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SynerMath-v2-15k

seed_id dict	question stringlengths 48 2.67k	thought stringlengths 372 17.4k	answer stringlengths 1 9.85k
{ "seed_index": 150, "rephrase_index": 2 }	A rectangular garden is designed such that its length is represented by the polynomial expression $ (x^2 + 3x + 2)(x^2 + 7x + 12) $ and its width is given by $ (x^2 + 5x - 6) $. First, factor both the length and width expressions as products of two non-constant polynomials. Next, express the area of the garden as a...	To solve this problem, we will first factor the polynomial expressions for the length and width of the garden. Then, we will calculate the area by multiplying the length and width expressions, and finally, we'll factor the resulting area expression. 1. Factor the Length Expression: The length is given by the polyn...	(x + 1)(x + 2)(x + 3)(x + 4), (x + 6)(x - 1)
{ "seed_index": 324, "rephrase_index": 1 }	Sally is saving for a trip to Sea World, where she has already saved $28. The expenses include the following costs: $10 for parking, $55 for entry, and $25 for a meal pass. Sea World is 165 miles away, and her car averages 30 miles per gallon, with gas priced at $3 per gallon. If Sally has two friends joining her for t...	To determine how much more Sally needs to save for her trip, we will follow the outlined steps carefully. 1. Calculate Total Costs: - Parking Cost: $10 - Entry Cost: $55 - Meal Pass Cost: $25 - Distance to Sea World: 165 miles - Car Mileage: 30 miles per gallon - *Gas Price:...	75
{ "seed_index": 1032, "rephrase_index": 5 }	The image of a point with coordinates $(-3,-1)$ under reflection across the line defined by $y=mx+b$ results in the point $(5,3)$. If the slope $m$ is constrained to be positive and must not exceed 2, determine the values of $m$ and $b$ such that the midpoint of the segment connecting these two points lies on the line,...	To solve the problem, we need to analyze the reflection of the point $(-3,-1)$ across the line defined by $y=mx+b$ which results in the point $(5,3)$. 1. Midpoint Calculation: First, we calculate the midpoint $M$ of the segment connecting the points $(-3,-1)$ and $(5,3)$. \[ M = \left(\frac{-3 +...	1
{ "seed_index": 235, "rephrase_index": 3 }	Christine must buy at least 45 fluid ounces of milk at the store, and the store sells milk only in 200 milliliter bottles, where 1 liter is equivalent to 33.8 fluid ounces. If each bottle costs $2.50, and Christine has a budget of $15, calculate the smallest number of bottles Christine can buy while ensuring she meets ...	To solve this problem, we need to determine how many 200 milliliter bottles of milk Christine must buy to meet both the fluid ounce requirement and the budget constraint. Step 1: Convert fluid ounces to milliliters. - We know that 1 liter is equivalent to 33.8 fluid ounces. Since 1 liter is also 1000 milliliters, ...	17.50
{ "seed_index": 106, "rephrase_index": 1 }	For integers $ a $ and $ T $, where $ T \neq 0 $ (ensuring that the points $ A $ and $ B $ are distinct, thus properly defining the parabola), a parabola is defined by the equation $ y = ax^2 + bx + c $ and it passes through the points $ A = (0,0) $, $ B = (2T,0) $, and $ C = (2T + 1,28) $. To find th...	To find the coefficients $ a $, $ b $, and $ c $ of the parabola defined by the equation $ y = ax^2 + bx + c $ that passes through the points $ A = (0,0) $, $ B = (2T,0) $, and $ C = (2T + 1,28) $, we will substitute each point into the equation to create a system of equations. 1. **Substituting Point A:...	27
{ "seed_index": 448, "rephrase_index": 1 }	A store sells an item for $1000_7$ in base 7. After applying a discount of $666_7$ (also in base 7), convert both prices to base 10. What is the final price of the item after applying the discount?	To solve the problem, we first need to convert both the original price and the discount from base 7 to base 10. After that, we will subtract the discount from the original price to find the final price. 1. Convert the original price $1000_7$ to base 10: - The number $1000_7$ can be expressed as: \[ ...	1
{ "seed_index": 674, "rephrase_index": 1 }	In a park, several birds are sitting in the branches of a crape myrtle tree. If there are exactly 2 swallows (which is half the number of bluebirds), then there are 4 bluebirds. Since there are three times as many cardinals as bluebirds, there are 12 cardinals. Given these numbers, determine the total number of birds i...	To find the total number of birds in the tree, we will first identify the number of each type of bird based on the provided relationships. 1. We know the initial number of swallows is given as 2. This is half the number of bluebirds. Therefore, we can find the number of bluebirds: \[ \text{Number of Bluebirds} =...	30
{ "seed_index": 613, "rephrase_index": 0 }	You have five keys: a house key, a car key, an office key, a mailbox key, and a gym key. You want to arrange these keys on a keychain with the following conditions: 1. The house key and car key must be adjacent to each other. 2. The mailbox key must not be adjacent to the office key. When counting the arrangements,...	To solve this problem, we begin by treating the house key and car key as a single block, which we will refer to as "HC". This reduces the problem to arranging four entities: HC, office key (O), mailbox key (M), and gym key (G). 1. Arranging the blocks: Since the arrangement is circular, we can fix one key to elim...	2
{ "seed_index": 795, "rephrase_index": 2 }	On a school trip to the local museum, Mr. Gordon observes the following: - There are 50 boys on the trip. - The number of girls is $ \frac{7}{5} $ times the number of boys. - Additionally, the bus carries a driver, an assistant, and Mr. Gordon as the teacher. Calculate the total number of people on the bus.	To find the total number of people on the bus, we need to calculate the number of girls and then sum all individuals involved in the trip. 1. Given Data: - Number of boys: $ B = 50 $ - Number of girls: $ G = \frac{7}{5} \times B $ 2. Calculate the Number of Girls: - Substituting the known num...	123
{ "seed_index": 950, "rephrase_index": 0 }	The population of a certain species is modeled by the rational function $ P(x) = \frac{5x^2-9}{3x^2+5x+2} $, where $x$ represents time in years. Determine the horizontal asymptote $y = a$ as $x$ approaches infinity, and interpret what this value signifies for the long-term behavior of the population. What is th...	To find the horizontal asymptote of the rational function $ P(x) = \frac{5x^2-9}{3x^2+5x+2} $ as $ x $ approaches infinity, we will analyze the degrees of the polynomial in the numerator and denominator. 1. Identify the degrees of the polynomials: - The numerator $ 5x^2 - 9 $ is a polynomial of degree 2. -...	\dfrac{5}{3}
{ "seed_index": 741, "rephrase_index": 0 }	Carmela has $7, and each of her four cousins has $2. Let $ x $ be the amount of money Carmela decides to give to each cousin. Calculate the maximum value of $ x $ such that after distributing this amount to her cousins, each cousin ends up with the same amount of money and Carmela retains at least $1. What is the l...	To find the maximum value of $ x $ that Carmela can give to each cousin while retaining at least $1, we will analyze the problem step-by-step. 1. Identify the initial amounts: - Carmela has $7. - Each of her 4 cousins has $2. 2. Define the final amounts: - After giving $ x $ to each cousin, Ca...	1.5
{ "seed_index": 637, "rephrase_index": 0 }	A dog is being treated for fleas. The first flea treatment eliminates half of the initial flea population. After each treatment cycle, the remaining fleas double in number before the next treatment. The second treatment eliminates one-third of the remaining fleas, the third treatment reduces the count by one-quarter, a...	Let $ x $ be the initial number of fleas. We will analyze each treatment step-by-step, keeping track of how the flea population changes after each treatment. 1. After the first treatment: - The first treatment eliminates half of the initial population, leaving: \[ \text{Remaining} = x - \frac{x}{2} = \f...	30
{ "seed_index": 1235, "rephrase_index": 2 }	Jenny is currently 5 years older than Charlie, who is 3 years older than Bobby. If we denote Jenny's current age as $ J $ years, Bobby's age as $ B $ years, and Charlie's age as $ C $ years, we can establish the following relationships: $ C = B + 3 $ and $ J = C + 5 $. Calculate how long it will take, in year...	To solve the problem, we need to establish the relationships between the ages of Jenny, Charlie, and Bobby based on the information given. 1. We have the relationships: - $ C = B + 3 $ (Charlie is 3 years older than Bobby) - $ J = C + 5 $ (Jenny is 5 years older than Charlie) 2. We can substitute $ C $ f...	11
{ "seed_index": 1262, "rephrase_index": 2 }	In this problem, you will analyze the relationship between three vectors in three-dimensional space. Consider the vectors $\mathbf{a} = \begin{pmatrix} 3 \\ 1 \\ -2 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 0 \\ 2 \\ -1 \end{pmatrix}$. Let $ \mathbf{c} = \begin{pmatrix} 4 \\ 1 \\ -4 \end{pmatrix} $. Determ...	To find the values of the scalars $p$, $q$, and $r$ that satisfy the vector equation $\mathbf{c} = p \mathbf{a} + q \mathbf{b} + r (\mathbf{a} \times \mathbf{b})$, we start by calculating the cross product $\mathbf{a} \times \mathbf{b}$. 1. Calculate $\mathbf{a} \times \mathbf{b}$: \[ \mathbf{a} ...	-\dfrac{5}{3}
{ "seed_index": 1055, "rephrase_index": 2 }	Given that $ 5^{2004} $ has exactly 1401 digits, we analyze the integers formed by the exponential growth of base 5 for data encoding, defined as $ S = \{5^k \mid k \in \mathbb{Z}, 0 \le k \le 2004\} $. We seek to find how many of these elements of $ S $ have a numeric representation that starts with the digit 1....	To find the count of integers $ 5^k $ that start with the digit 1 for $ k $ in the range $ 0 $ to $ 2004 $, we first need to analyze the logarithmic representation of $ 5^k $. 1. Logarithmic Representation: The number of digits $ d $ of a number $ n $ can be determined by the formula: \[ d = \...	604
{ "seed_index": 627, "rephrase_index": 2 }	Let $ S $ denote the value of the following sum: \[ S = \sum_{n=0}^{668} (-1)^{n} {2004 \choose 3n}. \] This sum represents the calculation of an alternating series of binomial coefficients for selecting groups of 3 from a set of 2004 objects. To determine the value of $ S $, you can utilize the binomial theore...	To evaluate the sum $ S = \sum_{n=0}^{668} (-1)^{n} {2004 \choose 3n} $, we can use generating functions and properties of binomial coefficients. 1. Generating Function: The binomial theorem states that: \[ (1+x)^{2004} = \sum_{k=0}^{2004} {2004 \choose k} x^k \] We are interested in the coefficients...	6
{ "seed_index": 417, "rephrase_index": 2 }	Lee wants to buy a pair of sneakers that cost $90. He has already saved $15. To buy the sneakers at $90 and still have $25 remaining, Lee needs a total of $115 from his sales. If the total revenue from selling the action figures must equal $115, and he plans to sell 10 action figures, how much should he charge per acti...	To find out how much Lee should charge per action figure, we need to determine the total revenue he needs from selling 10 action figures and then divide that total by the number of action figures he plans to sell. 1. Given Data: - Cost of sneakers = $90 - Amount saved = $15 - Amount Lee wants remaining a...	11.5
{ "seed_index": 537, "rephrase_index": 1 }	Consider a competition where 10 contestants are ranked with integers from 1 to 10. For each pair of adjacent contestants ranked in any given permutation, calculate the absolute difference between their rankings. Specifically, for each possible ranking (permutation) of these contestants, you need to determine the follow...	To solve the problem, we need to analyze the sum of absolute differences between adjacent contestants for all permutations of the rankings from 1 to 10. The goal is to find the average value of this sum over all possible rankings. 1. Understanding the Sum: The sum we need to calculate for a permutation \( (a_1, a_...	83
{ "seed_index": 1467, "rephrase_index": 1 }	Given a vector $\mathbf{v} = \begin{pmatrix} 2 \\ -3 \end{pmatrix}$ representing a direction in 2D space, determine the projection matrix that projects onto this vector. Then, calculate the projection of the point $\mathbf{p} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$. Additionally, interpret the significance of this proj...	To solve for the projection matrix that projects onto the vector $\mathbf{v} = \begin{pmatrix} 2 \\ -3 \end{pmatrix}$ and to compute the projection of the point $\mathbf{p} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$, we will follow these steps: 1. Calculate the projection matrix: The projection matrix $ P $ ...	\begin{pmatrix} -\frac{12}{13} \\ \frac{18}{13} \end{pmatrix}
{ "seed_index": 582, "rephrase_index": 0 }	Jason is trying to remember the five-digit combination to his safe, which consists only of the digits 1 through 5. The combination must satisfy the following conditions: every even digit (2, 4) must be followed by an odd digit (1, 3, 5), and every odd digit (1, 3, 5) must be followed by an even digit (2, 4). This means...	To find the total number of valid five-digit combinations based on the given conditions, we need to analyze how the digits can be arranged while adhering to the rules. The digits available are 1, 2, 3, 4, and 5. The even digits are 2 and 4, while the odd digits are 1, 3, and 5. According to the problem: - Every even d...	15
{ "seed_index": 795, "rephrase_index": 0 }	In a town, the heights of three consecutive trees are in a geometric sequence. The first tree has a height of 140 cm and the third tree has a height of $\frac{45}{28}$ meters. Given that the height of the second tree $a$ must be a positive integer, determine the height of the second tree in centimeters. Please prov...	To solve for the height of the second tree in a geometric sequence, we need to utilize the properties of geometric sequences. In a geometric sequence, the ratio of consecutive terms is constant. We know the heights of the first and third trees, which are given as follows: - Height of the first tree (first term, \(a_1\...	150
{ "seed_index": 1389, "rephrase_index": 2 }	Consider a triangle with two sides measuring 2 cm each and the third side measuring $x = \sqrt{6} - \sqrt{2}$ cm. In a real-world context where measuring errors could result in the side length being $x \pm 0.1$ cm, compute the angles of the triangle using the Law of Cosines. Present the angles in degrees and calcul...	To solve for the angles of the triangle with sides 2 cm, 2 cm, and $x = \sqrt{6} - \sqrt{2}$ cm, I will use the Law of Cosines, which states that for any triangle with sides $a$, $b$, and $c$, the angle opposite side $c$ can be calculated as: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \] In our case, the sides ...	75, 75, 30; 74, 74, 32; 76, 76, 28
{ "seed_index": 481, "rephrase_index": 2 }	In a recipe, let $ b $ represent the mass of flour in grams. The total weight of all the ingredients used in the recipe is given by the expression $ 6b + 11 $ grams, which includes both $ b $ grams of flour and $ 19 $ grams of sugar. The decimal $ 0.76 $ indicates the proportion of the total recipe weight tha...	We start with the given equation that relates the weight of flour $ b $ and sugar $ 19 $ to the total weight $ 6b + 11 $: \[ \frac{b + 19}{6b + 11} = 0.76. \] 1. Eliminate the fraction by multiplying both sides by $ 6b + 11 $: \[ b + 19 = 0.76(6b + 11). \] 2. Distribute $ 0.76 $ on the rig...	3, 0.5319
{ "seed_index": 1168, "rephrase_index": 2 }	Consider a triangular region formed by the lines $ y = x $, $ y = -x $, and $ y = h $, where $ h $ is a positive constant less than 6. First, determine the coordinates of the intersection points of these lines. Then, using these points, calculate the area of the triangle formed. Finally, if $ h $ is restricte...	To solve the problem, we need to find the area of the triangular region formed by the lines $ y = x $, $ y = -x $, and $ y = h $. We will first identify the intersection points of these lines, then calculate the area of the triangle they form. 1. Identify Intersection Points: - The line $ y = x $ inters...	8
{ "seed_index": 399, "rephrase_index": 0 }	Tameka is selling boxes of crackers for her scout troop. On Friday, she sold 40 boxes. On Saturday, she sold 10 fewer than twice the number sold on Friday. On Sunday, she sold half as many boxes as she sold on Saturday. Additionally, each box sold on Friday was priced at $2, while Saturday's boxes sold for $3, and Sund...	To solve the problem, we need to break it down into its components, calculate the number of boxes sold each day, the revenue generated from those sales, and finally compute the total number of boxes sold and the average boxes sold per day. 1. Boxes Sold on Each Day: - Friday: Tameka sold 40 boxes. - **Sa...	430
{ "seed_index": 310, "rephrase_index": 0 }	A farmer has 10 meters of fencing that he wants to use to create a rectangular pen for his animals. Let $x$ be the length and $y$ be the width of the pen. The perimeter $P$ of the pen is given by the equation $P = 2x + 2y = 10$. This leads to the constraint that $x + y = 5$. The farmer aims to minimize the co...	To solve for the minimum feeding cost of the rectangular pen, we will follow the steps outlined in the problem statement. 1. Express $y$ in terms of $x$: Given the constraint from the perimeter, we have: \[ x + y = 5 \implies y = 5 - x \] 2. **Substitute this expression into the cost function \(...	\dfrac{4}{5}
{ "seed_index": 995, "rephrase_index": 0 }	A company is designing a new type of cubic storage container for a shipment. The volume of the container is given by $V = s^3$, where $s$ is the side length in meters. If the side length is defined as $s = 16^{7/12}$, calculate the volume $V$ of the container in cubic meters. Provide your answer as a simplified...	To calculate the volume $V$ of the cubic storage container, we will use the formula $V = s^3$, where $s$ is the side length. We are given the side length as $s = 16^{7/12}$. 1. Calculate $s^3$: \[ V = (16^{7/12})^3 \] Using the property of exponents $(a^m)^n = a^{m \cdot n}$, we can simplif...	128
{ "seed_index": 521, "rephrase_index": 3 }	Jar A initially contains a total of 15 buttons: four red buttons, eight blue buttons, and three yellow buttons. Carla removes the same even number of red and blue buttons, denoted as 'x', from Jar A and places them into an empty Jar B, where $ x $ is a positive even integer with the constraint that $ x \leq 4 $. Af...	To solve the problem, we first analyze the given data and constraints. Given Data: - Jar A initially contains: - 4 red buttons - 8 blue buttons - 3 yellow buttons - Total buttons in Jar A: $4 + 8 + 3 = 15$ - Carla removes $x$ red and $x$ blue buttons (where $x$ is a positive even integer and \(x \leq...	\dfrac{1}{11}
{ "seed_index": 1155, "rephrase_index": 4 }	Consider a scenario where you have two cylindrical containers: Cylinder A with height $h$ and radius $r_A$, and Cylinder B where its height is equal to the radius of Cylinder A ($h_B = r_A$), and its radius is equal to the height of Cylinder A ($r_B = h$). Given that the volume of Cylinder A is twice the volu...	To solve the problem, we need to express the volumes of Cylinders A and B using their respective dimensions, and then set up an equation based on the given relationship between their volumes. 1. Volume of Cylinder A ($V_A$): The formula for the volume of a cylinder is given by: \[ V = \pi r^2 h \] Fo...	4
{ "seed_index": 1454, "rephrase_index": 0 }	Determine the minimum amplitude value of the function \[ f(x) = \frac{\sin^6 x + \cos^6 x + 1}{\sin^4 x + \cos^4 x + 1} \] over the interval $ [0, \frac{\pi}{2}] $. In the context of wave functions, "amplitude" refers to the maximum extent of a wave's oscillation, which in this case involves finding the minimum valu...	To find the minimum amplitude value of the function \[ f(x) = \frac{\sin^6 x + \cos^6 x + 1}{\sin^4 x + \cos^4 x + 1} \] over the interval $ [0, \frac{\pi}{2}] $, we will analyze the function by finding its critical points and evaluating it at the endpoints of the interval. 1. Evaluate at the endpoints: - At...	\dfrac{17}{18}
{ "seed_index": 1005, "rephrase_index": 2 }	Kaleb defined a clever integer as an even integer that is greater than 20, less than 120, and has the property that the sum of its digits equals 9. For instance, the number 36 is a clever integer because $3 + 6 = 9$. Considering this definition, first identify all clever integers that meet these criteria. Next, f...	To solve the problem, we need to follow these steps: 1. Identify the clever integers: These are defined as even integers greater than 20, less than 120, and whose digits sum to 9. 2. List the even integers within the specified range: The even integers greater than 20 and less than 120 are: \[ 22, 24, 2...	\dfrac{2}{5}
{ "seed_index": 383, "rephrase_index": 5 }	In a construction project, a ramp is being built from point A to point B, forming a straight line segment. The ramp intersects the ground at an angle of $52^\circ$. In the context of the right triangle formed by the ramp, the ground, and a vertical line perpendicular to the ground, angle $x$ is defined as the angle...	In the given problem, we need to determine the angle $x$ between the ramp and the vertical line. The ramp intersects the ground at an angle of $52^\circ$. Since the ramp, the vertical line, and the ground form a right triangle, we can use the relationship between angles in a right triangle to find $x$. 1. The su...	38
{ "seed_index": 657, "rephrase_index": 1 }	Rebecca bought a total of 22 camping items, which include tent stakes, packets of drink mix, and bottles of water. 1. Let $ t $ represent the number of tent stakes. 2. The number of packets of drink mix is three times the number of tent stakes: \[ \text{Drink Mix} = 3t \] 3. She purchased two more bottles of water ...	To find the maximum number of tent stakes $ t $ that Rebecca bought while ensuring the total volume of all items does not exceed 40 liters, we first analyze the given problem step-by-step. 1. Setting up the equations: - We know from the problem statement that: - $ t $: number of tent stakes - Drin...	4
{ "seed_index": 1154, "rephrase_index": 0 }	Mark and James need a total of 14 twelve-sided dice for their game. Mark has a collection of 10 dice, of which 60% are twelve-sided, resulting in 6 twelve-sided dice. James has a collection of 8 dice, of which 75% are twelve-sided, resulting in 6 twelve-sided dice as well. First, calculate the total number of twelve-si...	To solve this problem, we will break it down into several key components: calculating the total number of twelve-sided dice Mark and James currently have, determining how many more they need to reach 14, and finally calculating how many additional dice they can purchase within their budget. 1. **Calculate the number o...	2
{ "seed_index": 202, "rephrase_index": 0 }	Given the function $ G(x) = \|x+1\| - \|x-1\| $, first evaluate the function at the critical points of the function, specifically at $ x = -2, 0, $ and $ 2 $. After calculating these values, determine the range of $ G(x) $ for $ x $ constrained to the interval $ -3 \leq x \leq 3 $. Express your answer in interv...	To analyze the function $ G(x) = \|x+1\| - \|x-1\| $, we first need to understand how the absolute value functions behave at the critical points and the endpoints of the interval $[-3, 3]$. The critical points occur where the expressions inside the absolute values change sign, specifically at $ x = -1 $ and \( x = 1 ...	[-2, 2]
{ "seed_index": 193, "rephrase_index": 2 }	Marcus is having a water balloon party and needs to fill 100 balloons, each holding 3 ounces of water. How many bottles does he need to buy if each bottle holds 50 ounces of water? Additionally, if the bottles are priced at $2.50 each and he has two $10 bills, how much change will Marcus have after his purchase? Calcul...	To solve the problem, we will break it down into several steps: 1. Calculate Total Water Needed: Each balloon holds 3 ounces of water, and Marcus needs to fill 100 balloons. \[ \text{Total Water Needed} = \text{Number of Balloons} \times \text{Water per Balloon} = 100 \times 3 = 300 \text{ ounces} \] ...	5
{ "seed_index": 59, "rephrase_index": 0 }	Given the quadratic profit model represented by $ P(x) = 2x^2 + 8x + 6 $ (where $ P $ is profit in thousands of dollars), determine the range of production levels $ x $ (in units, thousands) such that the company does not incur a loss, i.e., $ 2x^2 + 8x + 6 \ge 0 $. Provide your answer in interval notation.	To determine the range of production levels $ x $ such that the profit model $ P(x) = 2x^2 + 8x + 6 $ does not incur a loss, we need to solve the inequality $ 2x^2 + 8x + 6 \ge 0 $. 1. Identify the quadratic equation: The quadratic equation is $ 2x^2 + 8x + 6 = 0 $. 2. Calculate the discriminant: ...	(-\infty, -3] \cup [-1, \infty)
{ "seed_index": 704, "rephrase_index": 4 }	An isosceles right triangle has a hypotenuse measuring $4\sqrt{2}$ units. Calculate the area of this triangle in square units using the formula for the area: $\text{Area} = \frac{1}{2} \times \text{leg} \times \text{leg}$. Each leg can be calculated by dividing the hypotenuse by $\sqrt{2}$.	To find the area of an isosceles right triangle with a hypotenuse measuring $4\sqrt{2}$ units, we can follow these steps: 1. Identify the relationship between the legs and the hypotenuse: In an isosceles right triangle, the legs are equal in length. The relationship between the legs $a$ and the hypotenuse \(c\...	8
{ "seed_index": 742, "rephrase_index": 3 }	At Central Middle School, there are originally 108 students who take the AMC 8. Each student usually enjoys an average of 2 cookies at their gathering. However, due to a big concert scheduled for the same night, attendance will be down by 25%. Given that Walter and Gretel are baking Bonnie's Best Bar Cookies (which mak...	To determine the number of full recipes Walter and Gretel should prepare, we need to follow these steps: 1. Calculate the number of students attending: Originally, there are 108 students. With a 25% decrease in attendance due to the concert, we calculate the number of students who will actually attend. \[ \t...	17
{ "seed_index": 319, "rephrase_index": 0 }	A chocolate factory produces an average of 50 candies per hour and operates for 10 hours each day under ideal circumstances. In a ten-day work period, there will be two maintenance days that will result in reduced production efficiency. On maintenance days, the production output is 40 candies per hour. Calculate the to...	To determine the total number of workdays required for the factory to fulfill an order of 4000 candies, we must consider the normal production rate and the reduced output on maintenance days. 1. Calculate the total production for a normal day: The factory produces 50 candies per hour and operates for 10 hours. ...	8
{ "seed_index": 166, "rephrase_index": 0 }	In a hypothetical calendrical system where leap years occur every four years, calculate the maximum possible number of leap years that can occur within a 150-year period. Furthermore, if every leap year is required to align with an event planned to happen every 10 years, determine how many of those events will coincide...	To analyze the problem, we will break it down into two parts: calculating the maximum number of leap years that can occur in a 150-year period and determining how many of those leap years coincide with events that happen every 10 years. 1. Leap Year Calculation: - Leap years occur every 4 years. - The range...	8
{ "seed_index": 1476, "rephrase_index": 0 }	Given the function \[ f(x) = \frac{5^x - 1}{5^x + 1}, \] 1. Calculate $ f(-x) $. 2. Determine whether $ f(-x) = f(x) $ (even), $ f(-x) = -f(x) $ (odd), or neither. 3. Graph the function over the interval $ x \in [-2, 2] $ and describe any observed symmetry. 4. Evaluate how the properties of $ f(x) $...	To analyze the function $ f(x) = \frac{5^x - 1}{5^x + 1} $, we will follow the steps outlined in the problem statement. 1. Calculate $ f(-x) $: \[ f(-x) = \frac{5^{-x} - 1}{5^{-x} + 1} \] We can rewrite $ 5^{-x} $ as $ \frac{1}{5^x} $: \[ f(-x) = \frac{\frac{1}{5^x} - 1}{\frac{1}{5^x} + 1...	odd
{ "seed_index": 918, "rephrase_index": 2 }	A local sports league requires that a team has a certain number of players conforming to the following conditions: The number of players must have a remainder of 1 when divided by 4, a remainder of 1 when divided by 3, and a remainder of 2 when divided by 5. Additionally, the number of players must be an even number. W...	To find the smallest whole number of players that meets the given conditions, we need to solve a system of congruences and ensure that the solution is an even number. The conditions can be expressed as: 1. $ n \equiv 1 \mod 4 $ (remainder 1 when divided by 4) 2. $ n \equiv 1 \mod 3 $ (remainder 1 when divided by ...	637
{ "seed_index": 108, "rephrase_index": 0 }	Consider a piecewise function defined as follows for real numbers $ x $: \[ f(x) = \left\{ \begin{array}{cl} x+2 & \text{ if } x > 3, \\ 2x + a & \text{ if } x \leq 3. \end{array} \right. \] To ensure that $ f(x) $ is continuous at $ x = 3 $, find the value of $ a $ such that the limit of $ f(x) $ from the ...	To determine the value of $ a $ such that the piecewise function $ f(x) $ is continuous at $ x = 3 $, we need to ensure that the limit of $ f(x) $ from the left as $ x $ approaches 3 is equal to the limit from the right as $ x $ approaches 3. 1. Calculate the left-hand limit as $ x $ approaches 3: ...	\text{No value of } a \text{ satisfies both conditions.}
{ "seed_index": 246, "rephrase_index": 1 }	Adam owns a wood carving shop and has the following stock: 15 blocks of basswood, 20 blocks of butternut wood, and 20 blocks of aspen wood. A block of basswood produces 3 figurines, while a block of butternut produces 4 figurines, and a block of aspen produces 6 figurines, which is double the output of basswood. If Ada...	To calculate the total number of figurines Adam can carve, we need to analyze the contribution of each type of wood while considering the constraints on the number of blocks he uses. 1. Given Data: - Basswood: 15 blocks available, produces 3 figurines per block. - Butternut wood: 20 blocks available, produce...	130
{ "seed_index": 1196, "rephrase_index": 2 }	In the context of a small business producing a new product, let $P(a, b) = a^3 + b^3 - c$ represent the profit (in hundreds of dollars) derived from using $a$ units of product A and $b$ units of product B, where $a$ and $b$ are positive integers. Assuming $c$ is a constant given by $c = 50$, determine the...	To solve for the values of positive integers $a$ and $b$ that maximize the profit function $P(a, b) = a^3 + b^3 - c$ where $c = 50$, we will evaluate $P(a, b)$ for all combinations of $a$ and $b$ within the specified range of $1 \leq a \leq 10$ and $1 \leq b \leq 10$. 1. **Setting up the profit funct...	1950
{ "seed_index": 188, "rephrase_index": 2 }	Given a point in three-dimensional space represented by the rectangular coordinates $ (2\sqrt{3} \pm 0.1, 6 \pm 0.1, -4 \pm 0.1) $, convert these coordinates to spherical coordinates $ (\rho, \theta, \phi) $. 1. First, recall that the conversion from rectangular coordinates $(x, y, z)$ to spherical coordinates ...	To convert the rectangular coordinates $ (x, y, z) = (2\sqrt{3} \pm 0.1, 6 \pm 0.1, -4 \pm 0.1) $ into spherical coordinates $ (\rho, \theta, \phi) $, we will follow the established conversion formulas and analyze the extreme values due to the uncertainties of $ \pm 0.1 $ for each coordinate. 1. **Identify the e...	(7.93, 1.165, 2.094) and (8.07, 1.146, 2.107)
{ "seed_index": 223, "rephrase_index": 0 }	At 3:00 p.m., a bacteria colony consists of 20 bacteria, with the population doubling every 3 minutes under optimal conditions. Determine the precise population of the bacteria at 3:15 p.m. Additionally, given that a researcher observed the population at 3:12 p.m. and noted it contained 160 bacteria, validate this obse...	To analyze the problem, we will break it down into several parts related to the population growth of the bacteria. 1. Given Data: - Initial population at 3:00 p.m.: $P_0 = 20$ bacteria - Doubling time: $3$ minutes - Time interval from 3:00 p.m. to 3:15 p.m.: $15$ minutes - Observed population at ...	640
{ "seed_index": 1114, "rephrase_index": 1 }	Given a right triangle where angle $A$ represents the angle of elevation of the top of a building from a point on the ground that is 20 meters away from the base, simplify the expression: \[ (1 + \cot A - \csc A)(1 + \tan A + \sec A), \] and identify the final numerical value when $A$ is determined to be \(30^\...	To simplify the expression $(1 + \cot A - \csc A)(1 + \tan A + \sec A)$ for $A = 30^\circ$, we first need to calculate the trigonometric values for $A$. 1. Trigonometric Values: - For $A = 30^\circ$: \[ \cot 30^\circ = \frac{1}{\tan 30^\circ} = \frac{1}{\frac{1}{\sqrt{3}}} = \sqrt{3} \] ...	2
{ "seed_index": 948, "rephrase_index": 1 }	Junior has 16 rabbits. On Monday, he bought 6 toys for his rabbits. On Wednesday, he bought twice as many toys as he did on Monday. On Friday, he bought four times as many toys as he did on Monday, and on the next day (Saturday) he bought half as many toys as he did on Wednesday. If Junior wishes to evenly distribute a...	To determine how many toys each rabbit will receive, we need to calculate the total number of toys Junior bought throughout the week and then divide that total by the number of rabbits. 1. First, we list the toys bought on each day: - Monday: Junior bought 6 toys. - Wednesday: He bought twice as many toy...	3
{ "seed_index": 547, "rephrase_index": 1 }	Porter is a painter who sold his most recent mural of wolves for $44,000. The sale price of this mural is $1,000 less than five times the price of the previous painting he sold. Determine how much, in US dollars, Porter made from selling his previous painting. Then, calculate the combined total revenue from both painti...	To solve this problem, we need to set up an equation based on the relationship between the sale prices of the two paintings. 1. Let $ x $ represent the price of the previous painting sold by Porter. 2. According to the problem, the sale price of the mural is $1,000 less than five times the price of the previous pai...	53000
{ "seed_index": 630, "rephrase_index": 0 }	A school has a total number of enrolled students that ranges from 150 to 200, inclusive. The total number of students must be divisible by 6. Additionally, if one student is absent, the reduced total (total number of students minus one) must also remain divisible by 6. Your task is to count how many distinct values of ...	To solve the problem, we need to determine the total number of students in a range from 150 to 200 that meets two criteria: the number must be divisible by 6, and when one student is absent, the resulting number must also remain divisible by 6. 1. Determine the range of possible student counts: - The total numb...	0
{ "seed_index": 55, "rephrase_index": 3 }	Given that $\mathbf{a}$ and $\mathbf{b}$ are unit vectors, and that the vector $\mathbf{v_1} = \mathbf{a} + 2 \mathbf{b}$ is orthogonal to the vector $\mathbf{v_2} = 5 \mathbf{a} - 4 \mathbf{b}$, determine the angle $\theta$ between the vectors $\mathbf{a}$ and $\mathbf{b}$ in degrees. Since vector $\mathbf{b}$ lies in...	To determine the angle $\theta$ between the unit vectors $\mathbf{a}$ and $\mathbf{b}$, we know that the vectors $\mathbf{v_1} = \mathbf{a} + 2\mathbf{b}$ and $\mathbf{v_2} = 5\mathbf{a} - 4\mathbf{b}$ are orthogonal. This means that their dot product must equal zero: \[ \mathbf{v_1} \cdot \mathbf{v_2} = 0 \...	60
{ "seed_index": 306, "rephrase_index": 0 }	Roger and his friend are traveling between two towns that are a total distance of 200 miles apart. They first cover 50 miles in 1 hour. After taking a lunch break for 1 hour, they continue their journey. Due to uneven terrain, the speed for the subsequent segment will be 75% of the speed they maintained for the initial...	To find the total time Roger and his friend took to travel between the two towns, we will break down the problem into several steps: 1. Calculate the speed for the first segment of the journey: - Distance for the first segment: 50 miles - Time for the first segment: 1 hour - Speed for the first segment ca...	6
{ "seed_index": 1072, "rephrase_index": 0 }	Given the sinusoidal function used to model tidal changes, represented by the equation $ y = a \sin(bx + c) + d $, the tidal height varies with a maximum of 3 meters and a minimum of -1 meter. (a) Calculate the amplitude $ a $ and the vertical shift $ d $. The amplitude can be calculated using the formula \...	To solve for the amplitude $ a $, vertical shift $ d $, and the value of $ b $ in the sinusoidal function representing tidal changes, we will carefully follow the provided formulas and perform the necessary calculations step by step. (a) 1. Calculate the amplitude $ a $ using the formula: \[ a ...	2, 1, \frac{\pi}{2}
{ "seed_index": 534, "rephrase_index": 2 }	Parker tests three bags of popcorn to determine their quality. In the first bag, 60 out of 75 kernels pop; in the second bag, 42 out of 50 kernels pop; and in the third bag, 82 out of 100 kernels pop. First, calculate the percentage of kernels that pop in each bag by dividing the number of popped kernels by the total n...	To solve the problem, we need to follow these steps: 1. Calculate the percentage of popped kernels for each bag. For each bag, we will use the formula: \[ \text{Percentage of popped kernels} = \left(\frac{\text{Number of popped kernels}}{\text{Total number of kernels}}\right) \times 100 \] - For ...	None
{ "seed_index": 219, "rephrase_index": 2 }	A circular garden is to be designed with its center at point $P(-3, 4)$ and passing through point $Q(9, -3)$. First, use the distance formula to calculate the radius $r$ of the circle defined by points $P$ and $Q$ as follows: \[ r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates of \(P\...	To find the radius $r$ of the circular garden centered at point $P(-3, 4)$ and passing through point $Q(9, -3)$, we will use the distance formula given by: \[ r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] 1. Identify the coordinates: - $P(-3, 4)$ means $x_1 = -3$ and $y_1 = 4$. - $Q(9, -3)$ means \(...	100\pi
{ "seed_index": 1156, "rephrase_index": 5 }	Two triangular-shaped plots of land, represented on a 3x3 grid where the distance between neighboring points is 1 unit, overlap. The first plot has vertices at coordinates (0,0), (2,1), and (1,2). The second plot has vertices at (2,2), (0,1), and (1,0). First, calculate the area of each triangular plot. Next, determine...	To solve the problem, we need to follow a series of steps to calculate the areas of the two triangular plots, find their intersection points, and then compute the area of the overlapping region. 1. Calculate the area of the first triangle (A1) with vertices at (0,0), (2,1), and (1,2). We can use the formula for th...	\frac{1}{2}
{ "seed_index": 904, "rephrase_index": 1 }	Given the equation $ ab - 6a + 5b = 373 $, where both $ a $ and $ b $ are positive integers, find all pairs $ (a, b) $ that satisfy this equation. After identifying these pairs, calculate the absolute differences $ \|a - b\| $ and determine the smallest possible value among them.	To solve the equation $ ab - 6a + 5b = 373 $ for positive integers $ a $ and $ b $, we will rearrange and analyze it step-by-step. 1. Rearranging the Equation: We start with the original equation and rearrange it: \[ ab + 5b - 6a = 373 \] We can factor this equation to express $ b $ in terms of...	31
{ "seed_index": 428, "rephrase_index": 2 }	Given the temperature readings at various times represented by the points (3, 10), (6, 20), (12, 35), (18, 40), and (20, 50), determine the sum of the $x$-coordinates of the points that represent temperatures strictly above the threshold line defined by the equation $y = 2x + 7$. First, identify which points are above ...	To solve the problem, we need to determine which of the given points (representing time and temperature) have temperatures strictly above the threshold line defined by the equation $y = 2x + 7$. 1. Identify the points: The points given are (3, 10), (6, 20), (12, 35), (18, 40), and (20, 50). 2. **Calculate th...	38
{ "seed_index": 590, "rephrase_index": 0 }	The fraction of an ingredient in a recipe for $8$ portions is $0.428125$. Convert $0.428125$ to the fraction $\frac{a}{b}$, ensuring $a$ and $b$ are in simplest terms. After doubling the recipe, the proportion of the ingredient will remain unchanged. Compute values $a'$ and $b'$ for the fraction represe...	To convert the decimal $0.428125$ to a fraction $\frac{a}{b}$ and ensure $a$ and $b$ are in simplest terms, we will follow these steps: 1. Convert the Decimal to a Fraction: - The decimal $0.428125$ can be expressed as $\frac{428125}{1000000}$ because it has six decimal places. 2. **Simplify the Fr...	914
{ "seed_index": 791, "rephrase_index": 1 }	In a certain chemical reaction, the concentration of a reactant in the 7th and 10th hours is quantified to be 7 moles and 21 moles, respectively, following a consistent growth pattern. Assuming the reactor operates under a geometric growth model, where the concentration of the reactant doubles for every three hours, ca...	To solve for the concentration of the reactant in the 13th hour given the concentrations at the 7th and 10th hours, we need to analyze the provided information under the assumption of geometric growth, where the concentration doubles every three hours. 1. Given Data: - Concentration at the 7th hour, \( C(7) = 7...	63
{ "seed_index": 1325, "rephrase_index": 5 }	Consider a cube with a side length of $6$ units. The vertices of the cube are labeled as $A, B, C, D, E, F, G, H$ such that: - $A(0, 0, 0)$ - $B(6, 0, 0)$ - $C(6, 6, 0)$ - $D(0, 6, 0)$ - $E(0, 0, 6)$ - $F(6, 0, 6)$ - $G(6, 6, 6)$ - $H(0, 6, 6)$ The vertices that are colored purple are labeled as \...	To find the volume of the tetrahedron formed by the vertices $A(0, 0, 0)$, $C(6, 6, 0)$, $E(0, 0, 6)$, and $G(6, 6, 6)$, we first need to compute the vectors $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$. 1. Define the vectors: - The vector $\mathbf{a} = \overrightarrow{AC}$: \[ \mathbf...	0
{ "seed_index": 682, "rephrase_index": 0 }	Let $ S = 1 - 2 + 3 - 4 + \ldots + 2009 - 2010 $. Follow these steps to compute $ S $: 1. Calculate the sum of all odd numbers up to 2010. 2. Calculate the sum of all even numbers up to 2010. 3. Combine these results to find $ S $. 4. Finally, determine the residue of $ S $ modulo 2010. What is the final resi...	To find the sum $ S = 1 - 2 + 3 - 4 + \ldots + 2009 - 2010 $, we can break the series into two parts: the sum of odd numbers and the sum of even numbers. 1. Identify the range: We have numbers from 1 to 2010. The odd numbers are $ 1, 3, 5, \ldots, 2009 $ and the even numbers are $ 2, 4, 6, \ldots, 2010 $. 2...	1015
{ "seed_index": 809, "rephrase_index": 4 }	A circular garden has an area of $324\pi$ square units. The local community wishes to inscribe a regular hexagonal flowerbed within this garden. 1. Determine the radius of the circular garden. 2. If the garden's radius is increased by 10%, find the new area of the regular hexagon inscribed in the expanded garden. ...	To solve the problem, we will first find the radius of the circular garden from its area, then calculate the area of the regular hexagon inscribed within the original garden, and finally find the area of the hexagon after increasing the radius of the garden by 10%. 1. Determine the radius of the circular garden: ...	588\sqrt{3}
{ "seed_index": 1073, "rephrase_index": 2 }	Brendan earns $6 per hour as a waiter and is scheduled for two 8-hour shifts and one 12-hour shift in a week. Additionally, he receives an average of $12 in tips for each hour worked. Calculate Brendan's total earnings from wages and tips for the week, then determine the amount of taxes he must pay, knowing that he pay...	To calculate Brendan's total earnings from wages and tips, and subsequently determine the taxes he must pay, we will follow these steps: 1. Calculate Total Hours Worked: - Brendan works two 8-hour shifts and one 12-hour shift. - Total hours from two 8-hour shifts: \[ 2 \times 8 = 16 \text{ hours} ...	56
{ "seed_index": 1372, "rephrase_index": 1 }	A triangular plot of land (triangle $ABC$) has sides measuring $AB = 6$ meters, $AC = 5$ meters, and $BC = 4$ meters. The Law of Cosines states that for a triangle with sides $a$, $b$, and $c$, the relationship is given by $c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$. This will help in calculating the measur...	To solve the problem, we start by analyzing the given triangle $ABC$ with sides $AB = 6$ meters, $AC = 5$ meters, and $BC = 4$ meters. We'll first find the angles $A$, $B$, and $C$ using the Law of Cosines, then calculate the necessary trigonometric values, and finally evaluate the given expression. 1. *...	\frac{11 - \sqrt{2}}{4}
{ "seed_index": 1328, "rephrase_index": 1 }	Given the rational function $ y = \frac{p(x)}{q(x)} $ where $ p(x) $ is a linear function and $ q(x) $ is a quadratic function, and the graph of the function shows vertical asymptotes at $ x = -3 $ and $ x = 2 $ and a value of 0 at $ x = 0 $. 1. Determine the specific forms of $ p(x) $ and $ q(x) $ ba...	To determine the specific forms of the functions $ p(x) $ and $ q(x) $ based on the given characteristics of the rational function $ y = \frac{p(x)}{q(x)} $, we can analyze the information provided regarding vertical asymptotes and the zero of the function. 1. Identify $ q(x) $: The vertical asymptotes occ...	\dfrac{1}{6}
{ "seed_index": 232, "rephrase_index": 3 }	Given the four-digit numeral $ 3AA1 $ is divisible by 9, first determine the sum of its digits. Define $ S = 3 + A + A + 1 $ and find all possible values of $ A $ such that $ S $ is divisible by 9. Calculate $ 3 + 2A + 1 $ and deduce which digit $ A $ can take that results in $ S $ being divisible by 9, e...	To determine the digit $ A $ in the numeral $ 3AA1 $ such that the number is divisible by 9, we first need to establish the sum of the digits in the numeral. The sum $ S $ of the digits is given by: \[ S = 3 + A + A + 1 = 3 + 2A + 1 = 4 + 2A \] Next, we need to find all possible values of $ A $ such that \( S...	7
{ "seed_index": 639, "rephrase_index": 1 }	A company incurs the following expenses: $247 for office supplies, $5 \times 39$ for printing, $7 \times 143$ for equipment maintenance, and $4 \times 15$ for miscellaneous expenses. a) Calculate the following expenses: 1. $5 \times 39$ (printing) 2. $7 \times 143$ (equipment maintenance) 3. $4 \times 15$ (misc...	To calculate the total expenses incurred by the company, we will first compute each individual expense as specified, then sum them up and finally find the total expenses modulo 13. 1. Calculate the Printing Expenses: \[ 5 \times 39 = 195 \] 2. Calculate the Equipment Maintenance Expenses: \[ 7 ...	8
{ "seed_index": 297, "rephrase_index": 0 }	A paperboy delivers newspapers to 10 houses along Main Street. He wishes to save effort, so he does not always deliver newspapers to every house, but to avoid being fired, he must adhere to the rule that he can never miss three consecutive houses. Additionally, on rainy days, he is required to deliver to at least 2 con...	To find the total number of distinct delivery patterns the paperboy can choose from, we will analyze it step by step, considering the given constraints. 1. Identify the constraints and variables: - Total houses: $ n = 10 $ - He cannot miss three consecutive houses. - On rainy days, he must deliver to a...	504
{ "seed_index": 169, "rephrase_index": 2 }	A rectangular prism has a volume of 8 cubic units, defined by the equation $ V = (x - 4)^3 $, where $ x $ represents the length of the prism. You are tasked with determining the value of $ x $ that results in this volume. 1. Find the value of $ x $. 2. If the length $ x $ is increased by 2 units, what will t...	To solve the problem, we will first address the equation for the volume of the rectangular prism, given by $ V = (x - 4)^3 $, and set it equal to the provided volume of 8 cubic units. 1. Setting Up the Equation: We start with the equation for volume: \[ (x - 4)^3 = 8 \] 2. Taking the Cube Root: ...	6; 64

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SynerMath-v2-15k

This is an anonymous dataset release accompanying a NeurIPS 2026 submission. Author and affiliation information is intentionally withheld to comply with the double-blind review policy.

Dataset Summary

SynerMath-v2-15k contains 15,000 English mathematical reasoning problems with generated chain-of-thought solutions and final answers. The dataset was produced by the SynerMath multi-agent synthesis pipeline from GSM8K and MATH seed problems.

Each record contains a rephrased math question, an LLM-generated reasoning trace, and a final short-form answer.

Files

SynerMath_v2_15k.jsonl: full dataset, one JSON object per line.
samples_100.jsonl: first 100 records from the full dataset for quick inspection.
croissant.json: Croissant metadata with Responsible AI fields for NeurIPS dataset submission.

Schema

Each JSONL record has the following fields:

Field	Type	Description
`seed_id.seed_index`	integer	Index of the originating seed problem.
`seed_id.rephrase_index`	integer	Rephrasing variant id.
`question`	string	Rephrased natural-language math problem.
`thought`	string	LLM-generated chain-of-thought solution.
`answer`	string	Final short-form answer.

Dataset Statistics

Records: 15,000
Unique seed indices: 1,499
Rephrase variant ids: 0-5
Average question length: approximately 556 characters
Average chain-of-thought length: approximately 1,908 characters
Empty question, thought, or answer fields: 0
Exact duplicate questions: 0
SHA256 of SynerMath_v2_15k.jsonl: 8242ff023a0bebb2ad5353cc9da8975fe291da414a5cdeca8a166af772d0a45c

Source Data and Generation

Seed problems are drawn from GSM8K and MATH, both of which are released under the MIT License. The released records are generated rephrasings and generated solutions rather than a direct redistribution of the original seed datasets.

The high-level generation pipeline is:

Select seed math problems.
Generate rephrased variants with a rephrasing agent.
Filter generated questions with a question-quality checking agent.
Generate chain-of-thought solutions and final answers with an answering agent.
Apply automated answer-quality checks and remove invalid records.

The associated anonymous code repository is provided in the paper appendix.

Intended Use

This dataset is intended for research on mathematical reasoning, supervised fine-tuning, chain-of-thought distillation, and analysis of synthetic reasoning data.

It is not intended for safety-critical, high-stakes, or production decision-making systems.

Limitations

The reasoning traces are generated by LLM agents and may still contain residual arithmetic or reasoning errors after filtering.
The dataset is English-only.
The distribution inherits topical and stylistic biases from GSM8K, MATH, and the generator model.
The examples are synthetic math word problems and should not be treated as naturally occurring human-written educational data.

Personal and Sensitive Information

The dataset contains synthetic math problems and solutions. We did not collect personal, demographic, or sensitive information about identifiable individuals. A scan for emails, URLs, and common API-key patterns found no matches.

License

SynerMath-v2-15k is released under the Creative Commons Attribution 4.0 International License (CC BY 4.0). The seed datasets GSM8K and MATH are MIT-licensed.

Maintenance

This anonymous release will remain accessible during the NeurIPS 2026 review period. Upon acceptance, the dataset will be re-released under a non-anonymous account with a persistent archival mirror.

license: cc-by-4.0 task_categories: - question-answering - text-generation language: - en tags: - mathematics - reasoning - chain-of-thought - synthetic pretty_name: SynerMath-v2-15k size_categories: - 10K<n<100K configs: - config_name: default data_files: - split: train path: SynerMath_v2_15k.jsonl