SAT Problem Solving Framework
Most SAT mistakes are setup mistakes, not arithmetic ones. This chapter gives you a repeatable framework for turning a word problem into an equation you can actually solve: translate the words, surface the hidden quantities, track the units, and use logic to eliminate. Drill these and the “I don’t know where to start” feeling disappears. Each topic has worked examples and practice prompts.
Topics
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Formula Reference Sheet
The four moves
| Translate | words → variables and an equation |
|---|---|
| Surface | name the quantity the problem hides |
| Track units | make the units cancel to what is asked |
| Eliminate | rule out impossible answers by logic |
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |