Modelling a real-world scenario as an equation

Every paper wraps its hardest question in a scenario — a depreciating asset, a logo, a canal, a golf shot. The algebra is standard; the translation step is what is actually being tested.

The translation method

Identify the ONE variable the question is actually asking about, and give it a clear label.
Write down every given numerical fact as an equation or substitution INVOLVING that variable — a starting value, a rate, a known point the model passes through.
Combine the given facts into a single equation in the one variable, using the SAME algebraic methods (quadratic, exponential, simultaneous) covered elsewhere in this standard.
Solve, then translate the answer back into the context's own units and wording — a bare number is rarely the full answer the schedule expects.

Worked example A laptop's depreciating value A laptop's value follows V = 40 + ke^(−0.5t), bought new for $900. How long until its value drops to 50% of the original? Find k using the starting condition: at t = 0, V = 900, so 900 = 40 + ke⁰ = 40 + k, giving k = 860. Target value is 50% of $900 = $450. Set up the equation: 450 = 40 + 860e^(−0.5t). Rearrange: 410 = 860e^(−0.5t) → e^(−0.5t) = 410/860 → −0.5t = ln(410/860). Solve: t = −2·ln(410/860) = −2 × (−0.741) ≈ 1.48 years. ✓ The starting condition (t = 0) is what finds k FIRST — the target-value equation cannot be set up without it. Always look for the "at the start" fact before anything else. ✕

Solving the algebra correctly but never answering the original question

A scenario question ends by asking something specific in context — "how long until…", "will it clear the tree", "does the boat fit" — not just "solve for t" or "find x". Finishing the algebra and stopping there, without translating the number back into a yes/no or a stated time/length with units, drops the final mark even when every calculation is correct.

Scenario type	The one variable to solve for
Depreciating value over time	Time t, given the model and a target value
A logo or shape with a fixed total area	A length or radius, given the area equation
A projectile's height at a given distance	Height, modelled as a quadratic in horizontal distance
A canal or container fitting an object	Depth or width, compared against the object's own dimension

Practice for this standard covers the whole topic — flashcards and quiz.