ConceptSets & Inequalities
← All conceptsRoot location, parameters, propositions, conditions
8 ways this goes wrong. Each one is a named misconception the questions are built to catch.
- 'Not positive' vs 'negative'Treats ≤0 as <0 (or ≥0 as >0) when translating a verbal comparison into an inequality.→
- Degenerate linear case missedForgets the case where the leading coefficient vanishes and the quadratic becomes linear.→
- Difference-of-bounds not flippedSubtracts interval bounds directly without negating/flipping the range of the subtracted variable when finding a range of α-β.→
- Discriminant instead of sign-of-f(k)Uses the discriminant when roots straddling a value k require f(k)<0.→
- Integer-solution count off by oneMiscounts how many integers lie in the solution set by one at an endpoint.→
- Quantifier negation wrongNegates a universal/existential proposition incorrectly.→
- Sufficient/necessary reversedSwaps the direction of sufficiency and necessity, or confuses subset direction with implication direction.→
- Universal/existential quantifier confusedJudges an existential claim as if universal (or vice versa) when testing truth.→
