Kenneth ChengMathematical modeling
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Find the intersection.

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TOPIC 01

2023 JM01

The endpoint 4 belongs; 6 does not.

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

01 / Standard#Your turn

Find the intersection.

M={x:x2−2x−8≥0},N=(0,6)M=\{x:x^2-2x-8\ge0\},\quad N=(0,6)

Official paper · jm01-2023 · I.1 · PDF 2

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A[−2,4][-2,4]
  2. Option B[−2,0)[-2,0)
  3. Option C(0,4](0,4]
  4. Option D(0,6)(0,6)
  5. Option E[4,6)[4,6)

Working and explanation

BUILD THE REASONING

Hint 1
Find the two roots.
Hint 2
An upward parabola is nonnegative outside its roots.
Worked solution

  1. Solve the quadratic inequality.

    (x−4)(x+2)≥0  ⟺  x≤−2 or x≥4(x-4)(x+2)\ge0\iff x\le-2\text{ or }x\ge4

  2. Intersect with the open interval.

    M∩N=[4,6)M\cap N=[4,6)

E: [4,6).

Checks and common pitfalls: The endpoint 4 belongs; 6 does not.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Solve the quadratic inequality.
    (x−4)(x+2)≥0  ⟺  x≤−2 or x≥4(x-4)(x+2)\ge0\iff x\le-2\text{ or }x\ge4
  • Intersect with the open interval.
    M∩N=[4,6)M\cap N=[4,6)

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