Find a from the stated intersection.

01 / Standard#Your turn

A=\{x:x^2-3x-4\le0\},\ B=\{x:3x+a\ge0\},\ A\cap B=[2,4]

Official paper · jm01-2024 · I.1 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Factor the quadratic.

Hint 2

Match the left endpoint of B with 2.

Worked solution

The quadratic is nonpositive between its roots.
$A=[-1,4],\quad B=[-a/3,\infty)$
The intersection begins at 2, so −a/3=2.
$a=-6$

B: a=−6.

Checks and common pitfalls: Dividing by positive 3 does not reverse the inequality.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The quadratic is nonpositive between its roots.
$A=[-1,4],\quad B=[-a/3,\infty)$
The intersection begins at 2, so −a/3=2.
$a=-6$

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

2024 JM01