# Two public formative checks

These are fresh fictional cases relative to cards and optional swaps. The teacher-targeted worked key is publicly accessible. Collect an initial attempt before showing it; the tasks are **not secure exams** or QCAA assessment instruments. Every route below requires the same exact values, reasons and checks.

## Check A · Day 5 fresh surd transfer

An invented display has two straight paper strips, a longer one of length `sqrt(243)` cm and a shorter one of length `sqrt(48)` cm. These are constructed lengths for mathematics practice, not measured objects.

1. Simplify both lengths using square factors and state the exact difference, longer minus shorter.
2. A draft says the difference is `sqrt(195)` cm because `243-48=195`. Explain the invalid rule with an exact comparison.
3. Estimate your exact difference to one decimal place. State which part of your response is exact and which is approximate.

**Routes:** write the factorisation and explanation; give a spoken derivation while someone records exact notation and your reason; use square-factor tiles to arrange both lengths and dictate the exact difference and error diagnosis.

## Check B · Day 10 fresh graph and surd transfer

The abstract rule `y=-(x-2)(x-8)` is invented for this check. Separately, a pure numerical ratio is `5/sqrt(11)`; it has no units and is not part of the graph model.

1. Find both x-intercepts, the axis of symmetry, turning point, y-intercept and opening direction of the graph. Show at least one substitution or sign check.
2. State where the graph is above the x-axis and justify using the factor signs or your sketch.
3. Rationalise `5/sqrt(11)` exactly. Explain why the denominator becomes rational and how you know the value has not changed.

**Routes:** write steps and a labelled sketch; explain aloud with coordinates, interval and radical equality captured by a scribe; use labelled point/axis and fraction tiles then dictate the same mathematical reasoning.