
absolute_conditional_convergence_confusedConvergence of the series was taken for convergence of the series of absolute values, or the reverse.
Test the series of absolute values as a separate question before claiming absolute convergence.
9 wrong answers written to catch it, 5 of them in calculus · concept gap
path_dependence_misjudgedA path-independent integral was treated as depending on the route taken, or a path-dependent one was treated as fixed by the endpoints.
Check whether the field has a potential function. If it does, only the endpoints matter; if it does not, the route is part of the answer.
6 wrong answers written to catch it, 4 of them in calculus · concept gap
growth_model_linearizedRepeated multiplication was replaced by repeated addition, so exponential growth or decay was extrapolated in equal steps.
Count how many times the quantity multiplies rather than how much it adds each step. Compounding and linear change agree only for one step.
4 wrong answers written to catch it · concept gap
invariance_property_misjudgedA quantity that a change of basis or a structure-preserving map holds fixed was treated as changing, or the reverse.
List what the transformation is allowed to change and what it must preserve, then judge the quantity against that list.
31 wrong answers written to catch it, 21 of them in linear algebra · concept gap
matrix_entries_misreadThe method is right, but entries or components were read from the wrong places: an off-diagonal for a diagonal, a row for a column, two components swapped, or one entry skipped.
Say which row and which column each number comes from before you use it. Reading the wrong entry is a silent error: the method looks right the whole way through.
24 wrong answers written to catch it, 20 of them in linear algebra · misread condition
trace_determinant_swappedThe sum and the product of the eigenvalues were interchanged.
Hold on to which one sums the eigenvalues and which one multiplies them, then check which the question wants.
18 wrong answers written to catch it · concept gap
rank_nullity_dimension_confusedRank plus nullity was balanced against the target space, or against the number of rows, rather than against the dimension of the domain.
Count the dimension of the domain first. Rank and nullity add up to that, not to the dimension of the space you are mapping into.
14 wrong answers written to catch it · wrong method
algebraic_geometric_multiplicity_confusedThe multiplicity of the eigenvalue in the characteristic polynomial was reported instead of the dimension of its eigenspace.
Compute the dimension of the eigenspace separately from the multiplicity of the root, and compare the two. They agree only when the matrix is diagonalisable.
4 wrong answers written to catch it · concept gap
defining_test_incompleteOne clause of the definition — closure, inverses, absorption, independence, or a boundary case — was never checked, so an object that fails it was accepted.
Run every clause of the definition, including the clause that looks too obvious to check. That is usually the one the item is built on.
197 wrong answers written to catch it, 60 of them in abstract algebra · concept gap
element_order_confused_with_group_orderThe size of the group, of a subgroup, or of the index was reported where the order of a single element was asked, or the reverse.
Check whether the question asks for the order of a single element or for the size of the whole group. The two are related but almost never equal.
35 wrong answers written to catch it · concept gap
prime_power_condition_misappliedThe order was classified without correctly checking whether it is a power of a single prime.
Factor the order into primes first, then apply the theorem to what the factorisation shows rather than to what the number looks like.
24 wrong answers written to catch it · concept gap
unit_zero_divisor_confusedAn element was classified as invertible when it is a zero divisor, or the reverse, without checking the coprimality condition that separates them.
Test directly whether the element has an inverse. The coprimality condition is what separates a unit from a zero divisor, and it is quick to check.
24 wrong answers written to catch it, 23 of them in abstract algebra · concept gap
operation_table_property_confusedThe chosen property is a genuine axiom of the structure, but not the one the term in the prompt picks out.
Name the axiom the term in the prompt actually picks out, then check the structure against that one. Several axioms hold; only one is being tested.
20 wrong answers written to catch it, 10 of them in abstract algebra · concept gap
stronger_property_assumedThe chosen answer asserts a condition that is sufficient or simply false here, rather than the one that is actually required.
Ask whether the property is required here or merely enough here. A condition that is enough for the conclusion cannot be used to justify the conclusion in general.
130 wrong answers written to catch it, 45 of them in real analysis · concept gap
boundary_case_misclassifiedThe strict or non-strict inequality at the boundary was chosen the wrong way, so the borderline case is misclassified.
Test the boundary point itself and see whether it belongs. Whether the inequality is strict is usually the whole question.
62 wrong answers written to catch it, 28 of them in real analysis · concept gap
logical_form_alteredThe quantifiers were reordered or the implication was reversed, which states a different condition from the definition being tested.
Read the quantifiers in the order they are written and keep the implication pointing the way the definition points. Swapping either states a different claim.
46 wrong answers written to catch it, 20 of them in real analysis · concept gap
permutation_used_for_combinationThe count was made as if the selections were ordered, so each unordered choice was counted more than once.
Decide whether two selections in a different order count as the same outcome before you choose a formula. That single decision picks the formula for you.
16 wrong answers written to catch it · wrong method
countability_misjudgedAn uncountable set was treated as countable (or the reverse), so the cardinality comparison fails.
Ask whether the set can be listed by a rule. An explicit listing or a diagonal argument settles it; intuition about size does not.
17 wrong answers written to catch it, 8 of them in real analysis · concept gap
pointwise_uniform_convergence_confusedA bound that depends on the point was treated as a bound that works for the whole interval at once, or the reverse.
Ask whether one bound works at every point at once, or whether the bound you found still depends on the point you picked.
10 wrong answers written to catch it, 6 of them in real analysis · concept gap
equilibrium_stability_reversedThe sign of the derivative at the equilibrium was read the wrong way, so a source was called a sink or the reverse.
Sketch the phase line and read whether nearby solutions move toward the equilibrium or away from it, rather than reading a sign off the algebra.
8 wrong answers written to catch it · concept gap
complex_polar_form_confusedThe real part, the imaginary part, the modulus, and the argument of a complex number were interchanged when moving between rectangular and polar form.
Draw the number in the plane and read the modulus and the argument off the picture before you convert anything.
18 wrong answers written to catch it, 16 of them in complex analysis · concept gap
The same 13 errors that appear in all three subject tests, counted inside GRE Math alone.
| Named error | Wrong answers in GRE Math |
|---|---|
| Reached for a neighbouring definition | 247 |
| Substituted the wrong given | 165 |
| Reported a different quantity than the one asked for | 137 |
| Left a factor out of the formula | 133 |
| Lost or flipped a sign | 116 |
| Stopped at an intermediate result | 97 |
| Right method, wrong power | 96 |
| Dropped a condition the problem stated | 94 |
| Combined the quantities with the wrong rule | 75 |
| Used the relationship in the wrong direction | 55 |
| Applied the version of the rule that fits a different case | 52 |
| Leaned on a quantity that does not enter | 40 |
| Treated the result as independent of the change | 4 |
GRE Mathematics Subject Test study hub — the syllabus, the free study notes, and the practice these items belong to.