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Year 12 Basic Algebra Skills Test

Year 12 Basic Algebra Skills Test
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2019-06-28 17:53
FunctionCoordinate GeometryCalculusParametric Equation
This example is a Year 12 Basic Algebra Skills Test with answers, exportable to PDF. It demonstrates how to use GeoGebra for algebraic operations and graphical plotting. Core math concepts involved include polynomials, partial fractions, expansion, factoring, solving equations, simplification, parametric curves, parabolas, etc. Key GeoGebra commands and objects used in construction are Random, RandomElement, Polynomial, PartialFractions, Expand, LaTeX, Factor, Solve, Take, Simplify, Polygon, Sequence, Element, ToBase. Suitable for Year 12 students or those reviewing basic algebra.

GeoGebra Commands & Parameters

  1. Random(3, 6 + (0 * dummy)) → a
  2. RandomElement({-3, -2, -1, 1, 2, 3 + (0 * dummy)}) → b
  3. Random(1, 5 + (0 * dummy)) → i
  4. RandomElement({-4, -3, -2, 2, 3, 4 + (0 * dummy)}) → d
  5. RandomElement({-4, -3, -2, 2, 3, 4 + (0 * dummy)}) → e
  6. RandomElement({-3, -2, -1, 1, 2, 3 + (0 * dummy)}) → c
  7. Polynomial((b * x) + c) → f
  8. PartialFractions((b * x) + c / x) → g
  9. RandomElement({f, g}) → h
  10. Expand(h(x)^(a)) → p
  11. PartialFractions(p) → r
  12. RandomElement(l1) → q
  13. LaTeX("\text{Q2. Differentiate }" + q) → q2
  14. Expand(s) → f_1
  15. Expand(t) → g_1
  16. Factor(t) → h_1
  17. Polynomial((b * x^(2)) + ((2 * c) * x) + d) → p_1
  18. LaTeX("\text{Year 12 Basic Skills Test - \bf{SHOW FULL WORKING}}") → text1
  19. Random(2, 5 + (0 * dummy)) → j
  20. Expand((((a * x) + b) * ((c * x) + d))) → k
  21. Solve(k) → l2
  22. RandomElement(l3) → l
  23. LaTeX($5) → a7
  24. Take(a7, 8, Length[a7] - 8) → text13
  25. Simplify(r_1) → s_1
  26. Take(text15, 8, Length[text15] - 9) → text16
  27. Polygon(Export_1, (x(Export_1), y(Export_2)), Export_2, (x(Export_2), y(Export_1))) → q3, ss, i_1, tt, j_1
  28. Sequence(Random[1, 1000000], i, 1, o) → seeds
  29. Element(seeds, n_1) → seed
  30. ToBase(seed, 36) → text18