通过线性方程解锁未知值

通过线性方程解锁未知值
几何画板及绘图内容加载中,请稍等……
2019-01-25 01:55
①本范例演示通过解线性方程组确定未知数值以解锁图形;②涉及核心数学概念包括线性方程、解析几何、几何作图;③构造中使用了Element, LaTeX, UnicodeToLetter命令及digit, questionList等对象进行交互式问题生成与验证;④适合高中数学教学,用于线性方程应用与几何问题解决能力的培养。

GeoGebra 命令及参数

  1. Element(questionList, questionListIndex) → questionNum
  2. Element(O2:O6, questionNum) → correctDigit4
  3. Element(K2:K6, questionNum) → correctDigit3
  4. Element(H2:H6, questionNum) → correctDigit2
  5. Element(D2:D6, questionNum) → correctDigit1
  6. LaTeX("\textbf{Question: }What combination will open the lock?") → QUESTION
  7. UnicodeToLetter(11015) → downArrow
  8. UnicodeToLetter(11014) → upArrow
  9. LaTeX((((("\textbf{Instructions: }Use the clues to determine the lock's combination. Set the combination\\using the up " * upArrow) * " and down ") * downArrow) * " buttons.")) → INSTRUCTIONS
  10. UnicodeToLetter(10003) → cmark
  11. LaTeX(digit1) → displayDigit1
  12. LaTeX(digit2) → displayDigit2
  13. LaTeX(digit3) → displayDigit3
  14. LaTeX(digit4) → displayDigit4
  15. LaTeX((("\text{\textbf{Digit 1 is \fbox{" * correctDigit1) * "}.} The graph crosses the \(x\)-axis at the \(x\)-intercept. To find the \(x\)-intercept,\\set \(y=0\) and solve for \(x\).}")) → feedbackDigit1
  16. LaTeX((((((("\text{\textbf{Digit 2 is \fbox{" * correctDigit2) * "}.} Find the value of \(y\) when \(x=") * Element[G2:G6, questionNum]) * "\), given the linear relation \(y=") * digit2Eqn) * "\).}")) → feedbackDigit2
  17. LaTeX((("\text{\textbf{Digit 3 is \fbox{" * correctDigit3) * "}.} Use the two points to find the slope of the line. Then use one point and\\the slope to solve for the \(y\)-intercept.}")) → feedbackDigit3
  18. LaTeX((((((("\text{\textbf{Digit 4 is \fbox{" * correctDigit4) * "}.} Find the value of \(x\) when \(y=") * Element[N2:N6, questionNum]) * "\), given the linear relation \(y=") * digit4Eqn) * "\).}")) → feedbackDigit4
  19. UnicodeToLetter(10007) → xmark
  20. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  21. LaTeX((("\text{\textbf{Digit 1 Clue:}\\For the linear relation \(y=" * Element[C2:C6, questionNum]) * "\), I am the value where the\\relation's graph crosses the \(x\)-axis.}")) → clueDigit1
  22. LaTeX((((((("\text{\textbf{Digit 2 Clue:}\\For the linear relation that starts at \(" * Element[E2:E6, questionNum]) * "\) and grows by \(") * Element[F2:F6, questionNum]) * "\), I am\\the dependent value that pairs with the independent value of \(") * Element[G2:G6, questionNum]) * "\).}")) → clueDigit2
  23. LaTeX((((("\text{\textbf{Digit 3 Clue:}\\For the linear relation with a graph that passes through \(" * Element[I2:I6, questionNum]) * "\)\\and \(") * Element[J2:J6, questionNum]) * "\), I am the value where the graph crosses the \(y\)-axis.}")) → clueDigit3
  24. LaTeX((((((("\text{\textbf{Digit 4 Clue:}\\For the linear relation that starts at \(" * Element[L2:L6, questionNum]) * "\) and grows by \(") * Element[M2:M6, questionNum]) * "\), I am\\the independent value that pairs with the dependent value of \(") * Element[N2:N6, questionNum]) * "\).}")) → clueDigit4

AI 绘图提示语参考

画一个交互式几何解锁问题,包含一个需要通过线性方程求解的组合锁。展示四个数字的线索和反馈,每个数字对应一个线性方程的解,通过x轴和y轴截距、点的坐标和斜率来描述。图形应包含一个文本区域显示问题和指令,以及四个数字的显示和解释,每个数字旁边有对应的数学解释和图形表示,如直线图和坐标点。
以上提示语为根据原始绘图命令整理而来,仅供参考。