| 103 | One step at a time | Easy | Lemma | Distributive lawBalancing | |
| 740 | Clear the fractions | Easy | Lemma | Linear equations | |
| 741 | A decimal coefficient | Easy | Lemma | Linear equations | |
| 742 | A line through two points | Easy | Lemma | Linear equations | |
| 743 | Brackets on both sides | Easy | Lemma | Linear equations | |
| 930 | Numbers in a given ratio with a difference | Easy | Hall & Knight | RatioDifference | |
| 1175 | Multiplying Complex Surds | Easy | Hall & Knight | imaginary numbersmultiplication | |
| 1176 | Difference of Two Squares with Complex Numbers | Easy | Hall & Knight | difference of squaresimaginary numbers | |
| 1177 | Exponential Complex Expression Product | Easy | Hall & Knight | exponential formdifference of squares | |
| 1178 | Quadratic Factor with Complex Roots | Easy | Hall & Knight | complex rootsquadratic polynomials | |
| 1179 | Rationalizing a Complex Denominator | Easy | Hall & Knight | rationalizationcomplex conjugates | |
| 1529 | Number of Terms in Trinomial Expansion | Easy | Hall & Knight | CombinatoricsMultinomial Theorem | |
| 1530 | Sum of Coefficients in Trinomial Expansion | Easy | Hall & Knight | Sum of CoefficientsMultinomial Theorem | |
| 929 | Find x from a duplicate ratio condition | Medium | Hall & Knight | Duplicate ratioProportion | |
| 931 | Number to add to a ratio | Medium | Hall & Knight | RatioAdjustment | |
| 932 | Proving an Algebraic Ratio Identity | Medium | Hall & Knight | ratioproportion+1 | |
| 933 | Continued Proportion Identity | Medium | Hall & Knight | continued proportionalgebraic manipulation+1 | |
| 934 | Symmetric Ratio Relation | Medium | Hall & Knight | ratiosymmetry+1 | |
| 936 | Fractional Sum with Cubes | Medium | Hall & Knight | ratiosubstitution+1 | |
| 937 | Reciprocal proportionality | Medium | Hall & Knight | proportionalitysymmetry | |
| 938 | Equality case of Cauchy–Schwarz | Medium | Hall & Knight | Cauchy–Schwarzproportionality | |
| 939 | Cyclic proportionality | Medium | Hall & Knight | cyclic symmetryratios | |
| 941 | Eliminate variables from a three‑equation system | Medium | Hall & Knight | determinantelimination | |
| 943 | Relation among three variables | Medium | Hall & Knight | systemssymmetry | |
| 949 | Coupled linear conditions | Medium | Hall & Knight | simultaneous equationssymmetry | |
| 956 | Proportion radical identity | Medium | Hall & Knight | proportionsratios | |
| 957 | Continued proportion identity I | Medium | Hall & Knight | continued proportionratios | |
| 958 | Continued proportion identity II | Medium | Hall & Knight | continued proportionratios | |
| 959 | Continued proportion identity III | Medium | Hall & Knight | continued proportionalgebraic identity | |
| 960 | Mean proportional algebraic relation | Medium | Hall & Knight | mean proportionalexponents | |
| 961 | Product proportion identity | Medium | Hall & Knight | proportionscomponendo and dividendo | |
| 962 | Solve rational equation | Medium | Hall & Knight | Rational equationsFactorisation | |
| 963 | Solve quartic rational equation | Medium | Hall & Knight | Rational equationsFactorisation | |
| 964 | Solve linear fractional equation | Medium | Hall & Knight | Cross‑multiplicationLinear equations | |
| 967 | Work‑men‑days proportion problem | Medium | Hall & Knight | ProportionWork problems | |
| 1180 | Rationalizing a Complex Quotient | Medium | Hall & Knight | rationalizationsurds | |
| 1199 | Product involving cube roots | Medium | Hall & Knight | Cube roots of unityPeriodicity of powers of omega | |
| 1200 | Power of binomials with omega | Medium | Hall & Knight | Cube roots of unityAlgebraic simplification | |
| 1202 | Sum of cubes factorization | Medium | Hall & Knight | Cube roots of unityPolynomial factorization | |
| 1293 | Radical Equation Solution | Medium | Hall & Knight | Algebraic manipulationRadical equations | |
| 1296 | Fractional Radical Equation | Medium | Hall & Knight | Cross-multiplicationRadical equations | |
| 1297 | Complex Radical Equation | Medium | Hall & Knight | Radical equationsSubstitution | |
| 1300 | Reciprocal Fractions Equation | Medium | Hall & Knight | Reciprocal substitutionAlgebraic simplification | |
| 1370 | Dividing 136 with Remainders | Medium | Hall & Knight | Diophantine equationsremainders | |
| 1371 | Purchasing Three Types of Animals | Medium | Hall & Knight | Diophantine equationsword problems | |
| 1372 | Coins in a Pocket | Medium | Hall & Knight | Diophantine equationscurrency word problem | |
| 1429 | Binomial coefficient sum relation | Medium | Hall & Knight | Binomial TheoremCombinatorial Identities | |
| 1431 | Weighted sum of binomial coefficients | Medium | Hall & Knight | Binomial TheoremIntegration | |
| 1432 | Sum of squared binomial coefficients | Medium | Hall & Knight | Binomial TheoremVandermonde's Identity | |
| 1498 | Coefficient Periodic Pattern | Medium | Hall & Knight | Generating FunctionsPower Series | |
| 1499 | Factorial Series Identity for Even n | Medium | Hall & Knight | Binomial CoefficientsCombinatorial Identities | |
| 1514 | Symmetric combinations of variables with omega (part 1) | Medium | Hall & Knight | Cube roots of unityAlgebraic identity | |
| 1515 | Symmetric combinations of variables with omega (part 2) | Medium | Hall & Knight | Cube roots of unityAlgebraic identity | |
| 1516 | Symmetric combinations of variables with omega (part 3) | Medium | Hall & Knight | Cube roots of unityAlgebraic identity | |
| 1531 | Alternating Binomial Coefficient Identity | Medium | Hall & Knight | Binomial TheoremCoefficient Extraction | |
| 1532 | Weighted Alternating Binomial Sum | Medium | Hall & Knight | Binomial TheoremDifferentiation | |
| 935 | Cyclic Sum Ratio Identity | Deep | Hall & Knight | ratiocyclic symmetry+1 | |
| 940 | Eliminant of a symmetric system | Deep | Hall & Knight | determinantsymmetry | |
| 942 | Quadratic ratios from cyclic definitions | Deep | Hall & Knight | cyclic equationsratios | |
| 948 | Relations among three fractional expressions | Deep | Hall & Knight | rationalisationsymmetry | |
| 965 | Prove proportion identity | Deep | Hall & Knight | ProportionalityAlgebraic manipulation | |
| 966 | Continued proportion identity | Deep | Hall & Knight | Continued proportionAlgebraic identities | |
| 995 | Planetary Attraction and Satellite Revolutions | Deep | Hall & Knight | ProportionalityAstrophysical formulas | |
| 1201 | Product of $2n$ factors with omega | Deep | Hall & Knight | Cube roots of unityProducts of sequences | |
| 1298 | Homogeneous Radical Equation | Deep | Hall & Knight | Homogeneous equationsFractional exponents | |
| 1299 | Radical Equation with Parameters | Deep | Hall & Knight | Radical equationsAlgebraic manipulation | |
| 1430 | Product of adjacent binomial coefficients | Deep | Hall & Knight | Binomial TheoremAlgebraic Manipulation | |
| 1433 | Sum of products of binomial coefficients | Deep | Hall & Knight | Binomial TheoremCombinatorial Identities | |
| 1496 | Middle Term Coefficient Identity | Deep | Hall & Knight | Binomial TheoremCoefficient Extraction | |
| 1497 | Expansion Form of Cubic Power | Deep | Hall & Knight | Binomial TheoremSeries Expansion | |
| 1503 | Quadratic form ratios | Deep | Hall & Knight | determinantssymmetry | |
| 1504 | Product identity for cofactors | Deep | Hall & Knight | determinantscofactor identity | |
| 1533 | Sum of Squares of Alternating Coefficients | Deep | Hall & Knight | Binomial TheoremCauchy Product | |
| 1897 | A joint work problem | Deep | Hall & Knight | Simultaneous equationsRate problems | |