Enhance math skills functionality and testing

- Updated `requirements-dev.txt` to include `sympy` for algebra answer recomputation in tests.
- Modified `math.js` to implement a new round system for skills with more than 10 questions, ensuring unsolved questions are prioritized.
- Adjusted question navigation logic to accommodate the new round system.
- Enhanced the user interface to reflect the current question progress based on rounds.
- Added tests in `test_math_skills.py` to verify the correctness of algebraic expressions and equations, ensuring marked answers are accurate.
- Implemented new tests in `test_sky_browser.py` to validate the round functionality and progress tracking for skills.

app/math_algebra9.json

@@ -418,836 +418,2824 @@
        "mistake": "sign_product"
       }
      ]
-    }
-   ]
-  },
-  {
-   "id": "t_simplify",
-   "unit": "t",
-   "name": "פישוט ביטויים בעזרת הפילוג המורחב",
-   "short": "פישוט ביטויים",
-   "prereqs": [
-    "t_ext"
-   ],
-   "description": "פותחים סוגריים בפילוג המורחב, שמים לב לסימן שלפני כל מכפלה ומכנסים איברים דומים.",
-   "month": "ספטמבר",
-   "questions": [
+    },
     {
-     "question": "פשטו: $(x + 2)(x + 3) − x(x + 4)$",
+     "question": "$(x − 2)(x + 8) = ?$",
      "choices": [
       {
-       "text": "$x + 6$",
+       "text": "$x² + 6x − 16$",
        "correct": true
       },
       {
-       "text": "$9x + 6$",
-       "mistake": "minus_paren"
+       "text": "$x² − 16$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$6 − 4x$",
-       "mistake": "ext_partial"
+       "text": "$x² − 6x − 16$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x² + 6x + 16$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פשטו: $(x − 1)(x + 5) + (x + 2)(x − 3)$",
+     "question": "$(3x + 1)(2x − 3) = ?$",
      "choices": [
       {
-       "text": "$2x² + 3x − 11$",
+       "text": "$6x² − 7x − 3$",
        "correct": true
       },
       {
-       "text": "$2x² − 11$",
+       "text": "$6x² − 3$",
        "mistake": "ext_partial"
       },
       {
-       "text": "$2x² − 3x − 11$",
+       "text": "$6x² + 7x − 3$",
        "mistake": "sign_mid"
       },
       {
-       "text": "$2x² + 3x + 11$",
+       "text": "$6x² − 7x + 3$",
        "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פשטו: $(2x + 1)(x + 4) − 2x²$",
+     "question": "$(3a + 2b)(a + 2b) = ?$",
      "choices": [
       {
-       "text": "$9x + 4$",
+       "text": "$3a² + 8ab + 4b²$",
        "correct": true
       },
       {
-       "text": "$8x + 4$",
+       "text": "$3a² + 4b²$",
        "mistake": "ext_partial"
       },
       {
-       "text": "$4$",
+       "text": "$3a² − 8ab + 4b²$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "$(x + 5)(3x − 5) = ?$",
+     "choices": [
+      {
+       "text": "$3x² + 10x − 25$",
+       "correct": true
+      },
+      {
+       "text": "$3x² − 25$",
        "mistake": "ext_partial"
       },
       {
-       "text": "$4x² + 9x + 4$",
-       "mistake": "minus_paren"
+       "text": "$3x² − 10x − 25$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$3x² + 10x + 25$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פשטו: $(x + 3)(x − 3) − (x − 1)(x + 2)$",
+     "question": "$(3a + 2b)(2a − 3b) = ?$",
      "choices": [
       {
-       "text": "$−x − 7$",
+       "text": "$6a² − 5ab − 6b²$",
        "correct": true
       },
       {
-       "text": "$x − 11$",
-       "mistake": "minus_paren"
-      },
-      {
-       "text": "$−7$",
+       "text": "$6a² − 6b²$",
        "mistake": "ext_partial"
       },
       {
-       "text": "$x − 7$",
+       "text": "$6a² + 5ab − 6b²$",
        "mistake": "sign_mid"
+      },
+      {
+       "text": "$6a² − 5ab + 6b²$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פשטו: $3x(x + 1) − (x + 2)(3x − 1)$",
+     "question": "$(7 − x)(x + 2) = ?$",
      "choices": [
       {
-       "text": "$2 − 2x$",
+       "text": "$−x² + 5x + 14$",
        "correct": true
       },
       {
-       "text": "$8x − 2$",
-       "mistake": "minus_paren"
+       "text": "$14 − x²$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$3x + 2$",
-       "mistake": "ext_partial"
+       "text": "$−x² − 5x + 14$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x² + 5x + 14$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פשטו: $(a + 2)(a + 5) − (a + 1)(a + 6)$",
+     "question": "$(x + 3)(x + 9) = ?$",
      "choices": [
       {
-       "text": "$4$",
+       "text": "$x² + 12x + 27$",
        "correct": true
       },
       {
-       "text": "$14a + 16$",
-       "mistake": "minus_paren"
+       "text": "$x² + 27$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$0$",
+       "text": "$x² + 12x + 12$",
+       "mistake": "const_added"
+      },
+      {
+       "text": "$x² + 27x + 12$",
        "mistake": "const_added"
       }
      ]
     },
     {
-     "question": "פשטו: $(2x − 3)(x + 1) − (x + 1)(x − 1)$",
+     "question": "$(x + 4)(x + 7) = ?$",
      "choices": [
       {
-       "text": "$x² − x − 2$",
+       "text": "$x² + 11x + 28$",
        "correct": true
       },
       {
-       "text": "$x² − x − 4$",
-       "mistake": "minus_paren"
+       "text": "$x² + 28$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x² + x − 2$",
-       "mistake": "sign_mid"
+       "text": "$x² + 11x + 11$",
+       "mistake": "const_added"
       },
       {
-       "text": "$x² − 2$",
-       "mistake": "ext_partial"
+       "text": "$x² + 28x + 11$",
+       "mistake": "const_added"
       }
      ]
     },
     {
-     "question": "איזה ביטוי שווה ל־$(x + 4)(x − 1) − x²$?",
+     "question": "$(9 − x)(x + 3) = ?$",
      "choices": [
       {
-       "text": "$3x − 4$",
+       "text": "$−x² + 6x + 27$",
        "correct": true
       },
       {
-       "text": "$−4$",
+       "text": "$27 − x²$",
        "mistake": "ext_partial"
       },
       {
-       "text": "$−3x − 4$",
+       "text": "$−x² − 6x + 27$",
        "mistake": "sign_mid"
       },
       {
-       "text": "$3x + 4$",
+       "text": "$x² + 6x + 27$",
        "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פשטו: $5 − (x + 1)(x − 2)$",
+     "question": "$(2a + 3b)(2a + b) = ?$",
      "choices": [
       {
-       "text": "$−x² + x + 7$",
+       "text": "$4a² + 8ab + 3b²$",
        "correct": true
       },
       {
-       "text": "$−x² − x + 3$",
-       "mistake": "minus_paren"
+       "text": "$4a² + 3b²$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$7 − x²$",
-       "mistake": "ext_partial"
+       "text": "$4a² − 8ab + 3b²$",
+       "mistake": "sign_mid"
       }
      ]
     },
     {
-     "question": "פשטו: $2(x + 3)(x − 1)$",
+     "question": "$(2a + b)(a + b) = ?$",
      "choices": [
       {
-       "text": "$2x² + 4x − 6$",
+       "text": "$2a² + 3ab + b²$",
        "correct": true
       },
       {
-       "text": "$4x² + 8x − 12$",
-       "mistake": "double_both"
+       "text": "$2a² + b²$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$2x² + 4x − 3$",
-       "mistake": "partial_dist"
+       "text": "$2a² − 3ab + b²$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "$(x − 8)(2x + 7) = ?$",
+     "choices": [
+      {
+       "text": "$2x² − 9x − 56$",
+       "correct": true
       },
       {
-       "text": "$2x² − 6$",
+       "text": "$2x² − 56$",
        "mistake": "ext_partial"
+      },
+      {
+       "text": "$2x² + 9x − 56$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$2x² − 9x + 56$",
+       "mistake": "sign_product"
       }
      ]
-    }
-   ]
-  },
-  {
-   "id": "t_ext_eq",
-   "unit": "t",
-   "name": "פתרון משוואות בעזרת הפילוג המורחב",
-   "short": "משוואה ופילוג",
-   "prereqs": [
-    "t_ext"
-   ],
-   "description": "פותחים סוגריים בפילוג המורחב, האיברים עם $x²$ מתבטלים, ופותרים משוואה ממעלה ראשונה.",
-   "month": "ספטמבר",
-   "questions": [
+    },
     {
-     "question": "פתרו: $(x + 2)(x + 3) = x² + 16$",
+     "question": "$(a + 2b)(2a − 2b) = ?$",
      "choices": [
       {
-       "text": "$x = 2$",
+       "text": "$2a² + 2ab − 4b²$",
        "correct": true
       },
       {
-       "text": "$x = 4.4$",
-       "mistake": "move_sign"
+       "text": "$2a² − 4b²$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x = 10$",
-       "mistake": "forgot_divide"
+       "text": "$2a² − 2ab − 4b²$",
+       "mistake": "sign_mid"
       },
       {
-       "text": "אין פתרון",
-       "mistake": "ext_partial"
+       "text": "$2a² + 2ab + 4b²$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פתרו: $(x + 4)(x − 1) = x² + 8$",
+     "question": "$(2x − 6)(x + 5) = ?$",
      "choices": [
       {
-       "text": "$x = 4$",
+       "text": "$2x² + 4x − 30$",
        "correct": true
       },
       {
-       "text": "$x = 4/3$",
-       "mistake": "move_sign"
+       "text": "$2x² − 30$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x = 12$",
-       "mistake": "forgot_divide"
+       "text": "$2x² − 4x − 30$",
+       "mistake": "sign_mid"
       },
       {
-       "text": "$x = −4$",
-       "mistake": "sign_mid"
+       "text": "$2x² + 4x + 30$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פתרו: $(2x − 1)(x + 3) = 2x² + 1$",
+     "question": "$(6 − x)(x + 8) = ?$",
      "choices": [
       {
-       "text": "$x = 0.8$",
+       "text": "$−x² − 2x + 48$",
        "correct": true
       },
       {
-       "text": "$x = −0.4$",
-       "mistake": "move_sign"
+       "text": "$48 − x²$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x = 4$",
-       "mistake": "forgot_divide"
+       "text": "$−x² + 2x + 48$",
+       "mistake": "sign_mid"
       },
       {
-       "text": "אין פתרון",
-       "mistake": "ext_partial"
+       "text": "$x² − 2x + 48$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פתרו: $(x − 3)(x − 5) = x² − 1$",
+     "question": "$(8 − x)(x + 4) = ?$",
      "choices": [
       {
-       "text": "$x = 2$",
+       "text": "$−x² + 4x + 32$",
        "correct": true
       },
       {
-       "text": "$x = −2$",
-       "mistake": "neg_divide"
+       "text": "$32 − x²$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x = −1.75$",
-       "mistake": "move_sign"
+       "text": "$−x² − 4x + 32$",
+       "mistake": "sign_mid"
       },
       {
-       "text": "$x = −16$",
-       "mistake": "forgot_divide"
+       "text": "$x² + 4x + 32$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פתרו: $x(x + 6) = (x + 2)(x + 3)$",
+     "question": "$(x − 9)(3x − 8) = ?$",
      "choices": [
       {
-       "text": "$x = 6$",
+       "text": "$3x² − 35x + 72$",
        "correct": true
       },
       {
-       "text": "$x = 1$",
+       "text": "$3x² + 72$",
        "mistake": "ext_partial"
       },
       {
-       "text": "$x = 6/11$",
-       "mistake": "move_sign"
+       "text": "$3x² + 35x + 72$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$3x² − 35x − 72$",
+       "mistake": "neg_times_neg"
       }
      ]
     },
     {
-     "question": "פתרו: $(x + 5)(x − 2) − x² = 11$",
+     "question": "$(2x − 1)(x + 6) = ?$",
      "choices": [
       {
-       "text": "$x = 7$",
+       "text": "$2x² + 11x − 6$",
        "correct": true
       },
       {
-       "text": "$x = −7$",
-       "mistake": "sign_mid"
+       "text": "$2x² − 6$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x = 21$",
-       "mistake": "forgot_divide"
+       "text": "$2x² − 11x − 6$",
+       "mistake": "sign_mid"
       },
       {
-       "text": "$x = 1/3$",
-       "mistake": "move_sign"
+       "text": "$2x² + 11x + 6$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פתרו: $(3 − x)(x + 4) = 10 − x²$",
+     "question": "$(2 − x)(x + 1) = ?$",
      "choices": [
       {
-       "text": "$x = 2$",
+       "text": "$−x² + x + 2$",
        "correct": true
       },
       {
-       "text": "$x = −2$",
-       "mistake": "neg_divide"
+       "text": "$2 − x²$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x = −22$",
-       "mistake": "move_sign"
+       "text": "$−x² − x + 2$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x² + x + 2$",
+       "mistake": "sign_product"
       }
      ]
     },
     {
-     "question": "פתרו: $(2x + 3)(x − 4) = 2(x² − 5)$",
+     "question": "$(x + 5)(x + 7) = ?$",
      "choices": [
       {
-       "text": "$x = −0.4$",
+       "text": "$x² + 12x + 35$",
        "correct": true
       },
       {
-       "text": "$x = −1.4$",
-       "mistake": "partial_dist"
+       "text": "$x² + 35$",
+       "mistake": "ext_partial"
       },
       {
-       "text": "$x = 0.4$",
-       "mistake": "neg_divide"
+       "text": "$x² + 12x + 12$",
+       "mistake": "const_added"
       },
       {
-       "text": "$x = 4.4$",
-       "mistake": "move_sign"
+       "text": "$x² + 35x + 12$",
+       "mistake": "const_added"
       }
      ]
-    },
+    }
+   ]
+  },
+  {
+   "id": "t_simplify",
+   "unit": "t",
+   "name": "פישוט ביטויים בעזרת הפילוג המורחב",
+   "short": "פישוט ביטויים",
+   "prereqs": [
+    "t_ext"
+   ],
+   "description": "פותחים סוגריים בפילוג המורחב, שמים לב לסימן שלפני כל מכפלה ומכנסים איברים דומים.",
+   "month": "ספטמבר",
+   "questions": [
     {
-     "question": "מכפלת $x + 1$ ב־$x + 7$ גדולה ב־$23$ מ־$x²$. מצאו את $x$.",
+     "question": "פשטו: $(x + 2)(x + 3) − x(x + 4)$",
      "choices": [
       {
-       "text": "$x = 2$",
+       "text": "$x + 6$",
        "correct": true
       },
       {
-       "text": "$x = −3.75$",
-       "mistake": "diff_order"
+       "text": "$9x + 6$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$6 − 4x$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x − 1)(x + 5) + (x + 2)(x − 3)$",
+     "choices": [
+      {
+       "text": "$2x² + 3x − 11$",
+       "correct": true
+      },
+      {
+       "text": "$2x² − 11$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$2x² − 3x − 11$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$2x² + 3x + 11$",
+       "mistake": "sign_product"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(2x + 1)(x + 4) − 2x²$",
+     "choices": [
+      {
+       "text": "$9x + 4$",
+       "correct": true
+      },
+      {
+       "text": "$8x + 4$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$4$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$4x² + 9x + 4$",
+       "mistake": "minus_paren"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x + 3)(x − 3) − (x − 1)(x + 2)$",
+     "choices": [
+      {
+       "text": "$−x − 7$",
+       "correct": true
+      },
+      {
+       "text": "$x − 11$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$−7$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$x − 7$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $3x(x + 1) − (x + 2)(3x − 1)$",
+     "choices": [
+      {
+       "text": "$2 − 2x$",
+       "correct": true
+      },
+      {
+       "text": "$8x − 2$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$3x + 2$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(a + 2)(a + 5) − (a + 1)(a + 6)$",
+     "choices": [
+      {
+       "text": "$4$",
+       "correct": true
+      },
+      {
+       "text": "$14a + 16$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$0$",
+       "mistake": "const_added"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(2x − 3)(x + 1) − (x + 1)(x − 1)$",
+     "choices": [
+      {
+       "text": "$x² − x − 2$",
+       "correct": true
+      },
+      {
+       "text": "$x² − x − 4$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$x² + x − 2$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x² − 2$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "איזה ביטוי שווה ל־$(x + 4)(x − 1) − x²$?",
+     "choices": [
+      {
+       "text": "$3x − 4$",
+       "correct": true
+      },
+      {
+       "text": "$−4$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−3x − 4$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$3x + 4$",
+       "mistake": "sign_product"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $5 − (x + 1)(x − 2)$",
+     "choices": [
+      {
+       "text": "$−x² + x + 7$",
+       "correct": true
+      },
+      {
+       "text": "$−x² − x + 3$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$7 − x²$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $2(x + 3)(x − 1)$",
+     "choices": [
+      {
+       "text": "$2x² + 4x − 6$",
+       "correct": true
+      },
+      {
+       "text": "$4x² + 8x − 12$",
+       "mistake": "double_both"
+      },
+      {
+       "text": "$2x² + 4x − 3$",
+       "mistake": "partial_dist"
+      },
+      {
+       "text": "$2x² − 6$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x + 7)(x − 5) + (x − 1)(x + 6)$",
+     "choices": [
+      {
+       "text": "$2x² + 7x − 41$",
+       "correct": true
+      },
+      {
+       "text": "$2x² − 41$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$2x² − 7x − 41$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $4(x + 7)(x − 2)$",
+     "choices": [
+      {
+       "text": "$4x² + 20x − 56$",
+       "correct": true
+      },
+      {
+       "text": "$4x² − 56$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$4x² + 20x − 14$",
+       "mistake": "partial_dist"
+      },
+      {
+       "text": "$16x² + 80x − 224$",
+       "mistake": "double_both"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x + 2)(x + 1) − x(x + 7)$",
+     "choices": [
+      {
+       "text": "$−4x + 2$",
+       "correct": true
+      },
+      {
+       "text": "$10x + 2$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$4x + 2$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$−7x + 2$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x − 7)(x + 5) − x(x + 1)$",
+     "choices": [
+      {
+       "text": "$−3x − 35$",
+       "correct": true
+      },
+      {
+       "text": "$−x − 35$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$3x − 35$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x + 3)(x + 2) − x(x + 2)$",
+     "choices": [
+      {
+       "text": "$3x + 6$",
+       "correct": true
+      },
+      {
+       "text": "$−3x + 6$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$−2x + 6$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$7x + 6$",
+       "mistake": "minus_paren"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x − 5)(x + 2) − (x + 7)(x + 4)$",
+     "choices": [
+      {
+       "text": "$−14x − 38$",
+       "correct": true
+      },
+      {
+       "text": "$−38$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$8x + 18$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$14x − 38$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "איזה ביטוי שווה ל־$(x − 5)(x + 7) − (x − 5)(x + 5)$?",
+     "choices": [
+      {
+       "text": "$2x − 10$",
+       "correct": true
+      },
+      {
+       "text": "$−10$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$2x − 60$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$−2x − 10$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x − 5)(x + 1) − (x + 5)(x − 4)$",
+     "choices": [
+      {
+       "text": "$−5x + 15$",
+       "correct": true
+      },
+      {
+       "text": "$5x + 15$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$15$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−3x − 25$",
+       "mistake": "minus_paren"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x − 6)(x − 7) − (x + 6)(x − 2)$",
+     "choices": [
+      {
+       "text": "$−17x + 54$",
+       "correct": true
+      },
+      {
+       "text": "$54$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−9x + 30$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$17x + 54$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "איזה ביטוי שווה ל־$(x − 2)(x + 3) − x(x − 3)$?",
+     "choices": [
+      {
+       "text": "$4x − 6$",
+       "correct": true
+      },
+      {
+       "text": "$−4x − 6$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$−2x − 6$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$3x − 6$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $3 − (x + 2)(x − 4)$",
+     "choices": [
+      {
+       "text": "$−x² + 2x + 11$",
+       "correct": true
+      },
+      {
+       "text": "$−x² + 11$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−x² − 2x − 5$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$−x² − 2x + 11$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "איזה ביטוי שווה ל־$(x + 7)(x − 5) + (x − 7)(x + 3)$?",
+     "choices": [
+      {
+       "text": "$2x² − 2x − 56$",
+       "correct": true
+      },
+      {
+       "text": "$2x² + 2x − 56$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$2x² − 56$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x + 3)(x − 4) − x²$",
+     "choices": [
+      {
+       "text": "$−x − 12$",
+       "correct": true
+      },
+      {
+       "text": "$x − 12$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$−12$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "איזה ביטוי שווה ל־$10 − (x − 5)(x − 1)$?",
+     "choices": [
+      {
+       "text": "$−x² + 6x + 5$",
+       "correct": true
+      },
+      {
+       "text": "$−x² − 6x + 5$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$−x² + 5$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−x² − 6x + 15$",
+       "mistake": "minus_paren"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $3(x − 2)(x − 5)$",
+     "choices": [
+      {
+       "text": "$3x² − 21x + 30$",
+       "correct": true
+      },
+      {
+       "text": "$3x² + 21x + 30$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$9x² − 63x + 90$",
+       "mistake": "double_both"
+      },
+      {
+       "text": "$3x² − 21x + 10$",
+       "mistake": "partial_dist"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $6 − (x − 6)(x + 1)$",
+     "choices": [
+      {
+       "text": "$−x² + 5x + 12$",
+       "correct": true
+      },
+      {
+       "text": "$−x² − 5x$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$−x² − 5x + 12$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$−x² + 12$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x − 6)(x + 7) + (x + 3)(x − 2)$",
+     "choices": [
+      {
+       "text": "$2x² + 2x − 48$",
+       "correct": true
+      },
+      {
+       "text": "$2x² − 48$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$2x² − 2x − 48$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(3x − 2)(x + 6) − 3x²$",
+     "choices": [
+      {
+       "text": "$16x − 12$",
+       "correct": true
+      },
+      {
+       "text": "$−16x − 12$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$−12$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $5 − (x − 3)(x + 1)$",
+     "choices": [
+      {
+       "text": "$−x² + 2x + 8$",
+       "correct": true
+      },
+      {
+       "text": "$−x² + 8$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−x² − 2x + 2$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$−x² − 2x + 8$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פשטו: $(x − 5)(x − 6) − x²$",
+     "choices": [
+      {
+       "text": "$−11x + 30$",
+       "correct": true
+      },
+      {
+       "text": "$30$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$11x + 30$",
+       "mistake": "sign_mid"
+      }
+     ]
+    }
+   ]
+  },
+  {
+   "id": "t_ext_eq",
+   "unit": "t",
+   "name": "פתרון משוואות בעזרת הפילוג המורחב",
+   "short": "משוואה ופילוג",
+   "prereqs": [
+    "t_ext"
+   ],
+   "description": "פותחים סוגריים בפילוג המורחב, האיברים עם $x²$ מתבטלים, ופותרים משוואה ממעלה ראשונה.",
+   "month": "ספטמבר",
+   "questions": [
+    {
+     "question": "פתרו: $(x + 2)(x + 3) = x² + 16$",
+     "choices": [
+      {
+       "text": "$x = 2$",
+       "correct": true
+      },
+      {
+       "text": "$x = 4.4$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 10$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "אין פתרון",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 4)(x − 1) = x² + 8$",
+     "choices": [
+      {
+       "text": "$x = 4$",
+       "correct": true
+      },
+      {
+       "text": "$x = 4/3$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 12$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = −4$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(2x − 1)(x + 3) = 2x² + 1$",
+     "choices": [
+      {
+       "text": "$x = 0.8$",
+       "correct": true
+      },
+      {
+       "text": "$x = −0.4$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 4$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "אין פתרון",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 3)(x − 5) = x² − 1$",
+     "choices": [
+      {
+       "text": "$x = 2$",
+       "correct": true
+      },
+      {
+       "text": "$x = −2$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = −1.75$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = −16$",
+       "mistake": "forgot_divide"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $x(x + 6) = (x + 2)(x + 3)$",
+     "choices": [
+      {
+       "text": "$x = 6$",
+       "correct": true
+      },
+      {
+       "text": "$x = 1$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$x = 6/11$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 5)(x − 2) − x² = 11$",
+     "choices": [
+      {
+       "text": "$x = 7$",
+       "correct": true
+      },
+      {
+       "text": "$x = −7$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x = 21$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 1/3$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(3 − x)(x + 4) = 10 − x²$",
+     "choices": [
+      {
+       "text": "$x = 2$",
+       "correct": true
+      },
+      {
+       "text": "$x = −2$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = −22$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(2x + 3)(x − 4) = 2(x² − 5)$",
+     "choices": [
+      {
+       "text": "$x = −0.4$",
+       "correct": true
+      },
+      {
+       "text": "$x = −1.4$",
+       "mistake": "partial_dist"
+      },
+      {
+       "text": "$x = 0.4$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = 4.4$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "מכפלת $x + 1$ ב־$x + 7$ גדולה ב־$23$ מ־$x²$. מצאו את $x$.",
+     "choices": [
+      {
+       "text": "$x = 2$",
+       "correct": true
+      },
+      {
+       "text": "$x = −3.75$",
+       "mistake": "diff_order"
+      },
+      {
+       "text": "$x = 16$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 3.75$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 6)(x + 1) = x(x − 7) + 4$",
+     "choices": [
+      {
+       "text": "$x = 5$",
+       "correct": true
+      },
+      {
+       "text": "$x = 10$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 10/7$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$x = 5/6$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(2x − 6)(x + 1) = 2x² − 2$",
+     "choices": [
+      {
+       "text": "$x = −1$",
+       "correct": true
+      },
+      {
+       "text": "$x = 2$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 1$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = 4$",
+       "mistake": "forgot_divide"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 5)(x − 8) = x² − 31$",
+     "choices": [
+      {
+       "text": "$x = −3$",
+       "correct": true
+      },
+      {
+       "text": "$x = 9$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 3$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = 71/3$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 3)(x + 2) = x² − 19$",
+     "choices": [
+      {
+       "text": "$x = −5$",
+       "correct": true
+      },
+      {
+       "text": "$x = −2.6$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 5$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x = −25$",
+       "mistake": "forgot_divide"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 6)(x + 5) = x(x + 8)$",
+     "choices": [
+      {
+       "text": "$x = −10$",
+       "correct": true
+      },
+      {
+       "text": "$x = 10$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = −30$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 3.75$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 3)(x − 7) − x² = 3$",
+     "choices": [
+      {
+       "text": "$x = −6$",
+       "correct": true
+      },
+      {
+       "text": "$x = 4.5$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 6$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = 24$",
+       "mistake": "forgot_divide"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 1)(x + 5) = x² + 2$",
+     "choices": [
+      {
+       "text": "$x = −0.5$",
+       "correct": true
+      },
+      {
+       "text": "$x = 0.5$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x = −3$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 7/6$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 5)(x − 3) = x² + 39$",
+     "choices": [
+      {
+       "text": "$x = −3$",
+       "correct": true
+      },
+      {
+       "text": "$x = 24$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 3$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = −6.75$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(2x + 7)(x + 5) = 2x² + 1$",
+     "choices": [
+      {
+       "text": "$x = −2$",
+       "correct": true
+      },
+      {
+       "text": "$x = −34$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 36/17$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 2$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 1)(x + 8) = x(x + 3)$",
+     "choices": [
+      {
+       "text": "$x = 2$",
+       "correct": true
+      },
+      {
+       "text": "$x = −2$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x = 8$",
+       "mistake": "forgot_divide"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 2)(x + 3) = x(x + 6)$",
+     "choices": [
+      {
+       "text": "$x = −1.2$",
+       "correct": true
+      },
+      {
+       "text": "$x = 1.2$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 6$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = −1$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 8)(x + 3) − x² = −59$",
+     "choices": [
+      {
+       "text": "$x = 7$",
+       "correct": true
+      },
+      {
+       "text": "$x = −35$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = −7$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = 16.6$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 3)(x − 4) − x² = −6$",
+     "choices": [
+      {
+       "text": "$x = −6$",
+       "correct": true
+      },
+      {
+       "text": "$x = 6$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = 18$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "אין פתרון",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פ��רו: $(x + 4)(x + 2) − x² = −22$",
+     "choices": [
+      {
+       "text": "$x = −5$",
+       "correct": true
+      },
+      {
+       "text": "$x = −30$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = −7/3$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 5$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 4)(x − 2) − x² = −7$",
+     "choices": [
+      {
+       "text": "$x = 0.5$",
+       "correct": true
+      },
+      {
+       "text": "$x = −7.5$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = −0.5$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x = 1$",
+       "mistake": "forgot_divide"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 4)(x − 3) = x(x + 8)$",
+     "choices": [
+      {
+       "text": "$x = 0.8$",
+       "correct": true
+      },
+      {
+       "text": "$x = −12$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = −0.8$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 1.5$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x − 1)(x − 4) = x(x + 7) − 5$",
+     "choices": [
+      {
+       "text": "$x = 0.75$",
+       "correct": true
+      },
+      {
+       "text": "$x = −9$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = −0.75$",
+       "mistake": "neg_divide"
+      },
+      {
+       "text": "$x = 1/12$",
+       "mistake": "move_sign"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 8)(x − 1) − x² = 48$",
+     "choices": [
+      {
+       "text": "$x = 8$",
+       "correct": true
+      },
+      {
+       "text": "$x = 40/7$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = −8$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "אין פתרון",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "מכפלת $x + 4$ ב־$x − 2$ גדולה ב־$8$ מ־$x²$. מצאו את $x$.",
+     "choices": [
+      {
+       "text": "$x = 8$",
+       "correct": true
+      },
+      {
+       "text": "$x = 16$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 0$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = −8$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "מכפלת $x + 1$ ב־$x + 6$ גדולה ב־$48$ מ־$x²$. מצאו את $x$.",
+     "choices": [
+      {
+       "text": "$x = 6$",
+       "correct": true
+      },
+      {
+       "text": "$x = −6$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x = 54/7$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "אין פתרון",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "פתרו: $(x + 5)(x + 3) = x(x + 4) + 2$",
+     "choices": [
+      {
+       "text": "$x = −3.25$",
+       "correct": true
+      },
+      {
+       "text": "$x = −13$",
+       "mistake": "forgot_divide"
+      },
+      {
+       "text": "$x = 4.25$",
+       "mistake": "move_sign"
+      },
+      {
+       "text": "$x = 3.25$",
+       "mistake": "sign_mid"
+      }
+     ]
+    }
+   ]
+  },
+  {
+   "id": "t_area",
+   "unit": "t",
+   "name": "השוואת שטחים בעזרת הפילוג",
+   "short": "השוואת שטחים",
+   "prereqs": [
+    "t_ext"
+   ],
+   "description": "מבטאים שטחים כמכפלות של ביטויים אלגבריים ומשווים ביניהם.",
+   "month": "ספטמבר",
+   "questions": [
+    {
+     "question": "אורך מלבן $x + 4$ ורוחבו $x + 1$. צלע ריבוע $x + 2$. בכמה שטח המלבן גדול משטח הריבוע?",
+     "choices": [
+      {
+       "text": "$x$",
+       "correct": true
+      },
+      {
+       "text": "$5x$",
+       "mistake": "forgot_middle"
+      },
+      {
+       "text": "$2$",
+       "mistake": "area_perimeter"
+      },
+      {
+       "text": "$−x$",
+       "mistake": "diff_order"
+      }
+     ]
+    },
+    {
+     "question": "אורך מלבן $x + 5$ ורוחבו $x − 2$. מה שטחו?",
+     "choices": [
+      {
+       "text": "$x² + 3x − 10$",
+       "correct": true
+      },
+      {
+       "text": "$x² − 10$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$4x + 6$",
+       "mistake": "area_perimeter"
+      },
+      {
+       "text": "$x² − 3x − 10$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "צלע ריבוע היא $x$. מגדילים צלע אחת ב־$3$ ומקטינים את הצלע השנייה ב־$3$, ומתקבל מלבן. מה קרה לשטח?",
+     "choices": [
+      {
+       "text": "השטח קטן ב־$9$",
+       "correct": true
+      },
+      {
+       "text": "השטח לא השתנה",
+       "mistake": "shift_balance"
+      },
+      {
+       "text": "השטח גדל ב־$9$",
+       "mistake": "diff_order"
+      }
+     ]
+    },
+    {
+     "question": "מלבן א׳: $x + 6$ על $x$. מלבן ב׳: $x + 2$ על $x + 3$. בכמה שטח מלבן א׳ גדול משטח מלבן ב׳?",
+     "choices": [
+      {
+       "text": "$x − 6$",
+       "correct": true
+      },
+      {
+       "text": "$11x + 6$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$6x − 6$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$6 − x$",
+       "mistake": "diff_order"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 4$ מוקפת בשביל ברוחב $1$ מכל צד. מה השטח של הגינה יחד עם השביל?",
+     "choices": [
+      {
+       "text": "$x² + 8x + 12$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 6x + 5$",
+       "mistake": "frame_one_side"
+      },
+      {
+       "text": "$x² + 12$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 4$ מוקפת בשביל ברוחב $1$ מכל צד. מה שטח השביל לבדו?",
+     "choices": [
+      {
+       "text": "$4x + 12$",
+       "correct": true
+      },
+      {
+       "text": "$12x + 12$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$2x + 5$",
+       "mistake": "frame_one_side"
+      }
+     ]
+    },
+    {
+     "question": "שטח מלבן שמידותיו $x + 7$ על $x − 1$ שווה לשטח ריבוע שצלעו $x + 2$. מצאו את $x$.",
+     "choices": [
+      {
+       "text": "$x = 5.5$",
+       "correct": true
+      },
+      {
+       "text": "$x = 11/6$",
+       "mistake": "forgot_middle"
+      },
+      {
+       "text": "$x = −2.75$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "צלע ריבוע היא $x$. אורך מלבן גדול ב־$5$ מצלע הריבוע, ורוחבו קטן ב־$2$ ממנה. בכמה שטח המלבן גדול משטח הריבוע?",
+     "choices": [
+      {
+       "text": "$3x − 10$",
+       "correct": true
+      },
+      {
+       "text": "$−10$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−3x − 10$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$6$",
+       "mistake": "area_perimeter"
+      }
+     ]
+    },
+    {
+     "question": "מלבן שמידותיו $x + 3$ על $x + 5$, וריבוע שצלעו $x + 4$. איזה שטח גדול יותר, ובכמה?",
+     "choices": [
+      {
+       "text": "שטח הריבוע, ב־$1$",
+       "correct": true
+      },
+      {
+       "text": "שטח המלבן, ב־$1$",
+       "mistake": "diff_order"
+      },
+      {
+       "text": "השטחים שווים",
+       "mistake": "shift_balance"
+      }
+     ]
+    },
+    {
+     "question": "ניצבי משולש ישר זווית הם $x + 4$ ו־$x − 2$. מה שטח המשולש?",
+     "choices": [
+      {
+       "text": "$(x² + 2x − 8) : 2$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 2x − 8$",
+       "mistake": "forgot_half_area"
+      },
+      {
+       "text": "$(x² − 8) : 2$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "אורך מלבן $x + 9$ ורוחבו $x + 2$. מה שטחו?",
+     "choices": [
+      {
+       "text": "$x² + 11x + 18$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 18$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$4x + 22$",
+       "mistake": "area_perimeter"
+      }
+     ]
+    },
+    {
+     "question": "אורך מלבן $x + 7$ ורוחבו $x + 9$. צלע ריבוע $x + 4$. בכמה שטח המלבן גדול משטח הריבוע?",
+     "choices": [
+      {
+       "text": "$8x + 47$",
+       "correct": true
+      },
+      {
+       "text": "$16x + 47$",
+       "mistake": "forgot_middle"
+      },
+      {
+       "text": "$−8x − 47$",
+       "mistake": "diff_order"
+      },
+      {
+       "text": "$16$",
+       "mistake": "area_perimeter"
+      }
+     ]
+    },
+    {
+     "question": "אורך מלבן $x + 4$ ורוחבו $x − 6$. מה שטחו?",
+     "choices": [
+      {
+       "text": "$x² − 2x − 24$",
+       "correct": true
+      },
+      {
+       "text": "$x² − 24$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$4x − 4$",
+       "mistake": "area_perimeter"
+      },
+      {
+       "text": "$x² + 2x − 24$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "מלבן שמידותיו $x + 1$ על $x + 9$, וריבוע שצלעו $x + 5$. איזה שטח גדול יותר, ובכמה?",
+     "choices": [
+      {
+       "text": "שטח הריבוע, ב־$16$",
+       "correct": true
+      },
+      {
+       "text": "שטח המלבן, ב־$16$",
+       "mistake": "diff_order"
+      },
+      {
+       "text": "השטחים שווים",
+       "mistake": "shift_balance"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 9$ מוקפת בשביל ברוחב $1$ מכל צד. מה שטח השביל לבדו?",
+     "choices": [
+      {
+       "text": "$4x + 22$",
+       "correct": true
+      },
+      {
+       "text": "$22x + 22$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$2x + 10$",
+       "mistake": "frame_one_side"
+      }
+     ]
+    },
+    {
+     "question": "אורך מלבן $x + 7$ ורוחבו $x − 5$. מה שטחו?",
+     "choices": [
+      {
+       "text": "$x² + 2x − 35$",
+       "correct": true
+      },
+      {
+       "text": "$x² − 35$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$4x + 4$",
+       "mistake": "area_perimeter"
+      },
+      {
+       "text": "$x² − 2x − 35$",
+       "mistake": "sign_mid"
+      }
+     ]
+    },
+    {
+     "question": "צלע ריבוע היא $x$. אורך מלבן גדול ב־$8$ מצלע הריבוע, ורוחבו קטן ב־$6$ ממנה. בכמה שטח המלבן גדול משטח הריבוע?",
+     "choices": [
+      {
+       "text": "$2x − 48$",
+       "correct": true
+      },
+      {
+       "text": "$−48$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−2x − 48$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$4$",
+       "mistake": "area_perimeter"
+      }
+     ]
+    },
+    {
+     "question": "מלבן א׳: $x + 6$ על $x + 9$. מלבן ב׳: $x + 5$ על $x + 7$. בכמה שטח מלבן א׳ גדול משטח מלבן ב׳?",
+     "choices": [
+      {
+       "text": "$3x + 19$",
+       "correct": true
+      },
+      {
+       "text": "$27x + 89$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$19$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−3x − 19$",
+       "mistake": "diff_order"
+      }
+     ]
+    },
+    {
+     "question": "מלבן שמידותיו $x + 7$ על $x + 11$, וריבוע שצלעו $x + 9$. איזה שטח גדול יותר, ובכמה?",
+     "choices": [
+      {
+       "text": "שטח הריבוע, ב־$4$",
+       "correct": true
+      },
+      {
+       "text": "שטח המלבן, ב־$4$",
+       "mistake": "diff_order"
+      },
+      {
+       "text": "השטחים שווים",
+       "mistake": "shift_balance"
+      }
+     ]
+    },
+    {
+     "question": "צלע ריבוע היא $x$. אורך מלבן גדול ב־$5$ מצלע הריבוע, ורוחבו קטן ב־$4$ ממנה. בכמה שטח המלבן גדול משטח הריבוע?",
+     "choices": [
+      {
+       "text": "$x − 20$",
+       "correct": true
+      },
+      {
+       "text": "$−20$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−x − 20$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$2$",
+       "mistake": "area_perimeter"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 7$ מוקפת בשביל ברוחב $2$ מכל צד. מה שטח השביל לבדו?",
+     "choices": [
+      {
+       "text": "$8x + 44$",
+       "correct": true
+      },
+      {
+       "text": "$22x + 44$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$4x + 18$",
+       "mistake": "frame_one_side"
+      }
+     ]
+    },
+    {
+     "question": "מלבן שמידותיו $x + 6$ על $x + 12$, וריבוע שצלעו $x + 9$. איזה שטח גדול יותר, ובכמה?",
+     "choices": [
+      {
+       "text": "שטח הריבוע, ב־$9$",
+       "correct": true
+      },
+      {
+       "text": "שטח המלבן, ב־$9$",
+       "mistake": "diff_order"
+      },
+      {
+       "text": "השטחים שווים",
+       "mistake": "shift_balance"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 6$ מוקפת בשביל ברוחב $1$ מכל צד. מה שטח השביל לבדו?",
+     "choices": [
+      {
+       "text": "$4x + 16$",
+       "correct": true
+      },
+      {
+       "text": "$16x + 16$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$2x + 7$",
+       "mistake": "frame_one_side"
+      }
+     ]
+    },
+    {
+     "question": "ניצבי משולש ישר זווית הם $x + 3$ ו־$x + 2$. מה שטח המשולש?",
+     "choices": [
+      {
+       "text": "$(x² + 5x + 6) : 2$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 5x + 6$",
+       "mistake": "forgot_half_area"
+      },
+      {
+       "text": "$(x² + 6) : 2$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "ניצבי משולש ישר זווית הם $x + 9$ ו־$x + 6$. מה שטח המשולש?",
+     "choices": [
+      {
+       "text": "$(x² + 15x + 54) : 2$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 15x + 54$",
+       "mistake": "forgot_half_area"
+      },
+      {
+       "text": "$(x² + 54) : 2$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 4$ מוקפת בשביל ברוחב $3$ מכל צד. מה השטח של הגינה יחד עם השביל?",
+     "choices": [
+      {
+       "text": "$x² + 16x + 60$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 10x + 21$",
+       "mistake": "frame_one_side"
+      },
+      {
+       "text": "$x² + 60$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 9$ מוקפת בשביל ברוחב $1$ מכל צד. מה השטח של הגינה יחד עם השביל?",
+     "choices": [
+      {
+       "text": "$x² + 13x + 22$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 11x + 10$",
+       "mistake": "frame_one_side"
+      },
+      {
+       "text": "$x² + 22$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "ניצבי משולש ישר זווית הם $x + 6$ ו־$x − 2$. מה שטח המשולש?",
+     "choices": [
+      {
+       "text": "$(x² + 4x − 12) : 2$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 4x − 12$",
+       "mistake": "forgot_half_area"
+      },
+      {
+       "text": "$(x² − 12) : 2$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "גינה מלבנית שמידותיה $x$ על $x + 8$ מוקפת בשביל ברוחב $1$ מכל צד. מה השטח של הגינה יחד עם השביל?",
+     "choices": [
+      {
+       "text": "$x² + 12x + 20$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 10x + 9$",
+       "mistake": "frame_one_side"
+      },
+      {
+       "text": "$x² + 20$",
+       "mistake": "ext_partial"
+      }
+     ]
+    },
+    {
+     "question": "מלבן א׳: $x + 5$ על $x + 8$. מלבן ב׳: $x + 8$ על $x + 1$. בכמה שטח מלבן א׳ גדול משטח מלבן ב׳?",
+     "choices": [
+      {
+       "text": "$4x + 32$",
+       "correct": true
+      },
+      {
+       "text": "$22x + 48$",
+       "mistake": "minus_paren"
+      },
+      {
+       "text": "$32$",
+       "mistake": "ext_partial"
+      },
+      {
+       "text": "$−4x − 32$",
+       "mistake": "diff_order"
+      }
+     ]
+    }
+   ]
+  },
+  {
+   "id": "t_formulas",
+   "unit": "t",
+   "name": "נוסחאות הכפל המקוצר",
+   "short": "כפל מקוצר",
+   "prereqs": [
+    "t_ext"
+   ],
+   "description": "$(a ± b)² = a² ± 2ab + b²$ ו־$(a + b)(a − b) = a² − b²$. אפשר לראות אותן גם כשטחים של ריבועים ומלבנים.",
+   "month": "ספטמבר",
+   "questions": [
+    {
+     "question": "$(2x − 3)² = ?$",
+     "choices": [
+      {
+       "text": "$4x² − 12x + 9$",
+       "correct": true
+      },
+      {
+       "text": "$4x² + 9$",
+       "mistake": "forgot_middle"
+      },
+      {
+       "text": "$4x² − 6x + 9$",
+       "mistake": "middle_no_2"
+      },
+      {
+       "text": "$2x² − 12x + 9$",
+       "mistake": "coef_not_raised"
+      }
+     ]
+    },
+    {
+     "question": "$(3x + 5)(3x − 5) = ?$",
+     "choices": [
+      {
+       "text": "$9x² − 25$",
+       "correct": true
+      },
+      {
+       "text": "$9x² + 25$",
+       "mistake": "diff_sign"
+      },
+      {
+       "text": "$3x² − 25$",
+       "mistake": "coef_not_raised"
+      },
+      {
+       "text": "$9x² − 30x + 25$",
+       "mistake": "diffsq_as_square"
+      }
+     ]
+    },
+    {
+     "question": "$(x + 6)² = ?$",
+     "choices": [
+      {
+       "text": "$x² + 12x + 36$",
+       "correct": true
+      },
+      {
+       "text": "$x² + 36$",
+       "mistake": "forgot_middle"
+      },
+      {
+       "text": "$x² + 6x + 36$",
+       "mistake": "middle_no_2"
+      },
+      {
+       "text": "$x² + 12x + 12$",
+       "mistake": "sq_as_double"
+      }
+     ]
+    },
+    {
+     "question": "$(x − 4)² = ?$",
+     "choices": [
+      {
+       "text": "$x² − 8x + 16$",
+       "correct": true
+      },
+      {
+       "text": "$x² − 16$",
+       "mistake": "diffsq_as_square"
+      },
+      {
+       "text": "$x² + 8x + 16$",
+       "mistake": "sign_mid"
+      },
+      {
+       "text": "$x² − 8x − 16$",
+       "mistake": "neg_times_neg"
+      }
+     ]
+    },
+    {
+     "question": "$(a + 2b)² = ?$",
+     "choices": [
+      {
+       "text": "$a² + 4ab + 4b²$",
+       "correct": true
+      },
+      {
+       "text": "$a² + 2ab + 4b²$",
+       "mistake": "middle_no_2"
+      },
+      {
+       "text": "$a² + 4ab + 2b²$",
+       "mistake": "coef_not_raised"
+      },
+      {
+       "text": "$a² + 4b²$",
+       "mistake": "forgot_middle"
+      }
+     ]
+    },
+    {
+     "question": "$(7 − x)(7 + x) = ?$",
+     "choices": [
+      {
+       "text": "$49 − x²$",
+       "correct": true
+      },
+      {
+       "text": "$x² − 49$",
+       "mistake": "diffsq_order"
+      },
+      {
+       "text": "$49 − 14x + x²$",
+       "mistake": "diffsq_as_square"
+      },
+      {
+       "text": "$14 − x²$",
+       "mistake": "sq_as_double"
+      }
+     ]
+    },
+    {
+     "question": "$(5x + 1)² = ?$",
+     "choices": [
+      {
+       "text": "$25x² + 10x + 1$",
+       "correct": true
+      },
+      {
+       "text": "$25x² + 5x + 1$",
+       "mistake": "middle_no_2"
+      },
+      {
+       "text": "$5x² + 10x + 1$",
+       "mistake": "coef_not_raised"
+      },
+      {
+       "text": "$25x² + 1$",
+       "mistake": "forgot_middle"
+      }
+     ]
+    },
+    {
+     "question": "ריבוע שצלעו $a + b$ מחולק לריבוע שצלעו $a$, לריבוע שצלעו $b$ ולשני מלבנים. מה סכום השטחים של שני המלבנים?",
+     "choices": [
+      {
+       "text": "$2ab$",
+       "correct": true
+      },
+      {
+       "text": "$ab$",
+       "mistake": "middle_no_2"
+      },
+      {
+       "text": "$a² + b²$",
+       "mistake": "other_quantity"
+      }
+     ]
+    },
+    {
+     "question": "חשבו בעזרת נוסחת הכפל המקוצר: $51² = ?$",
+     "choices": [
+      {
+       "text": "$2601$",
+       "correct": true
       },
       {
-       "text": "$x = 16$",
-       "mistake": "forgot_divide"
+       "text": "$2501$",
+       "mistake": "forgot_middle"
       },
       {
-       "text": "$x = 3.75$",
-       "mistake": "move_sign"
+       "text": "$2551$",
+       "mistake": "middle_no_2"
       }
      ]
     },
     {
-     "question": "פתרו: $(x − 6)(x + 1) = x(x − 7) + 4$",
+     "question": "חשבו בעזרת נוסחת הכפל המקוצר: $98 · 102 = ?$",
      "choices": [
       {
-       "text": "$x = 5$",
+       "text": "$9996$",
        "correct": true
       },
       {
-       "text": "$x = 10$",
-       "mistake": "forgot_divide"
-      },
-      {
-       "text": "$x = 10/7$",
-       "mistake": "ext_partial"
+       "text": "$10004$",
+       "mistake": "diff_sign"
       },
       {
-       "text": "$x = 5/6$",
-       "mistake": "sign_mid"
+       "text": "$9604$",
+       "mistake": "diffsq_as_square"
       }
      ]
-    }
-   ]
-  },
-  {
-   "id": "t_area",
-   "unit": "t",
-   "name": "השוואת שטחים בעזרת הפילוג",
-   "short": "השוואת שטחים",
-   "prereqs": [
-    "t_ext"
-   ],
-   "description": "מבטאים שטחים כמכפלות של ביטויים אלגבריים ומשווים ביניהם.",
-   "month": "ספטמבר",
-   "questions": [
+    },
     {
-     "question": "אורך מלבן $x + 4$ ורוחבו $x + 1$. צלע ריבוע $x + 2$. בכמה שטח המלבן גדול משטח הריבוע?",
+     "question": "חשבו בעזרת נוסחת הכפל המקוצר: $52² = ?$",
      "choices": [
       {
-       "text": "$x$",
+       "text": "$2704$",
        "correct": true
       },
       {
-       "text": "$5x$",
+       "text": "$2504$",
        "mistake": "forgot_middle"
       },
       {
-       "text": "$2$",
-       "mistake": "area_perimeter"
-      },
-      {
-       "text": "$−x$",
-       "mistake": "diff_order"
+       "text": "$2604$",
+       "mistake": "middle_no_2"
       }
      ]
     },
     {
-     "question": "אורך מלבן $x + 5$ ורוחבו $x − 2$. מה שטחו?",
+     "question": "$(x + 2)² = ?$",
      "choices": [
       {
-       "text": "$x² + 3x − 10$",
+       "text": "$x² + 4x + 4$",
        "correct": true
       },
       {
-       "text": "$x² − 10$",
-       "mistake": "ext_partial"
-      },
-      {
-       "text": "$4x + 6$",
-       "mistake": "area_perimeter"
+       "text": "$x² + 2x + 4$",
+       "mistake": "middle_no_2"
       },
       {
-       "text": "$x² − 3x − 10$",
-       "mistake": "sign_mid"
+       "text": "$x² + 4$",
+       "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "צלע ריבוע היא $x$. מגדילים צלע אחת ב־$3$ ומקטינים את הצלע השנייה ב־$3$, ומתקבל מלבן. מה קרה לשטח?",
+     "question": "$(x + 4)² = ?$",
      "choices": [
       {
-       "text": "השטח קטן ב־$9$",
+       "text": "$x² + 8x + 16$",
        "correct": true
       },
       {
-       "text": "השטח לא השתנה",
-       "mistake": "shift_balance"
+       "text": "$x² + 8x + 8$",
+       "mistake": "sq_as_double"
       },
       {
-       "text": "השטח גדל ב־$9$",
-       "mistake": "diff_order"
+       "text": "$x² + 4x + 16$",
+       "mistake": "middle_no_2"
+      },
+      {
+       "text": "$x² + 16$",
+       "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "מלבן א׳: $x + 6$ על $x$. מלבן ב׳: $x + 2$ על $x + 3$. בכמה שטח מלבן א׳ גד��ל משטח מלבן ב׳?",
+     "question": "$(x − 1)² = ?$",
      "choices": [
       {
-       "text": "$x − 6$",
+       "text": "$x² − 2x + 1$",
        "correct": true
       },
       {
-       "text": "$11x + 6$",
-       "mistake": "minus_paren"
+       "text": "$x² − 1$",
+       "mistake": "diffsq_as_square"
       },
       {
-       "text": "$6x − 6$",
-       "mistake": "ext_partial"
+       "text": "$x² + 1$",
+       "mistake": "forgot_middle"
       },
       {
-       "text": "$6 − x$",
-       "mistake": "diff_order"
+       "text": "$x² − 2x + 2$",
+       "mistake": "sq_as_double"
       }
      ]
     },
     {
-     "question": "גינה מלבנית שמידותיה $x$ על $x + 4$ מוקפת בשביל ברוחב $1$ מכל צד. מה השטח של הגינה יחד עם השביל?",
+     "question": "$(4x + 9)(4x − 9) = ?$",
      "choices": [
       {
-       "text": "$x² + 8x + 12$",
+       "text": "$16x² − 81$",
        "correct": true
       },
       {
-       "text": "$x² + 6x + 5$",
-       "mistake": "frame_one_side"
+       "text": "$16x² + 81$",
+       "mistake": "diff_sign"
       },
       {
-       "text": "$x² + 12$",
-       "mistake": "ext_partial"
+       "text": "$16x² − 72x + 81$",
+       "mistake": "diffsq_as_square"
+      },
+      {
+       "text": "$4x² − 81$",
+       "mistake": "coef_not_raised"
       }
      ]
     },
     {
-     "question": "גינה מלבנית שמידותיה $x$ על $x + 4$ מוקפת בשביל ברוחב $1$ מכל צד. מה שטח השביל לבדו?",
+     "question": "$(2x + 6)² = ?$",
      "choices": [
       {
-       "text": "$4x + 12$",
+       "text": "$4x² + 24x + 36$",
        "correct": true
       },
       {
-       "text": "$12x + 12$",
-       "mistake": "minus_paren"
+       "text": "$4x² + 12x + 36$",
+       "mistake": "middle_no_2"
       },
       {
-       "text": "$2x + 5$",
-       "mistake": "frame_one_side"
+       "text": "$2x² + 24x + 36$",
+       "mistake": "coef_not_raised"
+      },
+      {
+       "text": "$4x² + 36$",
+       "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "שטח מלבן שמידותיו $x + 7$ על $x − 1$ שווה לשטח ריבוע שצלעו $x + 2$. מצאו את $x$.",
+     "question": "$(a − 3b)² = ?$",
      "choices": [
       {
-       "text": "$x = 5.5$",
+       "text": "$a² − 6ab + 9b²$",
        "correct": true
       },
       {
-       "text": "$x = 11/6$",
-       "mistake": "forgot_middle"
+       "text": "$a² − 3ab + 9b²$",
+       "mistake": "middle_no_2"
       },
       {
-       "text": "$x = −2.75$",
-       "mistake": "ext_partial"
+       "text": "$a² − 6ab + 3b²$",
+       "mistake": "coef_not_raised"
+      },
+      {
+       "text": "$a² + 9b²$",
+       "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "צלע ריבוע היא $x$. אורך מלבן גדול ב־$5$ מצלע הריבוע, ורוחבו קטן ב־$2$ ממנה. בכמה שטח המלבן גדול משטח הריבוע?",
+     "question": "$(5x − 1)(5x + 1) = ?$",
      "choices": [
       {
-       "text": "$3x − 10$",
+       "text": "$25x² − 1$",
        "correct": true
       },
       {
-       "text": "$−10$",
-       "mistake": "ext_partial"
+       "text": "$25x² + 1$",
+       "mistake": "diff_sign"
       },
       {
-       "text": "$−3x − 10$",
-       "mistake": "sign_mid"
+       "text": "$25x² − 10x + 1$",
+       "mistake": "diffsq_as_square"
       },
       {
-       "text": "$6$",
-       "mistake": "area_perimeter"
+       "text": "$5x² − 1$",
+       "mistake": "coef_not_raised"
       }
      ]
     },
     {
-     "question": "מלבן שמידותיו $x + 3$ על $x + 5$, וריבוע שצלעו $x + 4$. איזה שטח גדול יותר, ובכמה?",
+     "question": "$(a − 4b)² = ?$",
      "choices": [
       {
-       "text": "שטח הריבוע, ב־$1$",
+       "text": "$a² − 8ab + 16b²$",
        "correct": true
       },
       {
-       "text": "שטח המלבן, ב־$1$",
-       "mistake": "diff_order"
+       "text": "$a² − 4ab + 16b²$",
+       "mistake": "middle_no_2"
       },
       {
-       "text": "השטחים שווים",
-       "mistake": "shift_balance"
+       "text": "$a² − 8ab + 4b²$",
+       "mistake": "coef_not_raised"
+      },
+      {
+       "text": "$a² + 16b²$",
+       "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "ניצבי משולש ישר זווית הם $x + 4$ ו־$x − 2$. מה שטח המשולש?",
+     "question": "חשבו בעזרת נוסחת הכפל המקוצר: $26 · 34 = ?$",
      "choices": [
       {
-       "text": "$(x² + 2x − 8) : 2$",
+       "text": "$884$",
        "correct": true
       },
       {
-       "text": "$x² + 2x − 8$",
-       "mistake": "forgot_half_area"
+       "text": "$916$",
+       "mistake": "diff_sign"
       },
       {
-       "text": "$(x² − 8) : 2$",
-       "mistake": "ext_partial"
+       "text": "$676$",
+       "mistake": "diffsq_as_square"
       }
      ]
-    }
-   ]
-  },
-  {
-   "id": "t_formulas",
-   "unit": "t",
-   "name": "נוסחאות הכפל המקוצר",
-   "short": "כפל מקוצר",
-   "prereqs": [
-    "t_ext"
-   ],
-   "description": "$(a ± b)² = a² ± 2ab + b²$ ו־$(a + b)(a − b) = a² − b²$. אפשר לראות אותן גם כשטחים של ריבועים ומלבנים.",
-   "month": "ספטמבר",
-   "questions": [
+    },
     {
-     "question": "$(2x − 3)² = ?$",
+     "question": "$(5x − 9)(5x + 9) = ?$",
      "choices": [
       {
-       "text": "$4x² − 12x + 9$",
+       "text": "$25x² − 81$",
        "correct": true
       },
       {
-       "text": "$4x² + 9$",
-       "mistake": "forgot_middle"
+       "text": "$25x² + 81$",
+       "mistake": "diff_sign"
       },
       {
-       "text": "$4x² − 6x + 9$",
-       "mistake": "middle_no_2"
+       "text": "$25x² − 90x + 81$",
+       "mistake": "diffsq_as_square"
       },
       {
-       "text": "$2x² − 12x + 9$",
+       "text": "$5x² − 81$",
        "mistake": "coef_not_raised"
       }
      ]
     },
     {
-     "question": "$(3x + 5)(3x − 5) = ?$",
+     "question": "חשבו בעזרת נוסחת הכפל המקוצר: $57 · 63 = ?$",
      "choices": [
       {
-       "text": "$9x² − 25$",
+       "text": "$3591$",
        "correct": true
       },
       {
-       "text": "$9x² + 25$",
+       "text": "$3609$",
        "mistake": "diff_sign"
       },
       {
-       "text": "$3x² − 25$",
-       "mistake": "coef_not_raised"
-      },
-      {
-       "text": "$9x² − 30x + 25$",
+       "text": "$3249$",
        "mistake": "diffsq_as_square"
       }
      ]
     },
     {
-     "question": "$(x + 6)² = ?$",
+     "question": "$(4x − 8)² = ?$",
      "choices": [
       {
-       "text": "$x² + 12x + 36$",
+       "text": "$16x² − 64x + 64$",
        "correct": true
       },
       {
-       "text": "$x² + 36$",
-       "mistake": "forgot_middle"
+       "text": "$4x² − 64x + 64$",
+       "mistake": "coef_not_raised"
       },
       {
-       "text": "$x² + 6x + 36$",
-       "mistake": "middle_no_2"
+       "text": "$16x² + 64$",
+       "mistake": "forgot_middle"
       },
       {
-       "text": "$x² + 12x + 12$",
-       "mistake": "sq_as_double"
+       "text": "$16x² − 32x + 64$",
+       "mistake": "middle_no_2"
       }
      ]
     },
     {
-     "question": "$(x − 4)² = ?$",
+     "question": "$(8 − x)(8 + x) = ?$",
      "choices": [
       {
-       "text": "$x² − 8x + 16$",
+       "text": "$64 − x²$",
        "correct": true
       },
       {
-       "text": "$x² − 16$",
-       "mistake": "diffsq_as_square"
+       "text": "$x² − 64$",
+       "mistake": "diffsq_order"
       },
       {
-       "text": "$x² + 8x + 16$",
-       "mistake": "sign_mid"
+       "text": "$64 − 16x + x²$",
+       "mistake": "diffsq_as_square"
       },
       {
-       "text": "$x² − 8x − 16$",
-       "mistake": "neg_times_neg"
+       "text": "$16 − x²$",
+       "mistake": "sq_as_double"
       }
      ]
     },
     {
-     "question": "$(a + 2b)² = ?$",
+     "question": "$(a − 5b)² = ?$",
      "choices": [
       {
-       "text": "$a² + 4ab + 4b²$",
+       "text": "$a² − 10ab + 25b²$",
        "correct": true
       },
       {
-       "text": "$a² + 2ab + 4b²$",
+       "text": "$a² − 5ab + 25b²$",
        "mistake": "middle_no_2"
       },
       {
-       "text": "$a² + 4ab + 2b²$",
+       "text": "$a² − 10ab + 5b²$",
        "mistake": "coef_not_raised"
       },
       {
-       "text": "$a² + 4b²$",
+       "text": "$a² + 25b²$",
        "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "$(7 − x)(7 + x) = ?$",
+     "question": "$(2x + 6)(2x − 6) = ?$",
      "choices": [
       {
-       "text": "$49 − x²$",
+       "text": "$4x² − 36$",
        "correct": true
       },
       {
-       "text": "$x² − 49$",
-       "mistake": "diffsq_order"
+       "text": "$4x² + 36$",
+       "mistake": "diff_sign"
       },
       {
-       "text": "$49 − 14x + x²$",
+       "text": "$4x² − 24x + 36$",
        "mistake": "diffsq_as_square"
       },
       {
-       "text": "$14 − x²$",
-       "mistake": "sq_as_double"
+       "text": "$2x² − 36$",
+       "mistake": "coef_not_raised"
       }
      ]
     },
     {
-     "question": "$(5x + 1)² = ?$",
+     "question": "$(a + 4b)² = ?$",
      "choices": [
       {
-       "text": "$25x² + 10x + 1$",
+       "text": "$a² + 8ab + 16b²$",
        "correct": true
       },
       {
-       "text": "$25x² + 5x + 1$",
+       "text": "$a² + 4ab + 16b²$",
        "mistake": "middle_no_2"
       },
       {
-       "text": "$5x² + 10x + 1$",
+       "text": "$a² + 8ab + 4b²$",
        "mistake": "coef_not_raised"
       },
       {
-       "text": "$25x² + 1$",
+       "text": "$a² + 16b²$",
        "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "ריבוע שצלעו $a + b$ מחולק לריבוע שצלעו $a$, לריבוע שצלעו $b$ ולשני מלבנים. מה סכום השטחים של שני המלבנים?",
+     "question": "$(3x − 2)² = ?$",
      "choices": [
       {
-       "text": "$2ab$",
+       "text": "$9x² − 12x + 4$",
        "correct": true
       },
       {
-       "text": "$ab$",
-       "mistake": "middle_no_2"
+       "text": "$9x² − 4$",
+       "mistake": "diffsq_as_square"
       },
       {
-       "text": "$a² + b²$",
-       "mistake": "other_quantity"
+       "text": "$9x² + 4$",
+       "mistake": "forgot_middle"
+      },
+      {
+       "text": "$3x² − 12x + 4$",
+       "mistake": "coef_not_raised"
       }
      ]
     },
     {
-     "question": "חשבו בעזרת נוסחת הכפל המקוצר: $51² = ?$",
+     "question": "$(a + 5b)² = ?$",
      "choices": [
       {
-       "text": "$2601$",
+       "text": "$a² + 10ab + 25b²$",
        "correct": true
       },
       {
-       "text": "$2501$",
-       "mistake": "forgot_middle"
+       "text": "$a² + 5ab + 25b²$",
+       "mistake": "middle_no_2"
       },
       {
-       "text": "$2551$",
-       "mistake": "middle_no_2"
+       "text": "$a² + 10ab + 5b²$",
+       "mistake": "coef_not_raised"
+      },
+      {
+       "text": "$a² + 25b²$",
+       "mistake": "forgot_middle"
       }
      ]
     },
     {
-     "question": "חשבו בעזרת נוסחת הכפל המקוצר: $98 · 102 = ?$",
+     "question": "$(2x + 3)(2x − 3) = ?$",
      "choices": [
       {
-       "text": "$9996$",
+       "text": "$4x² − 9$",
        "correct": true
       },
       {
-       "text": "$10004$",
+       "text": "$4x² + 9$",
        "mistake": "diff_sign"
       },
       {
-       "text": "$9604$",
+       "text": "$4x² − 12x + 9$",
        "mistake": "diffsq_as_square"
+      },
+      {
+       "text": "$2x² − 9$",
+       "mistake": "coef_not_raised"
       }
      ]
     }

requirements-dev.txt

@@ -2,6 +2,7 @@ fastapi>=0.110
 python-multipart>=0.0.9
 httpx>=0.27
 pytest>=8
+sympy>=1.12  # recomputes the algebra answers in tests/test_math_skills.py
 # Optional local PostgreSQL integration checks (bundled server; no Docker or project credentials).
 pgserver==0.1.4; sys_platform == 'linux'
 psycopg[binary]==3.3.6

static/math.js

@@ -6,7 +6,8 @@
    student moves to the next unsolved question, so a missed question comes back after the others. The choices are
    shuffled each time a question is shown, and a wrong answer does not reveal the right one, so a question that comes
    back is solved again, not remembered. Finished skills come back in a mixed review (see "spaced review" below). Progress is kept on this device, per account (mathly.progress.v1:<email>): `done` per
-   skill, and `solved` (indexes answered correctly) and `at` (the question to show) for skills with a list. */
+   skill, and `solved` (indexes answered correctly), `at` (the question to show) and `set` (the round's questions, see round())
+   for skills with a list. */
 (()=>{
 const css=document.createElement("link"); css.rel="stylesheet"; css.href=document.currentScript.src.replace("math.js","math.css");
 document.head.append(css);
@@ -67,9 +68,24 @@ const shuffled=a=>{ const out=a.slice(); for(let i=out.length-1;i>0;i--){ const
 // a multiple-choice question's buttons, in a new order each time it is shown
 const choiceButtons=q=>`<div class="mx-choices">${shuffled(q.choices||[]).map((c,i)=>`<button data-choice="${i}" data-m="${c.correct?"":esc(c.mistake)}"${c.correct?" data-right":""}>${fmt(c.text)}</button>`).join("")}</div>`;
 const figures=q=>`${q.graph?plot(q.graph):""}${q.diagram?geometryDiagram(q.diagram):""}${q.figure?figure(q.figure):""}`;
-// the question after `from` that is not solved yet; once all are solved, simply the next one
-const nextQ=(id,from)=>{ const n=QS(BY[id]).length, got=solvedOf(id);
-  for(let k=1;k<=n;k++){ const j=(from+k)%n; if(!got.has(j)) return j; } return (from+1)%n; };
+/* A round: a skill with more than ROUND questions asks a random ROUND of them (indexes into its list), the ones not
+   solved yet first. A round in progress keeps its questions (P.set); a finished skill gets a new one each time it is
+   opened. Progress from before rounds existed was on the first ROUND questions, so it stays there. */
+const ROUND=10;
+function round(id){
+  const n=QS(BY[id]).length; if(n<=ROUND) return [...Array(n).keys()];
+  let r=P.set[id];
+  if(!Array.isArray(r)||r.length!==ROUND||r.some(i=>!(Number.isInteger(i)&&i>=0&&i<n))){
+    if(!P.done[id]&&(P.solved[id]?.length||P.at[id]!=null)) r=[...Array(ROUND).keys()];
+    else { const got=solvedOf(id), all=shuffled([...Array(n).keys()]); r=[...all.filter(i=>!got.has(i)),...all.filter(i=>got.has(i))].slice(0,ROUND); }
+    P.set[id]=r;
+  }
+  return r;
+}
+const solvedIn=id=>{ const got=solvedOf(id); return round(id).filter(i=>got.has(i)).length; };
+// the round's question after `from` that is not solved yet; once all are solved, simply the next one
+const nextQ=(id,from)=>{ const r=round(id), got=solvedOf(id), at=r.indexOf(from), n=r.length;
+  for(let k=1;k<=n;k++){ const j=r[(at+k)%n]; if(!got.has(j)) return j; } return r[(at+1)%n]; };
 
 async function show(){
   document.documentElement.classList.add("math-on");
@@ -94,7 +110,7 @@ async function show(){
     try{ const r=await fetch("/api/math/skills"); if(!r.ok) throw new Error(`השרת ענה ${r.status}`); index(await r.json()); }
     catch(e){ path.innerHTML=`<p class="mx-note">לא הצלחנו לטעון את המסלול: ${esc(e.message)}. רעננו את העמוד ונסו שוב.</p>`; return; }
   }
-  P=window.MathlySky.ensure(Object.assign({done:{},tries:{},solved:{},at:{}},load())); SHOWN=new Set(shownUnits().map(u=>u.id));
+  P=window.MathlySky.ensure(Object.assign({done:{},tries:{},solved:{},at:{},set:{}},load())); if(!P.set||typeof P.set!=="object") P.set={}; SHOWN=new Set(shownUnits().map(u=>u.id));
   subjectOptions().length?drawSubjectPicker():selectSubject("מתמטיקה");
   window.MathlyAnswers?.configure({api,account:CFG.userId,enabled:CFG.answerScans,root,onGraded:({questionId,grading})=>{
     if(grading.result.verdict!=="correct"||P.done[questionId])return;
@@ -147,7 +163,7 @@ const unitOf=id=>G.units.find(u=>u.id===BY[id].unit);
 const unitIds=u=>ORDER.filter(id=>BY[id].unit===u.id);
 const live=id=>!BY[id].locked;
 const seenAt=id=>Date.parse(P.seen?.[id]||P.done[id]||0)||0;
-const goldNeed=id=>Sky.goldNeed(QS(BY[id]).length);
+const goldNeed=id=>Sky.goldNeed(Math.min(ROUND,QS(BY[id]).length));
 const inDays=d=>d===0?"היום":d===1?"מחר":`בעוד ${d} ימים`;
 function unitDone(u){ const ids=unitIds(u).filter(live); return ids.length>0&&ids.every(id=>P.done[id]); }
 function skyStats(){
@@ -344,9 +360,11 @@ function chips(ids){
 function open(id){
   stopPhone();
   cancelAdvance();
-  const s=BY[id], st=status(id), unit=G.units.find(u=>u.id===s.unit), all=QS(s), n=all.length;
-  curQ=Math.min(P.at[id]||0,n-1);
-  const q=all[curQ], openEnded=q.type==="open-ended", got=solvedOf(id);
+  const s=BY[id], st=status(id), unit=G.units.find(u=>u.id===s.unit), all=QS(s);
+  if(P.done[id]&&cur!==id) delete P.set[id];   // a finished skill opened again: a new round
+  const r=round(id), n=r.length;
+  curQ=r.includes(P.at[id])?P.at[id]:r[0];
+  const q=all[curQ], openEnded=q.type==="open-ended", got=solvedOf(id), gotN=r.filter(i=>got.has(i)).length;
   if(!cur) back=document.activeElement;
   cur=id; FIRST=true; REV=null;
   sheet.innerHTML=`<div class="mx-scrim" data-act="close"></div>
@@ -355,7 +373,7 @@ function open(id){
         <h3 id="mxTitle">${fmt(s.name)}</h3><small class="mx-src">${s.month?`בפריסה: ${esc(s.month)}`:esc(unit.source)}${st==="done"?" · הושלמה ✓":""}</small></div>
         <button class="mx-x" data-act="close" aria-label="סגירה">✕</button></div>
       <p>${fmt(s.description)}</p>
-      <div class="mx-q">${n>1?`<div class="mx-qprog"><span>שאלה ${curQ+1} מתוך ${n}</span><span class="mx-qdots" aria-label="נפתרו ${got.size} מתוך ${n}">${all.map((_,i)=>`<i class="${got.has(i)?"ok":""}${i===curQ?" now":""}"></i>`).join("")}</span></div>`:""}
+      <div class="mx-q">${n>1?`<div class="mx-qprog"><span>שאלה ${r.indexOf(curQ)+1} מתוך ${n}</span><span class="mx-qdots" aria-label="נפתרו ${gotN} מתוך ${n}">${r.map(i=>`<i class="${got.has(i)?"ok":""}${i===curQ?" now":""}"></i>`).join("")}</span></div>`:""}
         <p>${fmt(q.question)}</p>${figures(q)}
         ${st==="off"?'<p class="mx-note mx-off">השאלה הזו סגורה כרגע לתשובות. היא לא נדרשת כדי להתקדם במסלול.</p>':openEnded?'<div class="mx-answer"></div>':choiceButtons(q)}
         <div class="mx-fb" aria-live="polite"></div></div>
@@ -385,18 +403,19 @@ function autoAdvance(id,target){
 function answer(btn){
   if(btn.disabled) return;
   if(REV) return reviewAnswer(btn);
-  const id=cur, m=btn.dataset.m, fb=sheet.querySelector(".mx-fb"), n=QS(BY[id]).length, qi=curQ;
+  const id=cur, m=btn.dataset.m, fb=sheet.querySelector(".mx-fb"), n=round(id).length, qi=curQ;
   const buttons=sheet.querySelectorAll("[data-choice]");
   buttons.forEach(b=>b.classList.remove("right","wrong"));
   btn.classList.add(m?"wrong":"right");
   P.tries[id]=(P.tries[id]||0)+1;
   if(n>1) P.at[id]=nextQ(id,qi);
   if(!m){
-    const got=solvedOf(id); got.add(qi); P.solved[id]=[...got].sort((a,b)=>a-b);
+    const all=solvedOf(id); all.add(qi); P.solved[id]=[...all].sort((a,b)=>a-b);
+    const gotN=solvedIn(id);   // solved in this round
     const missed=new Set(P.missed[id]||[]), recovered=missed.delete(qi); P.missed[id]=[...missed];
     // done once every question is solved and the last answers were right at the first try
     const run=FIRST?(P.run[id]||0)+1:0, need=Sky.masterNeed(n);
-    const first=!P.done[id]&&got.size>=n&&run>=need, unitWas=unitDone(unitOf(id));
+    const first=!P.done[id]&&gotN>=n&&run>=need, unitWas=unitDone(unitOf(id));
     if(first){ P.done[id]=new Date().toISOString(); Sky.mastered(P,id); }
     COMBO=FIRST?COMBO+1:0;
     const persisted=!FIRST;
@@ -407,7 +426,7 @@ function answer(btn){
     const ok=`<b>${Sky.praise({recovered,persisted,combo:COMBO})}</b>${COMBO>=2?`<span class="mx-combo">${Sky.FLAME}${COMBO} ברצף</span>`:""}`;
     const after=rewards(id,{r,lit:first,unitWas}), then=go=>after.then(()=>{ if(cur===id&&!sheet.hidden&&fb.isConnected) go(); });   // not once another question is shown
     if(!P.done[id]){
-      const left=need-run, say=got.size<n?`פתרתם ${got.size} מתוך ${n} שאלות במיומנות הזו.`
+      const left=need-run, say=gotN<n?`פתרתם ${gotN} מתוך ${n} שאלות במיומנות הזו.`
         :n===1?"כדי לסיים צריך לענות נכון בניסיון הראשון. נסו את השאלה שוב, הפעם בסדר אחר."
         :`כל השאלות נפתרו. עוד ${left===1?"תשובה נכונה אחת":`${left} תשובות נכונות`} ברצף, בניסיון הראשון, כדי לסיים.`;
       fb.innerHTML=`<div class="mx-ok">${ok}<span>${say}</span>

tests/test_math_skills.py

@@ -1,5 +1,8 @@
 import copy
 import asyncio
+import re
+
+import pytest
 
 import httpx
 
@@ -59,7 +62,11 @@ def test_question_lists():
     skill = lambda sid: next(item for item in graph["skills"] if item["id"] == sid)
     listed = [s for s in graph["skills"] if "questions" in s]
     assert [s["id"] for s in graph["skills"] if "sample" in s] == ["a_30_side"]   # the photographed answer
-    assert len(listed) == 95 and all(len(s["questions"]) == 10 for s in listed)
+    assert len(listed) == 95
+    # טכניקה אלגברית 1 has 30 questions a skill, a round asks a random 10 of them; the others have 10
+    assert {s["id"]: len(s["questions"]) for s in listed if s["unit"] == "t"} == dict.fromkeys(
+        ["t_ext", "t_simplify", "t_ext_eq", "t_area", "t_formulas"], 30)
+    assert all(len(s["questions"]) == 10 for s in listed if s["unit"] != "t")
     skill("t_ext")["sample"] = skill("t_ext")["questions"][0]
     skill("t_gcf")["questions"] = []
     skill("q_props")["questions"][0] = {"type": "open-ended", "version": 1, "question": "Sketch it."}
@@ -163,3 +170,45 @@ def test_no_unit_has_more_than_six_subunits():
     graph = algebra9()
     count = Counter(skill["unit"] for skill in graph["skills"])
     assert all(1 <= count[unit["id"]] <= 6 for unit in graph["units"]), count
+
+
+def test_unit_t_answers_are_right_and_no_wrong_choice_is_equivalent():
+    """Recomputes, independently of how they were written, every unit-t question that is a bare expression,
+    an expression to simplify, or an equation: the marked answer is right and every other choice is not."""
+    sp = pytest.importorskip("sympy")
+    from sympy.parsing.sympy_parser import parse_expr, standard_transformations, implicit_multiplication_application
+    tf = standard_transformations + (implicit_multiplication_application,)
+    x = sp.Symbol("x")
+    names = {v: sp.Symbol(v) for v in "xab"}
+
+    def expr(t):
+        t = t.strip().strip("$").replace("−", "-").replace("²", "**2").replace("·", "*").replace(" : 2", "/2")
+        return sp.nsimplify(parse_expr(t, local_dict=names, transformations=tf), rational=True)
+
+    def solution(text):
+        if "$" not in text:
+            return None   # "אין פתרון"
+        return expr(text.split("=")[1])
+
+    checked = 0
+    for skill in algebra9()["skills"]:
+        if skill["unit"] != "t":
+            continue
+        for q in skill["questions"]:
+            body = re.fullmatch(r"(?:פשטו: |איזה ביטוי שווה ל־)?\$([^$]+)\$\??", q["question"])
+            eq = re.fullmatch(r"פתרו: \$([^$=]+)=([^$=]+)\$", q["question"])
+            if body and body[1].endswith("= ?") and not re.search(r"\d{2,}[²·]|^\d+ ·", body[1]):
+                value = sp.expand(expr(body[1][:-3]))
+                same = lambda c: sp.expand(expr(c["text"]) - value) == 0
+            elif body and "=" not in body[1]:
+                value = sp.expand(expr(body[1]))
+                same = lambda c: sp.expand(expr(c["text"]) - value) == 0
+            elif eq:
+                roots = sp.solve(sp.Eq(expr(eq[1]), expr(eq[2])), x)
+                same = lambda c: (solution(c["text"]) is None and not roots) or (solution(c["text"]) is not None and roots == [solution(c["text"])])
+            else:
+                continue
+            for c in q["choices"]:
+                assert same(c) == bool(c.get("correct")), (skill["id"], q["question"], c["text"])
+            checked += 1
+    assert checked >= 90

tests/test_sky_browser.py

@@ -211,3 +211,36 @@ def test_a_due_skill_comes_back_in_a_mixed_review(browser, server):
     page.locator(".mx-x").click()
     playwright.expect(page.locator(".mx-review")).to_have_count(0)      # nothing is due any more today
     assert not errors
+
+
+def test_a_round_asks_ten_of_thirty_and_a_finished_skill_gets_a_new_round(browser, server):
+    page, errors = page_with(browser, server, no_chance=True)
+    page.locator('.mx-star[data-id="t_ext"]').click()
+    playwright.expect(page.locator(".mx-qprog span").first).to_have_text("שאלה 1 מתוך 10")
+    page.locator(".mx-choices button[data-right]").first.click()
+    rnd = progress_of(page)["set"]["t_ext"]
+    assert len(rnd) == len(set(rnd)) == 10 and all(0 <= i < 30 for i in rnd)
+    page.locator(".mx-ok button[data-id]").first.click()
+    for _ in range(9):
+        page.locator(".mx-choices button[data-right]").first.click()
+        if page.locator(".sky-cele").count():
+            break
+        page.locator(".mx-ok button[data-id]").first.click()
+    while page.locator(".sky-cele [data-sky=go]").count():
+        page.locator(".sky-cele [data-sky=go]").first.click()
+    p = progress_of(page)
+    assert p["done"]["t_ext"] and sorted(p["solved"]["t_ext"]) == sorted(rnd)
+    page.locator(".mx-x").click()
+    page.locator('.mx-star[data-id="t_ext"]').click()   # practising it again: the questions not met yet come first
+    page.locator(".mx-choices button[data-right]").first.click()
+    again = progress_of(page)["set"]["t_ext"]
+    assert not set(again) & set(rnd)
+    assert not errors
+
+
+def test_progress_from_before_rounds_stays_on_the_first_ten(browser, server):
+    page, errors = page_with(browser, server, {"solved": {"t_ext": [0, 1, 2]}, "at": {"t_ext": 3}})
+    page.locator('.mx-star[data-id="t_ext"]').click()
+    playwright.expect(page.locator(".mx-qprog span").first).to_have_text("שאלה 4 מתוך 10")
+    playwright.expect(page.locator(".mx-qdots i.ok")).to_have_count(3)
+    assert not errors