Kenneth ChengMathematical modeling
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Write the real solution set.

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

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高一必修 第一册(A版).pdf · 1.1 · PDF 9 / printed page 2

TOPIC 01

Concept of a set

Build understanding of concept of a set through definitions, contrasting cases and justified applications.

What you will be able to explain

  • Apply concept of a set with explicit conditions.
  • Connect representations and justify the steps, including boundary cases.
  • Explain a solution and apply the idea to a changed situation.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

Write the real solution set.

(x−4)2=0(x-4)^2=0
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Check the membership rule and count distinct objects.
Hint 2
A zero square has zero base.
Worked solution

  1. Check the membership rule and count distinct objects.

  2. Calculate or simplify this relation.

    x=4;A={4}x=4;\quad A=\{4\}

  3. Multiplicity of a root is not the cardinality of its set.

The set is {4}.

Checks and common pitfalls: Multiplicity of a root is not the cardinality of its set.

Reasoning checklist · self / teacher assessment
  • State the relevant definition, condition or model.
  • Show a valid calculation, proof or counterexample.
  • Interpret the conclusion with its restrictions.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • What must be true before using the main rule for concept of a set?
  • Which representation makes this task easier, and why?
  • Change one assumption. Does the conclusion survive?

Board plan

  • Apply concept of a set with explicit conditions.
  • Membership: A set has definite membership and distinct elements.
    x∈Ax\in A
  • Representations: A roster lists members; set-builder notation specifies their domain and condition.
  • Close with: conditions → representation → reasoning → check.

Anticipated thinking

  • Expected reasoning: A set has definite membership and distinct elements.
  • Expected reasoning: A roster lists members; set-builder notation specifies their domain and condition.
  • Expected correction: Repeated entries do not add elements.

Assessment checklist

  • 1: identify the givens and required quantity.
  • 1: choose a valid definition, representation or method.
  • 1: present connected, correct reasoning.
  • 1: check conditions and explain the result.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗