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Number Patterns and Sequences Self Assessment Practice

Number Patterns and Sequences Self Assessment Practice
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2019-05-09 07:44
FunctionTrigonometrySequenceCoordinate Geometry
This example demonstrates how to construct and analyze general term number sequences involving linear, 'shifted' squares, and cubes using GeoGebra. Core math concepts include sequence general term formulas, linear functions, quadratic functions, cubic functions, and coordinate geometry. Construction highlights include commands like If, RandomElement, Sequence, Element, Textfield, Expand, TextToUnicode, IndexOf, First, LaTeX, and objects such as counter, k, d, c, b, a, e, listSequence1, textTitle, textSequence1, button1, answera, answerb, inputa, inputb, inputc, InputBox1, InputBox2, InputBox3, usera, answerc, userb, text1, userc, answerccorrect, answeracorrect, answerbcorrect, I_{a1}, I_{a2}, picacorrect, picawrong, piccwrong, picbwrong, I_{c1}, I_{c2}, picccorrect, I_{b1}, I_{b2}, picbcorrect, trieda. Suitable for high school students learning sequences, function graphing, and self-assessment practice.

GeoGebra Commands & Parameters

  1. If(counter < 11, 0, RandomElement[{-1, -2, 1, 2, 3, 1, 1, 1}]) → k
  2. If(counter > 8, If[counter > 10, 0, 1], 0) → d
  3. If(counter < 2, 0, If[counter < 5, RandomElement[{0, -3, -2, -1, 0, 1, 2, 3, 0}], If[counter < 11, RandomElement[{-2, -1, 0, 1, 2}], 0]]) → c
  4. If(counter < 7, RandomElement[{-3, -2, -1, 1, 2, 3, 4, 5}], 0) → b
  5. If(counter < 7, 0, If[counter < 9, 1, 0]) → a
  6. RandomElement({-3, -2, 2, 3}) → e
  7. Sequence((k * e^(n - 1)) + (d * n^(3)) + (a * n^(2)) + (b * n) + c, n, 1, 20) → listSequence1, {2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576}
  8. Element(listSequence1, 5) → answera
  9. Element(listSequence1, 12) → answerb
  10. Textfield(inputa) → InputBox1
  11. Textfield(inputb) → InputBox2
  12. Textfield(inputc) → InputBox3
  13. Expand(Simplify[If[1 ≤ n ≤ 200, (k * e^(n - 1)) + (d * n^(3)) + (a * n^(2)) + (b * n) + c]]) → answerc
  14. TextToUnicode(LaTeX[answerc]) → listFunctionwithIntervalUnicode
  15. IndexOf(44, listFunctionwithIntervalUnicode) → commaposition
  16. First(listFunctionwithIntervalUnicode, commaposition - 1) → listFunctionOnlyUnicode
  17. LaTeX(UnicodeToText[listFunctionOnlyUnicode]) → textFunctionOnly

AI Drawing Prompt Reference

Create a graph showing a sequence involving linear, quadratic, and cubic functions, with the general term formula displayed. Highlight the first 20 terms of the sequence in different colors, marking key values. Include text boxes for inputting and verifying the general term formula.
The prompt above was compiled from the original drawing commands and is for reference only.