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MATH
Mathematics
MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the algebra / test selection.
math
Full text: eligible public problems include text, images and discussion.
Reference links
At a glance
What a problem looks like
A problem statement in LaTeX, with its subject and difficulty level. The worked solution is not part of the prompt.
How it is scored
The source ships a step-by-step solution with every problem; this catalogue keeps it in restricted storage and never renders it.
Metric: accuracy on the final boxed answer
Why it is hard
The problems are written for students who have the technique and need to choose it. Difficulty is stated per problem, so level 5 items are hard by construction rather than by accident.
Cite
@article{hendrycks2021math,
title={Measuring Mathematical Problem Solving With the MATH Dataset},
author={Dan Hendrycks and Collin Burns and Saurav Kadavath and Akul Arora and Steven Basart and Eric Tang and Dawn Song and Jacob Steinhardt},
journal={arXiv preprint arXiv:2103.03874},
year={2021}
}Discussion
Contribute
Share a reproduction, report an evaluation issue, or suggest a correction to this benchmark overview.
Tasks
Whole public benchmark.
- Public problems
- 200
- Formats
- math (200)
- Problems with images
- 0
- Answer availability
- Answer published by the source (200)
- Configs
- algebra (200)
- Splits
- test (200)
- Awaiting a first discussion
- 200
- Problems with a discussion
- 0
- Public contributions
- 0
Provenance and terms
Pinned source revisions, newest first:
21a5633873b6a120296cce3e2df9d5550074f4a3· acquired 2026-09-12 · releaseae4d22a7a5ac21a5633873b6a120296cce3e2df9d5550074f4a3· acquired 2026-09-12 · release7febcb3508c0
- Given the functions f(x)=(x+5)/(3) and g(x)=(1)/(f^(−1)(x)+1), find the value of g(3).
Answer published by the source
- The difference of the roots of the quadratic equation x²+bx+c=0 is |b−2c|. If c≠0, then find c in terms of b.
Answer published by the source
- Given that f(x) is a function such that f(1)=2, f(4)=3, f(7)=4, and f^(−1)(x) is the inverse of f(x), what is f^(−1)(f^(−1)(3))?
Answer published by the source
- A sequence starts with the term 2222. Each succeeding term is found by adding…
Answer published by the source
- A bookstore is deciding what price it should charge for a certain book. After…
Answer published by the source
- Let f(x)=x+1 and g(x)=2x. Also denote the inverses to these functions as f^(−1) and g^(−1). Compute f(g^(−1)(f^(−1)(f^(−1)(g(f(5)))))).
Answer published by the source
- The vertex of the parabola described by the equation y=2x²−4x+4 is (m,n). What is m?
Answer published by the source
- Let m and n satisfy mn=7 and m+n=8. What is |m−n|?
Answer published by the source
- Of the four points (2,2), (9,11), (5,7), and (11,17), three lie on the same line. Which point is not on the line?
Answer published by the source
- For what real value of k is (13−√(131))/(4) a root of 2x²−13x+k?
Answer published by the source
- Find the domain of √(6−x−x²).
Answer published by the source
- If a and b are the solutions to the equation x²−5x+9=0, what is the value of (a−1)(b−1)?
Answer published by the source
- Two consecutive positive even numbers are each squared. The difference of the…
Answer published by the source
- What is the value of x in the equation (17^6-17^5)div16=17^x?
Answer published by the source
- If m is a real number and 2x²+mx+8 has two distinct real roots, then what are the possible values of m? Express your answer in interval notation.
Answer published by the source
- Suppose that f is a function and f^(−1) is the inverse of f. If f(1)=2, f(2)=6, and f(3)=5, then what is f^(−1)(f^(−1)(6))?
Answer published by the source
- Let a be a real number for which there exists a unique value of b such that the quadratic equation x²+2bx+(a−b)=0 has one real solution. Find a.
Answer published by the source
- The points (x,y) represented in this table lie on a straight line. The point (13,q) lies on the same line. What is the value of p + q? Express your answer as a decimal to the neare…
Answer published by the source
- A line ℓ passes through the points B(7,−1) and C(−1,7). The equation of this line can be written in the form y=mx+b; compute m+b.
Answer published by the source
- If a=8, what is the value of (16root[3](a²))^((1)/(3))?
Answer published by the source
- What is the largest integer n such that (1 + 2 + 3 + cdots+ n)^2 < 1^3 + 2^3 + cdots+ 7^3?
Answer published by the source
- Consider the function g(x)=3. Find g(2).
Answer published by the source
- Let f(x)=2^(x). Find √(f(f(f(f(1))))).
Answer published by the source
- Evaluate log₂64.
Answer published by the source
- Define f(x)=(x²+2x+3)/(x) and g(x)=x³+2. Evaluate g(f(x)) when x=−3.
Answer published by the source
- The function f(x) is graphed below. Each small box has width and height 1.
Answer published by the source
- The function f(n)=n²+n+17 for 0≤n≤15 generates prime numbers. What is the value of f(10)−f(9)?
Answer published by the source
- The height (in meters) of a shot cannonball follows a trajectory given by h(t)=−4.9t²+14t−0.4 at time t (in seconds). As an improper fraction, for how long is the cannonball above …
Answer published by the source
- Let f(x)=7x+5 and g(x)=x−1. If h(x)=f(g(x)), then what is the inverse of h(x)?
Answer published by the source
- Given that the point (8,8) is on the graph of y=(1)/(4)f((1)/(2)x), there is one point that must be on the graph of y=f(x). What is the sum of coordinates of that point?
Answer published by the source
- Solve for x: (√(12x)+12)(√(3x)−6)=4(x+3)+x−34
Answer published by the source
- Let a be the smallest integer satisfying the inequality x²−15<2x, and let b be the largest integer satisfying the same inequality. What is b−a?
Answer published by the source
- Eleven pencils cost as much as three pens. If seven pens cost 9.24, what is the cost, in cents, of one pencil?
Answer published by the source
- In a 8 fluid ounce bottle of Vitamin Water, there are 125 calories. How many…
Answer published by the source
- Let f(x) =
begin{cases}
k(x) &text{if }x>3,
x^2-6x+12&text{if }xleq3.
end{cases}
Find the function k(x) such that f is its own inverse.
Answer published by the source
- Find the radius of the circle with equation x²+8x+y²−6y=0.
Answer published by the source
- Let f(x) =
begin{cases}
3x + 5 &text{if }x<-3,
7-4x&text{if }xge -3.
end{cases}
Find f(−10).
Answer published by the source
- The solutions to the equation (x+1)(x+2)=x+3 can be written in the form m+√(n) and m−√(n), where m and n are integers. What is m+n?
Answer published by the source
- The solutions of x(x−3)=1 may be expressed in the form (a+√(b))/(c) and (a−√(b))/(c), where a, b, and c are prime numbers. Find abc.
Answer published by the source
- The expression 24x²−19x−35 can be written as (Ax−5)(2Bx+C), where A, B, and C are positive numbers. Find AB−3C.
Answer published by the source
- What is the sum of all of the multiples of 3 between 100 and 200?
Answer published by the source
- Find (1)/(a−1)+(1)/(b−1), where a and b are the roots of the quadratic equation 2x²−7x+2=0.
Answer published by the source
- Express 0.6(333)¯ as a common fraction.
Answer published by the source
- Eight pounds of feathers and two ounces of gold together cost 932. Fourteen pounds of feathers and three ounces of gold together cost 1402. What is the cost of five pounds of feath…
Answer published by the source
- Simplify (3−i)(6+2i).
Answer published by the source
- Given positive integers x and y such that 2x²y³+4y³=149+3x², what is the value of x+y?
Answer published by the source
- A horse 64 feet from the center of a merry-go-round makes 27 revolutions. In…
Answer published by the source
- For the arithmetic sequence 1000, ~987, ~974, ~961, ldots , what is the least positive integer in the sequence?
Answer published by the source
- The point (a,b) lies on the line with the equation 3x+2y=12. When a=4, what is the value of b?
Answer published by the source
- Evaluate root[3](12)×root[3](20)×root[3](15)×root[3](60).
Answer published by the source