import gradio as gr import re # 题目列表 questions = [ "1. 37^(-42)=", "2. lim_{x→0} x³/(tanx - x)=", "3. cos x = x 的实根为 x=", "4. f(x)=(x-1)e^(x+1)+√(2x)+1/x-ln²x 的最小值为", "5. f(x)=x/6 + sinx/x 的极值点数量为", "6. y=(x-e)e^x+ln²(x+1)-√(x+1) 在(0,e1)处的切线在x轴上的截距为", "7. 点(1, 0)关于直线5x-2y+3=0的对称点为", "8. (2+3i)^7的虚部为", "9. arg(3+7i)/(9-4i)=(弧度制)", "10. 5!11! mod 998244353=", "11. C₃₇¹⁵=", "12. (x+2)^5除以x²+x+1的商(忽略余式)为", "13. 设f(x)=x⁴e^(x²)则f^(4)(x)/e^(x²)展开后x⁴的系数为", "14. 102233201和123456789的最大公约数为", "15. 2025的所有因数之和为", "16. ∑_{n=1}^∞ n^(-n)=", "17. ∫₀¹x^(-x)dx=", "18. ∑_{n=1}^{25}∏_{k=1}^n(1+1/k²)=", "19. (11,45,14)×(19,198,10)=", "20. 以(−2,−1,−1),(−1,1,3),(2,−4,1),(2,2,0)为顶点的四面体的体积为", "21. 点(1,0)到y=arctanx的距离为", "22. 5¹²+8¹²的所有质因数之和为", "23. 因式分解:x⁵-6x⁴+12x³-8x²-7x-1=", "24. 因式分解:a³b-3a³+a²b²+2ab²-6ab+2b³=", "25. √1,√2,√3,…,√2025的方差为", "26. 过(−2,−1),(−1,1),(0,2),(1,−2),(3,0)的二次曲线的离心率为", "27. x³-3x-5=0的复数根的实部为", "28. 已知六点(−2,−27),(−1,13),(0,5),(1,3),(2,−11),(3,−7),用最小二乘法拟合直线的相关系数为", "29. 以(−1,−1),(0,5),(6,2)为顶点的三角形外接圆半径为 其垂心坐标为", "30. (x+2)^4(3x²-5)(x²-6x-1)的展开式中x⁴的系数为", "31. 设X~N(0,0.5²),则P(-0.2≤X≤0.3)=", "32. 曲线y=2^x-x²(x∈[-2,4])的长度为", "33. 椭圆x²/5+y²/2=1的周长为", "34. 曲线ρ=1-sinθ在点(1,0)处的曲率为", "35. 曲线2x²+y²-5y+4=0和x²+2xy-3y²-2=0的所有公切线斜率之积为", "36. (13579 BD)₁₅转换为10进制是", "37. f(x)=1/(1-x-x²)在x=0处的泰勒展开的前6项为", "38. [2025,5202]中的质数数量为", "39. 已知a₁=2,aₙ₊₁=aₙ-1/aₙ,则a₂₀₂₅=", "40. 已知a₁=2,a₂=3,aₙ₊₂=aₙ₊₁-1/aₙ,则a₂₀₂₅=", "41. 冰雹猜想:从27开始,迭代得到1的最少次数为", "42. 已知a₁=0,a₂=1,aₙ₊₂=(n+1)(aₙ+aₙ₊₁),则a₄₀₉₆ mod 998244353=", "43. 已知f²(x)f'(x)=xe^x,f(2)=3,则f(0)=", "44. 已知某分子和分母均小于1000的分数约等于0.294663573085847,则该分数为", "45. 满足2ⁿ中不出现重复数字的最大正整数n为", "46. 已知a^a+b^b+c^c+d^d=abcd(abcd为1~9的正整数),则abcd=", "47. 100! mod 998244353=", "48. √(eπ)小数点后第37位是", "49. 已知f''(x)=2f(x)+x,f(0)=2,f'(0)=-1/2,则f(1)=", "50. 3^(4^5)的各位数字之和为" ] # 答案列表(已按题目顺序整理并统一格式) answers = [ "1.3662e-66", # 1 "3", # 2 "0.73909", # 3 "0.08027", # 4 "4", # 5 "-1.6762", # 6 "(-1.7586,1.1034)", # 7 "4449", # 8 "1.5841", # 9 "797038588", # 10 "9364199760", # 11 "x³+9x²+30x+41", # 12 "492", # 13 "3607", # 14 "3751", # 15 "1.2913", # 16 "1.2913", # 17 "81.672", # 18 "(-2322,156,1323)", # 19 "15.833", # 20 "0.67234", # 21 "12691", # 22 "(x²-3x-1)(x³-3x²+4x+1)", # 23 "(a²+2b)(ab-3a+b²)", # 24 "112.34", # 25 "0.84984", # 26 "-1.1395", # 27 "0.09798", # 28 "3.9841 (0.92308,2.8462)", # 29 "-475", # 30 "0.38117", # 31 "10.750", # 32 "11.613", # 33 "1.0607", # 34 "176", # 35 "13947703", # 36 "1+x+2x²+3x³+5x⁴+8x⁵", # 37 "386", # 38 "-35.709", # 39 "-125.93", # 40 "111", # 41 "641190802", # 42 "1.2238", # 43 "127/431", # 44 "29", # 45 "3435", # 46 "35305197", # 47 "3", # 48 "3.8564", # 49 "2250" # 50 ] def verify_answers(*user_answers): """验证用户答案并返回评分结果""" results = [] score = 0 for idx, (user_ans, correct_ans) in enumerate(zip(user_answers, answers)): is_correct = False user_ans = str(user_ans).strip() # 数值型答案验证(保留五位有效数字) if re.match(r'^-?\d+\.\d+e?-?\d*$', correct_ans) or re.match(r'^-?\d+\.\d+$', correct_ans): try: # 统一科学计数法格式 user_num = float(user_ans.replace('×10^', 'e').replace('^', 'e')) correct_num = float(correct_ans.replace('×10^', 'e').replace('^', 'e')) # 计算有效数字位数 sig_figs = 5 - (0 if correct_num == 0 else len(str(int(abs(correct_num))))) user_rounded = round(user_num, sig_figs) if sig_figs > 0 else int(round(user_num)) correct_rounded = round(correct_num, sig_figs) if sig_figs > 0 else int(round(correct_num)) is_correct = abs(user_rounded - correct_rounded) < 1e-4 except: pass # 整数答案验证 elif correct_ans.isdigit() and user_ans.isdigit(): is_correct = user_ans == correct_ans # 向量/坐标答案验证(忽略空格和中英文符号) elif correct_ans.startswith('(') and correct_ans.endswith(')'): user_clean = user_ans.replace(' ', '').replace(',', ',').lower() correct_clean = correct_ans.replace(' ', '').replace(',', ',').lower() is_correct = user_clean == correct_clean # 多项式/因式分解答案验证(忽略空格和次方符号) elif 'x' in correct_ans: user_clean = user_ans.replace(' ', '').replace('^', '').lower() correct_clean = correct_ans.replace(' ', '').replace('^', '').lower() is_correct = user_clean == correct_clean # 分数答案验证 elif '/' in correct_ans: is_correct = user_ans == correct_ans # 纯文本答案验证 else: is_correct = user_ans == correct_ans # 生成结果反馈 if is_correct: results.append(f"✅ 题目 {idx+1} 正确!") score += 1 else: results.append(f"❌ 题目 {idx+1} 错误,正确答案:{correct_ans}") results.append(f"------------------------\n总分:{score}/{len(questions)}") return "\n".join(results) # 创建Gradio界面 with gr.Blocks(title="GeoGebra数学测试题", theme=gr.themes.Soft()) as app: gr.Markdown("# GeoGebra数学应用能力测试") gr.Markdown("### 说明:非整数答案请保留五位有效数字,直接输入数字或表达式") # 动态生成题目输入框 input_components = [] with gr.Column(): for idx, q in enumerate(questions): with gr.Row(): gr.Markdown(f"**{idx+1}. {q}**") input_box = gr.Textbox( label=f"题目 {idx+1} 答案", placeholder="在此输入答案...", container=False ) input_components.append(input_box) # 提交按钮与结果显示 gr.Markdown("---") with gr.Row(): submit_btn = gr.Button("提交答案", variant="primary") clear_btn = gr.Button("清空答案") result_display = gr.Textbox( label="答题结果", lines=15, placeholder="提交后将在此显示每道题的对错及总分..." ) # 绑定事件 submit_btn.click( fn=verify_answers, inputs=input_components, outputs=result_display ) clear_btn.click( fn=lambda: [""]*len(input_components), inputs=None, outputs=input_components ) # 启动应用 if __name__ == "__main__": app.launch(share=True)