← Senior Mathematics Studio

LEARN · EXPLAIN · REVISE

Which statement is correct?

Read the idea, work independently, then explain what changed.

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高一必修第一册(A版).pdf · 3.2 · PDF 83 / printed page 76

Revisit first: Vertex form and completing the square Quadratic signs and solution sets

Teacher preparation and assessment

40-minute lesson

Minutes	Focus	Teaching and student action
5	Check admissibility	Use both interval diagnostics before calculating.
8	Build candidate table	Compare the two endpoints and the allowed vertex.
10	Change the domain	Pairs replace closed by open endpoints and explain attainment.
12	Balance worst cases	Groups draw the two endpoint-distance curves for the minimax task.
5	Exit comparison	Ask which candidates remain under integer inputs.

Question sequence

Which candidates are forbidden before any calculation?
Are we minimising f or the largest value of f?

Board development

Use an admissible candidate table.
$L,h,U$
Balance endpoint distances.
$a+1=2-a$

Expected correct and incorrect responses

“Vertex outside, so use the nearest endpoint” is justified for a>0.
“The minimum is zero” on (0,1) confuses attainment with a bound.

Follow-up questions

How does the candidate role reverse if a<0?

Remediation

Shade the domain before plotting the vertex; circle excluded candidates.

Exit check

For −(x−1)² on [2,4], find both extrema. Expected maximum −1, minimum −9.

Assessment checklist and sample responses

2 marks: candidate validity.
Full: endpoint and interior checks; partial: global vertex without domain.
2 marks: minimax proof.
Full: distances sum 3, maximum at least 1.5, equality at a=0.5; partial: guessed midpoint only.