# 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=12#results)[1](/en/practice/?page=1#results) … [12](/en/practice/?page=12#results) 13 [14](/en/practice/?page=14#results) [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=14#results) 360 results · Page 13 of 15 Question batch · 100 questions ## [Oriented Integral, Parity, and Finite-Sum Error Depth](/en/practice/batch-20261007-advance-20261009-r06-definite-integral-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Signed polynomial definite integrals on finite intervals batch-20261007-advance-20261009-r06-definite-integral-foundations Question batch · 100 questions ## [Primitive Coefficient, Constant, and Anchor Depth](/en/practice/batch-20261007-advance-20261009-r05-antiderivative-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Polynomial antiderivatives and the choice of constant batch-20261007-advance-20261009-r05-antiderivative-foundations Question batch · 100 questions ## [Polynomial Differentiation Order and Coefficient Depth](/en/practice/batch-20261007-advance-20261009-r04-derivative-rules-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Differentiating polynomial sums, products, and compositions batch-20261007-advance-20261009-r04-derivative-rules-foundations Question batch · 100 questions ## [Punctured Limit Witness and Point-Value Depth](/en/practice/batch-20261007-advance-20261009-r03-function-limit-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Function limits on punctured real domains batch-20261007-advance-20261009-r03-function-limit-foundations Question batch · 100 questions ## [Nonempty Finite Tree Foundations](/en/practice/batch-20261007-advance-20261009-r02-tree-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Nonempty finite trees: connectivity, cycles, and unique paths batch-20261007-advance-20261009-r02-tree-foundations Question batch · 100 questions ## [Continuous FTC and Oriented Endpoint Foundations](/en/practice/batch-20261007-advance-20261009-r01-fundamental-theorem-calculus-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Fundamental theorem of calculus: continuity and oriented endpoints batch-20261007-advance-20261009-r01-fundamental-theorem-calculus-foundations Question batch · 100 questions ## [Signed Polynomial Integral and Finite Left Sum Foundations](/en/practice/batch-20261007-advance-20261008-r07-definite-integral-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Signed polynomial definite integrals on finite intervals batch-20261007-advance-20261008-r07-definite-integral-foundations Question batch · 100 questions ## [Polynomial Antiderivative and Constant Foundations](/en/practice/batch-20261007-advance-20261008-r06-antiderivative-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Polynomial antiderivatives and the choice of constant batch-20261007-advance-20261008-r06-antiderivative-foundations Question batch · 100 questions ## [Polynomial Differentiation Rule Foundations](/en/practice/batch-20261007-advance-20261008-r05-derivative-rules-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Differentiating polynomial sums, products, and compositions batch-20261007-advance-20261008-r05-derivative-rules-foundations Question batch · 100 questions ## [Real Derivative and Finite Quotient Foundations](/en/practice/batch-20261007-advance-20261008-r04-derivative-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Real derivatives at a point and finite difference quotients batch-20261007-advance-20261008-r04-derivative-foundations Question batch · 100 questions ## [Real Point Value and Continuity Foundations](/en/practice/batch-20261007-advance-20261008-r03-continuity-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Point values and continuity of real functions batch-20261007-advance-20261008-r03-continuity-foundations Question batch · 100 questions ## [Punctured Real Function Limit Foundations](/en/practice/batch-20261007-advance-20261008-r02-function-limit-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Function limits on punctured real domains batch-20261007-advance-20261008-r02-function-limit-foundations Question batch · 100 questions ## [Sequence Limits and Exact Tail Cutoff Foundations](/en/practice/batch-20261007-advance-20261008-r01-sequence-limit-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Sequence limits and exact tail cutoffs batch-20261007-advance-20261008-r01-sequence-limit-foundations Question batch · 100 questions ## [Plane Coordinate Isometry and Uniform Scaling Foundations](/en/practice/batch-20261006-advance-20261007-r07-geometric-transformations-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Plane-coordinate isometries and uniform scaling batch-20261006-advance-20261007-r07-geometric-transformations-foundations Question batch · 100 questions ## [Specified Positive-Scale Triangle Similarity Foundations](/en/practice/batch-20261006-advance-20261007-r06-similarity-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Labeled triangle similarity with a specified positive scale batch-20261006-advance-20261007-r06-similarity-foundations Question batch · 100 questions ## [Labeled Nondegenerate Triangle Congruence Foundations](/en/practice/batch-20261006-advance-20261007-r05-congruence-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Congruence of nondegenerate triangles with explicit correspondence batch-20261006-advance-20261007-r05-congruence-foundations Question batch · 100 questions ## [Real 2×2 Eigenvalue and Nonzero Eigenvector Foundations](/en/practice/batch-20261006-advance-20261007-r04-eigenvalue-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Real eigenvalues and nonzero eigenvectors of 2×2 matrices batch-20261006-advance-20261007-r04-eigenvalue-foundations Question batch · 100 questions ## [Real 2×2 Determinant Foundations](/en/practice/batch-20261006-advance-20261007-r03-determinant-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Determinants of real 2×2 matrices batch-20261006-advance-20261007-r03-determinant-foundations Question batch · 100 questions ## [Real Plane Matrix Linear Map Foundations](/en/practice/batch-20261006-advance-20261007-r02-linear-transformation-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Matrix-represented linear maps on the real plane batch-20261006-advance-20261007-r02-linear-transformation-foundations Question batch · 100 questions ## [Finite Real Matrix Foundations](/en/practice/batch-20261006-advance-20261007-r01-matrix-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Finite matrices: dimensions, indexing, and transpose batch-20261006-advance-20261007-r01-matrix-foundations Question batch · 100 questions ## [Nonempty Observation List Descriptive Statistics Foundations](/en/practice/batch-20261005-advance-20261006-r07-descriptive-statistics-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Descriptive summaries of nonempty observation lists batch-20261005-advance-20261006-r07-descriptive-statistics-foundations Question batch · 100 questions ## [Half-Open Rectangle and Unit-Cell Area Foundations](/en/practice/batch-20261005-advance-20261006-r06-area-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Exact area of half-open rectangles and unit-cell unions batch-20261005-advance-20261006-r06-area-foundations Question batch · 100 questions ## [Circle Boundaries and Zero-Radius Foundations](/en/practice/batch-20261005-advance-20261006-r05-circle-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Circle boundaries and zero-radius degeneracy batch-20261005-advance-20261006-r05-circle-foundations Question batch · 100 questions ## [Equal-Unit Orthonormal Euclidean Distance Foundations](/en/practice/batch-20261005-advance-20261006-r04-distance-formula-foundations/?from=%2Fen%2Fpractice%2F%3Fpage%3D13) Euclidean distance in an equal-unit orthonormal frame batch-20261005-advance-20261006-r04-distance-formula-foundations [← Previous](/en/practice/?page=12#results)[1](/en/practice/?page=1#results) … [12](/en/practice/?page=12#results) 13 [14](/en/practice/?page=14#results) [15](/en/practice/?page=15#results)[Next →](/en/practice/?page=14#results) 360 results · Page 13 of 15