Randomizers

Randomization makes each student see different numbers in a question while ensuring the question remains solvable. Here are the key functions.

randint($min, $max)

Returns a random integer between $min and $max (inclusive).

$a = randint(2, 9);      // random integer from 2 to 9
$n = randint(-5, 5);     // random integer from -5 to 5

rand($min, $max)

Returns a random float (decimal) between $min and $max.

$x = rand(0, 1);         // random float like 0.4327
$rate = rand(0.01, 0.15); // random rate between 1% and 15%

pickone($value1, $value2, ...)

Returns one of the provided values at random.

$sign = pickone(1, -1);
$word = pickone("increasing", "decreasing");
$coeff = pickone(2, 3, 5, 7);

pickunique($n, $value1, $value2, ...)

Returns an array of $n values chosen from the list without repetition. Useful for selecting distinct options.

$choices = pickunique(3, 1, 2, 3, 4, 5, 6);
// might return array(4, 1, 6)

shuffle($array)

Randomizes the order of an array. Commonly used to randomize the order of multiple choice options.

$options = array("increasing", "decreasing", "constant", "undefined");
shuffle($options);

Avoiding Bad Values

Always check that random values don't produce degenerate cases (division by zero, negative radicands, etc.):

do {
    $a = randint(-5, 5);
} while ($a == 0);    // ensure $a ≠ 0

For quadratics, ensure the discriminant is non-negative if you want real roots:

do {
    $b = randint(-6, 6);
    $c = randint(-9, 9);
} while ($b**2 - 4*$c < 0);

Ensuring Distinct Values

When you need multiple different values:

$a = randint(1, 9);
do {
    $b = randint(1, 9);
} while ($b == $a);

Or use pickunique:

$pair = pickunique(2, 1, 2, 3, 4, 5, 6, 7, 8, 9);
$a = $pair[0];
$b = $pair[1];

Seeding and Reproducibility

Each student receives a unique seed that determines their random values. The same seed always produces the same values for a given student — so if a student starts a new attempt, they may see the same values (depending on how attempts are configured). This is by design: it allows instructors to verify a student's specific values when reviewing their work.

Example: Full Randomized Question Setup

// Pick two distinct nonzero integers
$pair = pickunique(2, -5, -4, -3, -2, 2, 3, 4, 5);
$a = $pair[0];
$b = $pair[1];

// Compute answer
$product = $a * $b;
$sum = $a + $b;

Question text:

<p>Find a quadratic with roots `$a` and `$b`.</p>
<p>Write it in the form `x^2 + bx + c`.</p>