Math practice problems with worked solutions
Pick a subject, try a problem on paper, then open the full solution. Every answer and every step on these pages is produced and checked by the exact math engine, not written by hand or guessed by AI.
Algebra problems
Linear and quadratic equations, functions, inequalities, systems, polynomials, exponentials and logarithms.
A two-step linear equation: undo the addition, then the multiplication.
Variables on both sides: collect the x-terms on one side first.
Distribute before collecting like terms.
A quadratic that factors over the integers.
Leading coefficient other than one: the quadratic formula works every time.
Remember both square roots.
Rise over run between the two points.
A negative discriminant gives complex roots.
The solution is negative; check it in the original equation.
Calculus problems
Limits, derivatives, integrals, series and multivariable ideas, with verified step-by-step work.
A direct application of the power rule.
A product of two functions needs the product rule.
The chain rule with a linear inner function.
The Fundamental Theorem with the power rule for antiderivatives.
Antiderivative x squared, evaluated at the bounds.
A basic trigonometric antiderivative; do not forget the constant.
Chain rule with the natural logarithm.
The area of a triangle with base 4 and height 4.
Arithmetic problems
Whole numbers, fractions, decimals and percentages: the number sense every later course relies on.
Compare prime factorizations and keep the shared primes.
The smallest number both divide into.
Take each prime at its highest power.
Fractions need a common denominator before adding.
Rewrite both over twelfths.
Convert the percentage to a decimal and multiply.
Divide the part by the whole.
Geometry problems
Angles, triangles, circles, area and volume, coordinate geometry and proof.
Statistics problems
Describing data, the normal distribution, confidence intervals, correlation and regression.
How to get the most from practice problems
Work the problem yourself before you look. Reading a solution feels like understanding, but recall is what builds skill: write down your method and your answer, then open the solution and compare line by line.
When your answer differs, find the first step where your working and the solution part ways. That step is the idea to review. Each problem page links to the matching calculator and to the solver, where you can check an answer of your own or reveal the method one hint at a time.
Mix problem types once a topic feels comfortable. Switching between, say, linear equations, quadratics and derivatives forces you to choose a method instead of repeating the last one, which is closer to how tests work.
Have your own problem? Use the step-by-step solver.