SAT Math / High Yield Lessons

Solve Harder SAT Problems with the Desmos Tilde

Solve the SAT's hardest systems, models, and word problems by typing every condition into one Desmos entry, then check that the answer Desmos gives is the one the question asks for.

Part of the full libraryOpens January 2, 2027 · $97 for a year
What’s included

Three equations, a plus b plus c equals 21, 2a minus b equals 9, and b plus 3c equals 32, are typed into one Desmos input box as two lists joined by a tilde. A panel opens under it showing a equals 7, b equals 5, c equals 9, and an error of 0. A gray pointer moves to the next input box, where a c minus b shows 58. Next, the graph of p squared minus 14p plus 33 crosses the axis at 3 and 11; the pointer moves to its tilde entry, a condition p greater than 7 is added in braces, and the panel shows p equals 11. Finally, the graph of q squared minus 18q plus 65 crosses the axis at 5 and 13: choose the condition that gives the greater solution, using the buttons after the picture.

You’ll leave with these skills

  1. Turn every fact into one tilde entry
  2. Find a function's constants from its values
  3. Find the constant that makes an equation true for every x

This lesson is part of the full library

207 lessons that teach every skill the SAT tests
  • 71Math
  • 40Reading
  • 24Grammar
  • 10 full-length practice tests to build test-day stamina and confidence
  • A Desmos simulator to solve math questions faster
  • A step-by-step guide to every practice test question
  • The Bluebook Simulator, so test day feels familiar
  • A drawing for every key term, so new ideas make sense at a glance

Explore the full library