Intersect the quadratic-inequality set with the absolute-value set.

01 / Standard#Your turn

A=\{x:x^2+x-2\le0\},\quad B=\{x:|x-1|\ge1\}

Official paper · jm01-2026 · I.1 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Factor the quadratic and locate its two roots.

Hint 2

The absolute value describes two exterior intervals.

Worked solution

The upward quadratic is nonpositive between its roots.
$(x+2)(x-1)\le0\iff -2\le x\le1$
Keep only points in both sets.
$B=(-\infty,0]\cup[2,\infty),\quad A\cap B=[-2,0]$

A: [−2,0].

Checks and common pitfalls: The symbol ≥ includes both boundary points of B.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The upward quadratic is nonpositive between its roots.
$(x+2)(x-1)\le0\iff -2\le x\le1$
Keep only points in both sets.
$B=(-\infty,0]\cup[2,\infty),\quad A\cap B=[-2,0]$

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

2026 JM01