SAT Math · Study & Practice
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
1
Translating Word Problems
Start →
2
Identifying Hidden Variables
Start →
3
Unit Analysis
Start →
4
Logical Elimination
Start →
Keep going
Formula Reference Sheet
This chapter
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 |
Digital SAT reference
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° |
🖩 Graphing Calculator