Algebra
Linear equations161 problems · 9 skills
Brackets and distributing 18Consecutive even and odd numbers 18🔒Consecutive integers 17🔒Equations with decimals 18🔒Equations with fractions 18🔒Number from a description 18🔒One- and two-step equations 18🔒Solving proportions 18🔒Variables on both sides 18🔒
Rational equations53 problems · 3 skills
Equations with reciprocals 17Extraneous roots 18🔒Rational equations 18🔒
Radical equations59 problems · 4 skills
Cube root equations 18Nested radical equations 11🔒Radicals with absolute values 12🔒Square root equations 18🔒
Quadratic equations220 problems · 13 skills
Completing the square 18Conditions on the roots 17🔒Equations reducible to quadratics 16🔒Expressions in the roots 18🔒Integer roots with a parameter 17🔒Minimum of a quadratic 18🔒Prime roots of quadratics 16🔒Quadratic bounds on an interval 17🔒Quadratic formula 17🔒Quadratics with integer coefficients 12🔒Solving by factoring 18🔒Sums and products of solutions 18🔒Zeros of a quadratic function 18🔒
Polynomials264 problems · 20 skills
Chains of quadratics 3Common roots 18🔒Constant term of a polynomial 11🔒Degree of a polynomial 18🔒Factor theorem 17🔒Horner's method 15🔒Irreducibility and factorisation 11🔒Iterated polynomials 7🔒Polynomial divisibility 14🔒Polynomial from its values 15🔒Polynomial functional equations 7🔒Polynomials from their roots 12🔒Power sums of roots 14🔒Quartics and quintics 16🔒Rational roots 4🔒Real and nonreal roots 17🔒Remainder theorem 17🔒Roots of cubics 17🔒Sums over roots 13🔒Vieta for cubics 18🔒
Expressions and identities284 problems · 18 skills
Comparing coefficients 15Conjugate surds 18🔒Custom operations 18🔒Cyclic fraction sums 17🔒Difference of squares 18🔒Evaluating cubic expressions 17🔒Evaluating expressions 18🔒Factoring 18🔒Like terms and monomials 8🔒Opposites and reciprocals 13🔒Partial fractions 13🔒Perfect square trinomials 7🔒Rational expressions 16🔒Sum and difference of cubes 17🔒Sum, product and sum of squares 18🔒Undefined values of fractions 18🔒Values from given conditions 17🔒x plus 1/x 18🔒
Systems of equations204 problems · 14 skills
A line meets a curve 14🔒Combining equations 11🔒Consistency and parameters 17🔒Elimination 17🔒Infinitely many solutions 12🔒Parameters from a known solution 6🔒Substitution 16🔒Symmetric sums of three variables 18🔒Symmetric systems 18🔒Systems from ratios 6🔒Systems with reciprocals 18🔒Systems with roots 18🔒Three or more unknowns 17🔒Two numbers from sum and difference 16🔒
Absolute value102 problems · 7 skills
Absolute value equations 18🔒Absolute value graphs 9🔒Expressions with absolute values 18🔒Extremes of absolute value sums 18🔒Non-negative terms summing to zero 17🔒Regions bounded by absolute values 9🔒Sums of solutions 13🔒
Inequalities100 problems · 7 skills
Absolute value inequalities 16🔒Best constant in an inequality 10🔒Greatest and least integer solutions 17🔒Integer solutions of inequalities 15🔒Linear programming 16🔒Quadratic inequality solution sets 18🔒Sign analysis of products 8🔒
Binomial theorem107 problems · 7 skills
Alternating binomial sums 14🔒Binomial sums 12🔒Coefficients in binomial expansions 18🔒Coefficients in products 17🔒Constant term 15🔒Parity of binomial coefficients 13🔒Sums of coefficients 18🔒
Maximum and minimum of expressions257 problems · 19 skills
Best approximation 8🔒Cyclic fractions 17🔒Cyclic products and signs 7🔒Extrema of cubic expressions 11🔒Extrema of quadratic forms 18🔒Extrema of square-root expressions 17🔒Extrema on a circle or conic 18🔒Extrema under product constraints 14🔒Integer maximisation 7🔒Maximum of products 6🔒Maximum sum of squares 8🔒Minimax problems 18🔒Minimum of sums of squares 18🔒Minimum over sequences 16🔒Quartic expressions and products 14🔒Reciprocal sums 18🔒Sums of pairwise products 10🔒Symmetric expressions under constraints 17🔒Two numbers with fixed sum or product 15🔒