SAT Math · Study & Practice
Linear Inequalities
Inequalities describe ranges of solutions rather than single values, and the SAT tests them in algebra and in word problems about limits and constraints. This chapter covers solving inequalities, compound inequalities, interval notation and number-line representation. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.
Topics
1
Solving Inequalities
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2
Compound Inequalities
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3
Interval Notation
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4
Number Line Representation
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Chapter test
Formula Reference Sheet
This chapter
Solving rules
| Same as equations | add/subtract/multiply/divide both sides |
|---|---|
| Flip rule | multiplying or dividing by a negative reverses the inequality |
| Symbols | < ≤ > ≥ |
Notation
| Open interval | (a, b): endpoints excluded (< >) |
|---|---|
| Closed interval | [a, b]: endpoints included (≤ ≥) |
| Compound (and) | a < x < b |
| Number line | open circle = strict, closed = inclusive |
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° |
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