Formulas: Hon Wai Lau's examples

Hon Wai Lau's examples

Example 1.1: Minimal question

For a minimal question, you must define a sub-question with:

• mark
• answer
• grading criteria
• question text (optional)

General
  Question name!       Minimal question
Main question
  Question text!       What is 2 + 2?
Part 1
  Part's mark*         1
  Answer type          Number
  Answer*              4
  Grading criteria*    Relative error < 0.01

The Formulas question should look like this:

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Example 1.2: Generate random data

Random data can be defined in the random variables, such as a = {2,3,4,5}. Upon quiz generation, one deterministic value will be chosen.

General
  Question name!       Generate random data
Variables
  Random variables     a = {2,3,4,5};
Main question
  Question text!       In this instantiation, a takes the value {a}.
Part 1
  Part's mark*         1
  Answer type          Number
  Answer*              a
  Grading criteria*    Relative error < 0.01
  Part's text          Enter the value of a:

The Formulas question should look like this:

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Example 1.3: Multiple parts

By default, all parts will be added at the end of the question. If placeholders are used, the parts will be inserted at the location of placeholders.

General
  Question name        Multiple parts
Main question
  Question text        This is the beginning of the main question text.
                       {#1}
                       This is the continuation of the main question text.
                       {#2}
                       This is the continuation and the end of the main question text.
Part 1
  Part's mark          1
  Answer type          Number
  Answer               3
  Grading criteria     Relative error < 0.01
  Placeholder name     #1
  Part's text          This is the text of Part 1. The correct answer is 3:
Part 2
  Part's mark          1
  Answer type          Number
  Answer               1
  Grading criteria     Relative error < 0.01
  Placeholder name     #2
  Part's text          This is the text of Part 2. The correct answer is 1:
Part 3
  Part's mark          1
  Answer type          Number
  Answer               4
  Grading criteria     Relative error < 0.01
  Part's text          This is the text of Part 3. The correct answer is 4:

With the question behaviour set to Interactive with multiple tries, the Formulas question should look like this:

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With the question behaviour set to Adaptive mode, the Formulas question should look like this:

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An important advantage of the Adaptive mode behaviour is that all the answers do not have to be entered before they can be checked by clicking the Check button. Thus, the answers for each part can be checked one at a time or as they are entered.

Example 1.4: Placeholders of numbers and unit

This question shows different display methods of the number and unit boxes.

General
  Question name        04  Placeholders of numbers and unit
Variables
Random variables       v = {20:100:10};
                       dt = {2:6};
Global variables       s = v*dt;
Main question
  Question text        If a car travels {s} m in {dt} s, what is the speed of the car?
Part 1
  Part's mark          1
  Answer type          Number
  Answer               v
  Grading criteria     Relative error < 0.01
  Unit                 m/s
  Part's text          Number box and unit box side by side
                       {_0}{_u}
Part 2
  Part's mark          1
  Answer type          Number
  Answer               v
  Grading criteria     Relative error < 0.01
  Unit                 m/s
  Part's text          Number box and unit box side by side
                       {_0} {_u}
Part 3
  Part's mark          1
  Answer type          Number
  Answer               v
  Grading criteria     Relative error < 0.01
  Unit                 m/s
  Part's text          No unit box
                       {_0} m/s
Part 4
  Part's mark          1
  Answer type          Number
  Answer               v
  Grading criteria     Relative error < 0.01
  Unit                 m/s
  Part's text          No unit box
                       speed = {_0} m/s

The Formulas question should look like this:

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Example 3.2: Variable multiple and variable range

This question is similar to Example: Multiples of 7 between 10 and 100 (Mark = 0, 0.5 or 1), except that the multiples are multiple of a variable d which can be 5, 6, 7, 8 or 9, and that the range is variable by requiring that x satisfies a < x < b where a = k*d-3, b = (k+2)*d-2 and k ranges from 4 to 9.

General
  Question name        3.2  Variable multiple and variable range
Variables
  Random variables     k = {4:10:1};
                       d = {5,6,7,8,9};
  Global variables     a = k*d-3;
                       b = (k+2)*d-2;
Main question
  Question text        Two Grading criteria are defined here, each of which is worth half a mark.
Part 1
  Part's mark*         1
  Answer type          Number
  Answer*              k*d
  Grading variables    criterion1 = _0 % d == 0;
                       criterion2 = a <= _0 && _0 <= b;
  Grading criteria     (criterion1 + criterion2)/2
  Part's text          Give a number x that is a multiple of {d} and satisties {a} < x < {b}:

The Formulas question should look like this:

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Example 5.5: Roots of a quadratic function

This question is a good example of how a question can be built by taking advantage of the power of the Formulas question. By formulating the solution in reverse, results can often be obtained that would be difficult or impossible to achieve otherwise.

The technique is illustrated by the problem of finding the roots of a quadratic function. Here is what is easily obtained: the coefficients of the quadratic function are variable and whole numbers, and the roots are always two, real and whole numbers. Here is how it is done:

Let
      f(x) = x² + bx + c = 0
where
      b = -(r₁ + r₂)
and
      c = r₁*r₂
Thus,
      x² - (r₁ + r₂)x + r₁r₂ = 0
with roots
      x₁, x₂ = [ (r₁ + r₂) ± √ (r₁ + r₂)² - 4 r₁ r₂ ] / 2
            = r₁, r₂

The 'trick' is to define the coefficients of the quadratic as a function of the roots.

General
  Question name        5.5 Roots of a quadratic function
Variables
  Random variables     r1 = {-9:-5};
                       r2 = {-5:-1};
                       symbol = {"t","w","x","z"};
Main question
  Question text        Roots of a quadratic function
Part 1
  Part's mark          1
  Local variables      b = -(r1 + r2);
                       c = r1*r2;
  Answer type          Number
  Answer               [r1,r2]
  Grading criteria     Absolute error == 0
  Part's text          What are the roots of the quadratic function f({symbol}) = {symbol}<sup>2</sup> + {b}{symbol} + {c}?
                       Enter the smaller root first
                       {symbol} = {_0}  and  {symbol} = {_1}

The Formulas question should look like this:

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Informed students could quickly find the value of the roots as soon as they realize that the negative value of their sum is equal to coefficient b of the quadratic function and that the negative value of their product is equal to coefficient c. If this is the case, the question could be made more complex and therefore less easy. Anyway, the purpose of this example was to illustrate the technique of the inverse solution, which is often useful when making up Formulas questions.

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