SAT Math Shortcuts
On the SAT, the fastest correct method beats the most elegant one. This chapter covers the four highest-value shortcuts: backsolving from the answer choices, picking concrete numbers for variables, testing choices against conditions, and recognising patterns. Used at the right moment, each turns a slow algebra problem into a few seconds of arithmetic. Each topic has worked examples and practice prompts.
Topics
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Formula Reference Sheet
When choices exist
| Backsolve | plug the answer choices into the problem |
|---|---|
| Start from B or C | middle values let you adjust up or down |
When variables appear
| Pick numbers | choose easy values, compute, match a choice |
|---|---|
| Avoid 0 and 1 | they make too many choices look equal |
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° |