Hard math problems for advanced students
Generate hard math problems for advanced middle and high school students: multi-step, contest-style questions in algebra, geometry, and number theory.
Free · No account · Up to 40 problems · Answer key included
Tip: Describe the specific skill or topic. The generator calibrates complexity to the grade level you pick.
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What makes a math problem hard?
Hard math problems are problems where the difficulty comes from finding the idea that starts the solution, such as a pattern, a substitution, or a case split, more than from long computation. This generator writes challenging sets with an answer key. Work each problem before assigning it, since generated hard problems can contain errors.
Where the difficulty comes from
Some contest problems need a pattern: powers of 7 end in 7, 9, 3, 1 in turn, so 7^100 ends in 1. Others combine topics, need an extra line in a diagram, or reward working backward. Name the kind you want:
Number theory: divisibility, remainders, prime factorization
Counting: arrangements with conditions, the pigeonhole principle
Geometry: similar triangles, auxiliary lines, area arguments
Algebra: substitutions, Vieta's formulas, inequalities
Strategies: working backward, looking for invariants
The AMC and MATHCOUNTS ladder
Each step up asks for more technique and less arithmetic, so name the contest and level you want.
MATHCOUNTS (grades 6-8): Sprint Round of 30 problems in 40 minutes, no calculator
MATHCOUNTS also has Target (8 problems in pairs), Team, and Countdown rounds
AMC 8: 25 multiple-choice problems in 40 minutes, 8th grade and below
AMC 10 and AMC 12: 25 problems in 75 minutes
AIME: 15 problems in 3 hours, for high AMC 10 and 12 scorers
Contest style and olympiad style
Olympiad problems (USAJMO, USAMO) take sustained work and are answered with proofs, unlike the short numerical answers of AMC and MATHCOUNTS. Ask for proof-style problems by name and review the generated solutions closely.
How the math problem generator works
- 1
Describe the set
The topic and the format, such as two-step equations or fraction word problems about cooking.
- 2
Set the details
Grade, difficulty, and number of problems. It usually takes 10 to 20 seconds.
- 3
Check and print
Work a few problems yourself, then print the student copy and the answer key.
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Grading the completed problem sets?
GradeWithAI reads handwritten math from scans or phone photos and gives partial credit under your rubric or answer key. You review each score before it posts.
Grading the completed math work? See how the AI math grader gives partial credit
They make useful extra practice. For serious preparation, also work through past contests: past AMC problems and solutions are posted on the Art of Problem Solving wiki, and MATHCOUNTS offers past competition materials.
Aim for a set where your student solves some problems quickly, works hard on a few, and misses some. If everything is easy, move up a level (AMC 8 to AMC 10); if almost nothing gets solved, step down and build the underlying topic first.
Yes. Name it in the description ('hard geometry problems, AMC 10 level' or 'challenging counting problems for 7th grade') and choose the grade closest to your student.
Addition, subtraction, multiplication, division (including long division), fractions, decimals, ratios, percents, pre-algebra, Algebra 1 and 2, and geometry.
Yes. Ask for word problems in the description, and add a context such as sports, animals, or food if you like.
Pick the grade, which sets the kind of numbers and operations, then choose easy, medium, or hard.
Yes. Every problem has an answer, printed on a separate page. Work a few problems yourself before handing the set out, since AI-generated math can contain mistakes.
No. It writes problems. To grade completed work, upload it to GradeWithAI, which reads handwritten math and gives partial credit under your rubric or answer key.
Yes, with no account.
Math problems by grade and topic
Starting points with the grade and topic filled in.
By operation
- Addition problems generator
- Addition word problems generator
- Subtraction problems generator
- Subtraction word problems generator
- Multiplication word problems generator
- Division problems generator
- Division word problems generator
- Long division problems generator
- Long division practice problems by level
- Fraction problems generator
- Fraction word problems generator
- Addition and subtraction word problems
- Multiplication and division word problems
By grade
- Math word problems generator
- 1st grade math word problems
- 2nd grade math word problems
- 3rd grade math word problems
- 4th grade math word problems
- 5th grade math word problems
- 6th grade math word problems
- Math problems for 2nd graders
- 3rd grade math problems
- 4th grade math problems
- 5th grade math problems
- 1st grade math problems
- 6th grade math problems
- 7th grade math problems
- 8th grade math problems
Difficulty
Algebra
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