Passport to Advanced Math

Quadratic Equations

Factor, complete the square, and apply the quadratic formula. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on quadratic equations is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 What are the solutions to the equation x^2 - 11x + 30 = 0? easy 400-500 Open
2 What are the solutions to the equation x^2 + 5x - 6 = 0? easy 400-500 Open
3 What are the solutions to the equation x^2 - 1x - 12 = 0? easy 400-500 Open
4 What are the solutions to the equation x^2 + 5x - 14 = 0? easy 400-500 Open
5 What are the solutions to the equation x^2 + 5x + 6 = 0? easy 400-500 Open
6 What are the solutions to the equation x^2 - 4x + 3 = 0? easy 400-500 Open
7 What are the solutions to the equation x^2 - 3x + 2 = 0? easy 500-600 Open
8 What are the solutions to the equation x^2 + 5x + 6 = 0? easy 500-600 Open
9 What are the solutions to the equation x^2 + 9x + 20 = 0? medium 500-600 Open
10 What are the solutions to the equation x^2 + 3x - 18 = 0? medium 500-600 Open
11 What are the solutions to the equation x^2 + 1x - 6 = 0? medium 500-600 Open
12 What are the solutions to the equation x^2 + 0x - 36 = 0? medium 500-600 Open
13 What are the solutions to the equation x^2 - 3x - 18 = 0? medium 600-700 Open
14 What are the solutions to the equation x^2 - 12x + 35 = 0? medium 600-700 Open
15 What are the solutions to the equation x^2 - 12x + 35 = 0? medium 600-700 Open
16 What are the solutions to the equation x^2 - 5x + 6 = 0? medium 600-700 Open
17 What are the solutions to the equation x^2 + 4x - 12 = 0? medium 600-700 Open
18 What are the solutions to the equation x^2 + 2x - 3 = 0? medium 600-700 Open
19 What are the solutions to the equation x^2 + 3x - 10 = 0? hard 600-700 Open
20 What are the solutions to the equation x^2 - 4x - 5 = 0? hard 700-800 Open
21 What are the solutions to the equation x^2 + 1x - 20 = 0? hard 700-800 Open
22 What are the solutions to the equation x^2 - 1x - 30 = 0? hard 700-800 Open
23 What are the solutions to the equation x^2 + 4x - 12 = 0? hard 700-800 Open
24 What are the solutions to the equation x^2 + 0x - 49 = 0? hard 700-800 Open
25 What are the solutions to the equation x^2 + 9x + 20 = 0? hard 700-800 Open