# Question batches 36,000 questions have bilingual step-by-step derivations. Browse original batches or search and filter in the question explorer. [Search all questions & derivations →](/en/explore/) [← Previous](/en/practice/?page=8#results)[1](/en/practice/?page=1#results) … [8](/en/practice/?page=8#results) 9 [10](/en/practice/?page=10#results) … [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=10#results) 360 results · Page 9 of 15 Question batch · 100 questions ## [Strict Finite-Metric Tail Audits versus Infinite Limit Witnesses](/en/practice/batch-20261013-advance-20261023-r04-metric-convergence-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Convergence in a metric space batch-20261013-advance-20261023-r04-metric-convergence-foundations Question batch · 100 questions ## [Complete Finite Subgroup and Homomorphism Obligations](/en/practice/batch-20261013-advance-20261023-r03-subgroup-homomorphism-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Subgroups and group homomorphisms batch-20261013-advance-20261023-r03-subgroup-homomorphism-foundations Question batch · 100 questions ## [Finite Real-Coordinate Linear Combinations and Span Witnesses](/en/practice/batch-20261013-advance-20261023-r02-linear-combination-span-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Linear combinations and span batch-20261013-advance-20261023-r02-linear-combination-span-foundations Question batch · 100 questions ## [Exact Ordered-Pair Conjugation and Modulus-Squared Invariants](/en/practice/batch-20261013-advance-20261023-r01-complex-modulus-conjugate-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Complex modulus and conjugation batch-20261013-advance-20261023-r01-complex-modulus-conjugate-foundations Question batch · 100 questions ## [Exact Finite PMFs, Events, Expectations and Pushforwards](/en/practice/batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Finite discrete probability distribution batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations Question batch · 100 questions ## [Complete Finite Distance Tables and All Triangle Inequalities](/en/practice/batch-20261013-advance-20261022-r06-metric-space-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Metric space batch-20261013-advance-20261022-r06-metric-space-foundations Question batch · 100 questions ## [Complete Cayley Tables and Every Finite Group Obligation](/en/practice/batch-20261013-advance-20261022-r05-finite-group-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Finite group batch-20261013-advance-20261022-r05-finite-group-foundations Question batch · 100 questions ## [Exact Coordinate Instances in Fixed Real Vector Spaces](/en/practice/batch-20261013-advance-20261022-r04-real-vector-space-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Real vector space batch-20261013-advance-20261022-r04-real-vector-space-foundations Question batch · 100 questions ## [Ordered Integer-Pair Complex Arithmetic and Real Embedding](/en/practice/batch-20261013-advance-20261022-r03-complex-number-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Complex number batch-20261013-advance-20261022-r03-complex-number-foundations Question batch · 100 questions ## [Exact Fixed-Period Present Values and Compound-Discount Roundtrips](/en/practice/batch-20261013-advance-20261022-r02-present-value-discounting-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Present value and discounting batch-20261013-advance-20261022-r02-present-value-discounting-foundations Question batch · 100 questions ## [Positive Oscillator Parameters, Point Residuals and State-Energy Values](/en/practice/batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Linear harmonic-oscillator model batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations Question batch · 100 questions ## [Exact Bounded Discrete Logistic Increment Models](/en/practice/batch-20261013-advance-20261021-r07-discrete-logistic-growth-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Discrete logistic increment model batch-20261013-advance-20261021-r07-discrete-logistic-growth-foundations Question batch · 100 questions ## [Canonical Finite LP Grids, Feasibility and All Tied Optimizers](/en/practice/batch-20261013-advance-20261021-r06-linear-programming-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Linear programming batch-20261013-advance-20261021-r06-linear-programming-foundations Question batch · 100 questions ## [Declared Sign-Bracket Updates, Early Stops and Exact Widths](/en/practice/batch-20261013-advance-20261021-r05-bisection-method-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Finite sign-bracket updates in the bisection method batch-20261013-advance-20261021-r05-bisection-method-foundations Question batch · 100 questions ## [Polynomial IVP Candidates: Initial Data and Finite Residual Grids](/en/practice/batch-20261013-advance-20261021-r04-initial-value-problem-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Initial-value problem batch-20261013-advance-20261021-r04-initial-value-problem-foundations Question batch · 100 questions ## [Finite Orbits: Returns, Least Periods and Transient States](/en/practice/batch-20261013-advance-20261021-r03-orbit-fixed-periodic-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Orbits, fixed points and periodic points batch-20261013-advance-20261021-r03-orbit-fixed-periodic-foundations Question batch · 100 questions ## [Synthetic Rule-Agreement Records without Learner Diagnosis](/en/practice/batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Diagnostic mathematical assessment records batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations Question batch · 100 questions ## [Explicit Rule, Pair and Finite-Table Semantic Bridges](/en/practice/batch-20261013-advance-20261021-r01-mathematical-representation-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Mathematical representation batch-20261013-advance-20261021-r01-mathematical-representation-foundations Question batch · 100 questions ## [Fixed-Period Compound Models without Cash Flows](/en/practice/batch-20261013-advance-20261020-r07-compound-interest-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Compound-interest model batch-20261013-advance-20261020-r07-compound-interest-foundations Question batch · 100 questions ## [Fixed-Factor Exact Discrete Exponential Models](/en/practice/batch-20261013-advance-20261020-r06-discrete-exponential-growth-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Discrete exponential growth model batch-20261013-advance-20261020-r06-discrete-exponential-growth-foundations Question batch · 100 questions ## [Ordered L-M-T Dimension Vectors and Necessary Consistency](/en/practice/batch-20261013-advance-20261020-r05-dimensional-analysis-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Dimensional analysis batch-20261013-advance-20261020-r05-dimensional-analysis-foundations Question batch · 100 questions ## [Complete Finite Feasibility and All Tied Optimizers](/en/practice/batch-20261013-advance-20261020-r04-optimization-problem-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Optimization problem batch-20261013-advance-20261020-r04-optimization-problem-foundations Question batch · 100 questions ## [Exact Rational Errors and Inclusive Tolerance Bounds](/en/practice/batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Numerical approximation and error batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations Question batch · 100 questions ## [Polynomial ODE Candidates: Point Residuals and Initial Conditions](/en/practice/batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D9) Ordinary differential equation batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations [← Previous](/en/practice/?page=8#results)[1](/en/practice/?page=1#results) … [8](/en/practice/?page=8#results) 9 [10](/en/practice/?page=10#results) … [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=10#results) 360 results · Page 9 of 15