Find the number of elements in P∩Q.

01 / Standard#Your turn

P=\{1,2,3,5,7,11\},\quad Q=\{x:x^2-15x+36<0\}

Official paper · jm01-2021 · I.1 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Factor the quadratic defining Q.

Hint 2

Keep only listed elements strictly between the roots.

Worked solution

The upward-opening quadratic is negative between its roots.
$(x-3)(x-12)<0\Rightarrow Q=(3,12)$
Intersect with the finite set.
$P\cap Q=\{5,7,11\};\quad|P\cap Q|=3$

B: 3 elements.

Checks and common pitfalls: The endpoint 3 is excluded by the strict inequality.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The upward-opening quadratic is negative between its roots.
$(x-3)(x-12)<0\Rightarrow Q=(3,12)$
Intersect with the finite set.
$P\cap Q=\{5,7,11\};\quad|P\cap Q|=3$

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

2021 JM01