Practice Exercises
Randomly generated exercises with guaranteed nice values — solve them on paper, then check the worked solution step by step.
Determinant — Practice
Randomly generated determinant exercises. Solve them on paper, then check the worked solution.
Matrix Inversion — Practice
Randomly generated inversion exercises — every matrix has an integer inverse. Solve on paper, then check the worked solution.
Diagonalization — Practice
Randomly generated matrices with distinct integer eigenvalues. Diagonalize on paper, then check the worked solution.
Linear Systems — Practice
Randomly generated systems with unique integer solutions. Solve on paper, then check the worked solution.
Quadratic Equations — Practice
Randomly generated equations with rational roots. Solve on paper, then check the worked solution.
Percentages — Practice
Randomly generated percentage problems with whole-number answers. Solve on paper, then check the worked solution.
Logarithms — Practice
Randomly generated logarithm exercises — every one has an exact rational answer. Solve on paper, then check the worked solution.
Fractions — Practice
Random fraction arithmetic: add, subtract, multiply or divide two fractions. Solve on paper, then check the worked solution.
GCD & LCM — Practice
Random pairs of numbers with moderate values and exact answers. Solve on paper, then check the worked solution.
Prime Factorization — Practice
Random composite numbers in a hand-computable range. Factor on paper, then check the worked solution.
Combinatorics — Practice
Random factorials, permutations and combinations with moderate values. Solve on paper, then check the worked solution.
Sequences & Series — Practice
Random arithmetic and geometric sequences with exact fraction answers. Solve on paper, then check the worked solution.
Derivatives & Integrals — Practice
Random polynomial exercises: derivatives, antiderivatives and definite integrals with exact answers. Solve on paper, then check the worked solution.
Binomial Distribution — Practice
Random binomial exercises with clean probabilities: point probabilities, cumulative probabilities, expected value and variance — all exact fractions. Solve on paper, then check the worked solution.
Statistics — Practice
Random small data sets with an integer mean and a clear mode. Compute on paper, then check the worked solution.
Equation of a Line — Practice
Random pairs of integer points: find the slope, the intercepts and the equation of the line exactly. Solve on paper, then check the worked solution.
Polynomial Division — Practice
Random divisions with integer quotients and remainders. Solve on paper, then check the worked solution.
Matrix Powers — Practice
Random 2×2 integer matrices raised to the power 2 or 3. Compute on paper, then check the worked solution.
Matrix Arithmetic — Practice
Random additions and multiplications of 2×2 integer matrices. Compute on paper, then check the worked solution.
Base Conversion — Practice
Random conversions between binary, ternary, quinary, octal, decimal and hexadecimal. Convert on paper, then check the worked solution.
Eigenvalues — Practice
Random matrices with distinct integer eigenvalues. Find them on paper, then check the worked solution.
Pythagorean Theorem — Practice
Randomly generated right-triangle problems with whole-number answers. Solve on paper, then check the worked solution.
Scientific Notation — Practice
Randomly generated scientific-notation problems with exact, clean answers. Solve on paper, then check the worked solution.