Quadratic Inequalities — Quick Reference Cheatsheet
A focused companion to the main Quadratic Inequalities topic page on ACT Math.
ACT Math Intermediate Algebra One-page reference
This is a one-page reference for Quadratic Inequalities on the ACT math section. Solve ax² + bx + c > 0 by factoring and reasoning about sign on intervals. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Quadratic Inequalities topic page.
What this topic is
A Quadratic Inequalities question tests more advanced algebraic structures — quadratics, complex numbers, sequences, logarithms, and matrices. This is where the ACT separates good from elite scores.
Core formulas you must memorise
- Quadratic formula
- i² = −1
- Arithmetic seq: aₙ = a₁ + (n − 1)d
- Geometric seq: aₙ = a₁ · rⁿ⁻¹
- log_b(x) = y ⇔ bʸ = x
If any of these formulas are not yet automatic, drill them via the Intermediate Algebra formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
ACT questions on Quadratic Inequalities typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Quadratic Inequalities is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
Identify the family (quadratic, sequence, log, complex) before reaching for any formula — applying the wrong family wastes 90 seconds.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked Quadratic Inequalities questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our Quadratic Inequalities strategy guide. For category-wide context, browse all Intermediate Algebra topics. For score-targeted study plans, see the score-band guides.