Find the intersection with the finite set.

01 / Standard#Your turn

A=\{x:x^2+3x-4\ge0\},\quad B=\{-4,-2,0,3\}

Official paper · jm01-2025 · I.1 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Factor the quadratic.

Hint 2

Test which listed elements lie outside its roots.

Worked solution

The upward quadratic is nonnegative outside its roots.
$(x+4)(x-1)\ge0\iff x\le-4\ \text{or}\ x\ge1$
Filter the four listed elements.
$A\cap B=\{-4,3\}$

A: {−4,3}.

Checks and common pitfalls: The root −4 is included because the inequality is non-strict.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The upward quadratic is nonnegative outside its roots.
$(x+4)(x-1)\ge0\iff x\le-4\ \text{or}\ x\ge1$
Filter the four listed elements.
$A\cap B=\{-4,3\}$

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

2025 JM01