Calculated Question Type¶

Students enter algebraic or mathematical expressions that are simplified and evaluated for correctness.

Basic Syntax¶

[calculated]
answer = x^2 + 2*x + 1;

Options¶

`answer` (required)¶

The correct mathematical expression in simplified form.

[calculated]
answer = (x+1)^2;

`simplify`¶

full (default) — Both sides must simplify to the same form
none — Student answer must match exactly
basic — Basic simplification only (combine like terms)

[calculated]
answer = 2*x + 3;
simplify = full;  // Accepts: 2x+3, 4x+6-2x-3, etc.

`variable`¶

Define which variable(s) to use. Defaults to x.

[calculated]
answer = m*t + b;
variable = m, t, b;

`ansdisplaymode`¶

How to display the answer: - 1 — Simplified form (default) - 2 — Factored form - 3 — Expanded form

[calculated]
answer = (x+2)*(x-3);
ansdisplaymode = 1;  // Shows: x^2 - x - 6

Examples¶

Polynomial Simplification¶

$a = rand(1, 5);
$b = rand(1, 5);

Expand and simplify: $(x + $a)(x + $b)$

[calculated]
answer = x^2 + ($a + $b)*x + ($a * $b);
simplify = full;

Fraction Simplification¶

Simplify: `(x^2 - 4)/(x - 2)`

[calculated]
answer = x + 2;
simplify = full;

Multi-Variable Expression¶

$r = rand(2, 8);

Solve for distance using the formula `d = rt` where `r = $r`:

[calculated]
answer = $r * t;
variable = t;
simplify = full;

Grading¶

The system: 1. Parses both the student answer and the correct answer as symbolic expressions 2. Applies simplification rules (if enabled) 3. Compares the two expressions algebraically 4. Returns Correct if they are mathematically equivalent

Example: - Student enters: 2*(x + 1) + 3 - Answer defined as: 2*x + 5 - With simplify = full: Both simplify to 2*x + 5 → Correct

Common Mistakes¶

Forgetting to multiply: Entering (x+1)(x+1) instead of (x+1)*(x+1)
Order of operations: Entering 2x^2 when you meant (2x)^2
Implicit multiplication: 2x should be written as 2*x