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af85612d-b460-4b7c-9610-aa83096042a2
As shown in the figure, there is a flower bed in front of a school building. The flower bed is composed of a regular hexagon $$ABCDEF$$ and 6 circles with a radius of 1 meter, centered at the vertices of the hexagon $$\odot A$$, $$\odot B$$, $$\odot C$$, $$\odot D$$, $$\odot E$$, and $$\odot F$$. It is planned to plant...
$$2\pi$$
math
[ "The user wants me to find the total area of the shaded regions in the given figure.\n\n**1. Analyze the geometry:**\n* There is a regular hexagon $ABCDEF$.\n* There are 6 circles, each with a radius $r = 1$ meter.\n* The centers of these circles are the vertices of the hexagon: $A, B, C, D, E, F$.\n* The s...
5ad772d9-e53f-477a-acb2-1106d33a0852
The result of the following pseudocode after execution is ___.
$$21$$
math
[ "The user wants me to determine the output of the provided pseudocode.\n\n**1. Analyze the pseudocode:**\n* **Initialization:** `p <- 1`. So, initially, $p = 1$.\n* **Loop:** `For k From 1 To 10 Step 3`.\n * This means the loop variable $k$ takes values starting from 1, increasing by 3 each time, as long a...
1fbb0461-8686-4bdd-ac3e-a12f8dbdd030
As shown in the figure, points $$E$$ and $$F$$ are the midpoints of sides $$AB$$ and $$CD$$ of square $$ABCD$$, respectively. Now, the square is folded along $$EF$$ to form a dihedral angle of $$60^{\circ}$$. The cosine of the angle between the skew lines $$AE$$ and $$BF$$ is ___.
$$\dfrac{\sqrt{5}}{10}$$
math
[ "The user wants me to find the cosine of the angle between two skew lines, $AE$ and $BF$, after a square $ABCD$ is folded along the line $EF$.\n\n**1. Analyze the initial state (before folding):**\n* $ABCD$ is a square. Let the side length be $2a$.\n* $E$ is the midpoint of $AB$. So $AE = EB = a$.\n* $F$ is t...
c1012f16-e58d-45d3-83e6-adf7c389ff39
As shown in the figure, BD is a diagonal of rectangle ABCD, and points E and F are the midpoints of BD and DC, respectively. If AB = 4 and BC = 3, then the length of AE + EF is.
4
math
[ "The user wants me to find the length of $AE + EF$ based on the provided image and text.\n\n**1. Analyze the given information:**\n* **Shape:** Rectangle $ABCD$.\n* **Dimensions:** $AB = 4$, $BC = 3$. Since it's a rectangle, $CD = AB = 4$ and $AD = BC = 3$.\n* **Diagonal:** $BD$ is a diagonal.\n* **Point E:...
27ede552-6009-4cdb-970e-b1f227f1dcce
As shown in the figure, the graphs of the functions $$y=2x$$ and $$y=ax+5$$ intersect at point $$A\left(m,3\right)$$. The solution set of the inequality $$2x< ax+5$$ is ___.
$$x<\dfrac{3}{2}$$
math
[ "The user wants me to find the solution set for the inequality $2x < ax + 5$.\n\n1. **Analyze the given information:**\n * There are two linear functions: $y = 2x$ and $y = ax + 5$.\n * Their graphs intersect at point $A(m, 3)$.\n * The graph shows $y=2x$ passing through the origin with a positive s...
b69da01e-6b29-4b87-aedd-cf3086572283
Each basket of waxberries is based on a standard of 5 kilograms. Excess kilograms are recorded as positive numbers, and deficiencies are recorded as negative numbers, as shown in the figure. What is the total weight of the 4 baskets of waxberries in kilograms?
20.1
math
[ "The user wants me to calculate the total weight of 4 baskets of waxberries based on the provided image and text.\n\n**1. Analyze the input:**\n* **Image:** Shows four baskets of waxberries (lychees, it looks like, but the text says waxberries). Above each basket is a number:\n * Basket 1: -0.1\n * Bask...
8cb9c388-233d-4f29-99d1-7ec3885db905
According to the pseudocode shown below, when the inputs $$a$$ and $$b$$ are $$2$$ and $$3$$ respectively, the final value of $$m$$ that is output is ___.
$$3$$
math
[ "The user wants me to determine the output of the provided pseudocode given specific inputs.\n\n**1. Analyze the Pseudocode:**\nThe pseudocode is a simple algorithm to find the maximum of two numbers.\n- **Read $a, b$**: This step takes two input values. Let's call them $a$ and $b$.\n- **If $a > b$ Then**: This is ...
ca4c2a67-3e0c-4c57-a493-9cf73a4a6f06
The solution set of the inequality -2x + a ≤ 2 for x is shown in the figure. What is the value of a?
0
math
[ "The user wants me to find the value of 'a' given an inequality and its graph.\n\n**1. Analyze the inequality:**\nThe given inequality is $-2x + a \\le 2$.\n\n**2. Solve the inequality for x:**\nI need to isolate $x$.\nSubtract $a$ from both sides:\n$-2x \\le 2 - a$\n\nDivide by $-2$. Remember that dividing an ineq...
41540a65-16e0-4a46-89c9-2d4f4cdff4c1
As shown in the figure, $$OA=1$$. A point $$B$$ is randomly chosen on the semicircular arc with center $$O$$ and radius $$OA$$. The probability that the area of $$\triangle AOB$$ is less than $$\dfrac{1}{4}$$ is ___.
$$\dfrac{1}{3}$$
math
[ "The user wants me to solve a geometry probability problem based on an image.\n\n**1. Analyze the problem statement:**\n* **Given:** A semicircle with center $O$ and radius $OA = 1$.\n* **Point B:** A point chosen randomly on the semicircular arc. This implies a uniform distribution along the arc length.\n* *...
31415d78-ca79-43db-ab5f-939aed6dfda5
In the figure, in △ABD, ∠D = 90°, CD = 6, AD = 8, ∠ACD = 2∠B, the length of BD is.
16
math
["The user wants me to find the length of BD based on the provided image and text.\n\n**1. Analyze t(...TRUNCATED)
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Dataset card for MMK12-QWEN35-9B-VERIFIED

Strongich/MMK12-QWEN35-9B-VERIFIED is a filtered teacher-trace dataset built from FanqingM/MMK12 using Qwen/Qwen3.5-9B. The goal is to provide high-quality multimodal reasoning traces that can be used for off-policy distillation into smaller models.

Each row keeps the original MMK12 example fields and adds a responses column. The responses column contains a list of verified Qwen responses that survived the filtering pipeline, so a question can end up with fewer than 8 kept responses even though 8 rollouts were sampled initially.

Creation Process

1. Rebuild the MMK12 splits

The original FanqingM/MMK12 test split contains only multiple-choice questions. Because of that, the original train and test splits were merged and then re-split deterministically with:

  • test_size = 2000
  • seed = 1337

The published train and test splits in this dataset therefore do not match the original MMK12 split boundary.

2. Generate 8 Qwen rollouts per question

For each question-image pair, Qwen/Qwen3.5-9B was sampled for up to 8 rollouts with the following system prompt:

R1_STYLE_SYSTEM_PROMPT_GRPO = (
    "You are a visual agent and should provide concise answers."
    "The user asks a question, and the Assistant solves it. "
    "The assistant first thinks about the reasoning process in the mind "
    "and then provides the user with the answer. "
    "Let's think step by step and output the final answer within \\boxed{}."
)

Rollout generation used a maximum completion budget of 16384 tokens.

3. Keep only questions with strong rollout agreement

After rollout evaluation, only questions for which Qwen produced at least 6 correct rollouts out of 8 were kept. This biases the dataset toward examples where the teacher is consistently correct rather than occasionally lucky. As a result, the retained questions are useful not only for off-policy distillation, but also as a higher-confidence prompt pool for on-policy distillation setups such as GOLD, where stable teacher behavior is desirable.

4. Filter individual responses

Even for kept questions, each candidate response still had to pass several filters:

  • it had to contain </think>, so incomplete reasoning traces were dropped
  • the combined prompt and response length had to be <= 16384 tokens
  • its 4-gram repetition ratio had to be <= 0.30

Intended Use

This dataset is meant for off-policy distillation of smaller models from a stronger multimodal teacher. In practice, the responses list gives multiple filtered teacher traces per question, which makes the dataset useful for SFT-style training, response selection, or other teacher-student training setups.

Code Availability

The dataset generation code is not included in this release. It will be released later.

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