Polynomial or rational inequalities by the sign of factors

CAT has tested this idea 4 times across 4 papers, from 2017 to 2024. Solve one, and the others are the same method with different numbers or wording, which is why repeated concepts are the most efficient thing to practise.

Question	What it asks	Answer
CAT 2021 Slot 1 · QA Q1	when a ratio of quadratics is negative	A
CAT 2024 Slot 2 · QA Q20	1/(x + 5) ≤ 1/(2x − 3)	B
CAT 2017 Slot 1 · QA Q26	count integers satisfying a quadratic inequality	11
CAT 2018 Slot 2 · QA Q14	smallest integer making a cubic positive	8

Part of Inequalities & Modulus (49 questions since 2017).