SAT Math · Study & Practice
Ratios and Proportions
Ratios and proportions are among the most heavily tested ideas on the SAT — they power rate, scale, mixture and unit-conversion questions. This chapter covers ratios, equivalent ratios, proportions, direct and inverse variation, scale factors and unit rates. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.
Topics
1
Ratios
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2
Equivalent Ratios
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3
Proportions
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4
Direct Variation
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5
Inverse Variation
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6
Scale Factors
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7
Unit Rates
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Chapter test
Formula Reference Sheet
This chapter
Ratios & proportions
| Ratio | a : b (compares two quantities) |
|---|---|
| Proportion | a/b = c/d |
| Cross-multiplication | a/b = c/d ⇒ a·d = b·c |
| Total parts | a : b → split a whole into (a + b) parts |
Variation & rates
| Direct variation | y = kx (y/x constant) |
|---|---|
| Inverse variation | y = k/x (xy constant) |
| Unit rate | quantity ÷ number of units |
| Scale factor | ratio of corresponding lengths |
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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