기출분석 및 풀이ㅣ대성고등학교 2026 1-2 중간고사ㅣ공통수학2ㅣ최봉근T

Main ideas / lessons conveyed

1. Purpose of the video

   • The speaker, Bong-gun Choi, reviews the math midterm exam paper and explains the most important/high-difficulty questions from the Daeseon High School 2026 first-year, second-semester “Common Math 2” midterm (held the previous day).

2. Overall exam structure and pacing strategy

   • The exam includes many questions, so time management is crucial.
   • Main strategy:
     • Solve medium/low difficulty questions early and quickly with no mistakes.
     • Use the remaining time at the end to solve the high-difficulty differentiating questions.
   • Spending too long on easier questions can prevent you from doing well on the difficult ones.

3. Key characteristics / changes from the previous year

   • Handouts (“printouts”) link exists, but not uniformly
     • For easier/mid-level questions, some connection to the school handouts may appear.
     • For high-difficulty differentiating questions, the connection to handouts is minimal or absent.
   • Assessment type balance changed
     • Last year (approx.): more short-answer questions relative to multiple choice.
     • This year: fewer short-answer questions and more reading/interpretation (“encyclopedia-style”) type content (as described by the speaker).
   • Implication for preparation
     • Don’t rely on handouts alone for differentiating problems.
     • Top students need separate preparation for questions that “separate ranks.”

4. Difficulty distribution and what questions “differentiate”

   • Difficulty counts (as stated):
     • Low difficulty: ~15 questions
     • Medium difficulty: 13 questions
     • Difficult: 7 questions
   • Differentiating questions highlighted:
     • Multiple choice #29, #30
     • Short answer #4, #5
   • The speaker’s argument:
     • The hard questions are hard because the differentiating content appears outside the handouts.

5. Perceived difficulty and rank competition

   • Since many questions are medium-or-below, some students may feel the exam is relatively easier.
   • However, the real ranking battle comes from the few difficult questions, including one likened to a “Snake Star Spirit” (in that context).
   • Cutoff expectation (prediction):
     • Likely determined by the set questions / those weighted for rank (speaker’s phrasing).
     • Students missing ~3 questions or fewer are likely competitive.
     • Top ranking may be around the mid-to-high 80s (cautious prediction).

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Preparation methodology / instructions (detailed)

A. For all first-year Daeseon students (general exam approach)

• Step 1: First pass (earlier questions)

  • Prioritize medium/low difficulty questions.
  • Answer them quickly.
  • Avoid mistakes early, because early errors cost too much time overall.

• Step 2: Second pass (end / differentiating problems)

  • Use all remaining time for the high-difficulty questions.
  • Treat the late questions as the main opportunity to improve ranking.

• Time management rule

  • Do not spend extra time “meticulously” on earlier questions.
  • If you do, you won’t have time to solve the difficult ones later.

B. How to use school handouts (“printouts”)

• For mid/lower ranks

  • Thoroughly familiarize yourself with the handouts and use them for finals preparation.
  • Caution from the speaker:
    • The school may or may not provide printouts starting from finals, so relying only on future printouts is risky.

• For top-tier students

  • The speaker claims handouts are less meaningful for the highest-difficulty differentiating questions, because those problems are mostly not connected to the handouts.
  • Therefore, top-tier students must still prepare separately for differentiating content.

C. Special preparation for discriminating-style content (speaker’s emphasis)

Because differentiating questions are not linked to handouts:

• Solve many high-difficulty problems regularly
• Practice with past mock exam questions
• Don’t expect full mastery from only one exposure during the exam
• The key is consistent, repeated exposure to difficult problems

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Question walkthrough: speaker’s explanations (high-difficulty examples)

Multiple-choice Question #30 (highest point multiple-choice)

• Core description

  • Consider 100 students (labeled 1 to 100).
  • A circle is given with:
    • center (1, ?)
    • radius 1
  • Each student repeats one of three transformations 100 times:
    • Trial A: reflection across the X-axis
    • Trial B: reflection across the Y-axis
    • Trial C: reflection across the origin
  • After 100 iterations, the result corresponds to a circle with a certain center value.

• Conceptual solution approach

  • Let the number of each trial be:
    • A = a, B = b, C = c, with a + b + c = 100
  • Choose values to make the target expression as large as possible:
    • make the “plus” component large and the “minus” component small (speaker references an expression involving coefficients of a, b, c)
  • The speaker checks feasibility for candidate values of b and rules out impossible cases.

• Final result

  • Maximum value is 93 (as concluded by the speaker).

Short-answer Question #5 (highest point short answer)

• Setup

  • Circle C is tied to x² + y² = 16, so:
    • radius = 4
    • center = the origin
  • Point P lies outside the circle with coordinates involving t, where t > 4.
  • A line through P with slope m intersects the circle at two distinct points A and B.
  • A condition is given relating lengths involving AB, PA, and PB (speaker phrases it as a ratio/equality).

• General reasoning structure

  • Use circle geometry:
    • chord properties
    • the perpendicular from the center to the chord bisects the chord
  • Introduce auxiliary variables and distances (speaker uses placeholders like h, s, and scaling references).
  • Determine a set of slopes that satisfy the condition, then convert that into inequalities about parameters.
  • Apply geometry constraints (example constraints include:
    • 0 < h < 4
    • ensuring the appropriate existence condition for two intersection-like lines)
  • Through algebraic elimination and factoring, derive a condition on t.
  • Determine the minimum k (speaker’s “k0”) based on the minimum t that yields the required set-size behavior.

• Final statement

  • The answer is 28 (speaker uses a “bow/rounded” phrasing, but indicates the computed final value).

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Speakers / sources featured

• Cho (최봉근), Bong-gun Choi — Posi Math Academy (main speaker/teacher)
• Daeseon High School — exam context/source