SAT Math formula guide
Know the formula—and recognize the moment it matters.
The Digital SAT supplies a reference sheet, but recognition is still the real skill. Students need to see a situation, identify the relevant relationship, preserve units, and know what the question actually asks. Use this guide as a compact review—not as a substitute for solving varied problems.
Lines and linear relationships
For a line, slope is change in output divided by change in input. In slope-intercept form, y = mx + b, m is the slope and b is the value of y when x is zero. Parallel lines have equal slopes; nonvertical perpendicular lines have slopes whose product is −1.
- Slope: (y₂ − y₁)/(x₂ − x₁)
- Slope-intercept form: y = mx + b
- Point-slope form: y − y₁ = m(x − x₁)
- Distance: √((x₂ − x₁)² + (y₂ − y₁)²)
- Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2)
Quadratics, exponents, and growth
Quadratic questions may ask for roots, vertex behavior, equivalent forms, or the meaning of constants. Exponential questions often hide the growth factor inside a percent change. A percent increase of r percent corresponds to multiplication by 1 + r/100; a decrease uses 1 − r/100.
- Quadratic formula: x = (−b ± √(b² − 4ac))/(2a)
- Discriminant: b² − 4ac
- Difference of squares: a² − b² = (a − b)(a + b)
- Exponential model: y = a(b)ˣ
- Compound change over t periods: initial × (growth factor)ᵗ
Percent, ratio, and rate
Write units beside quantities before calculating. Many wrong answers come from using the wrong baseline, confusing percent with percentage points, or returning a total when the question asks for the increase alone.
- Percent change: (new − original)/original × 100%
- Part = percent × whole
- Average rate = total change/total time
- Proportion: a/b = c/d
- Weighted mean = sum of weighted values/sum of weights
Area, volume, and circles
The reference sheet includes common area and volume formulas, but questions frequently test scale factor, radius versus diameter, or a missing dimension. If lengths scale by k, areas scale by k² and volumes by k³.
- Triangle area: ½bh
- Circle area: πr²; circumference: 2πr
- Circle equation: (x − h)² + (y − k)² = r²
- Rectangular solid volume: lwh
- Cylinder volume: πr²h
- Sphere volume: 4πr³/3
- Cone volume: πr²h/3
Right triangles and trigonometry
Label the sides relative to the stated angle before choosing a trigonometric ratio. Similar triangles preserve angle measures and proportional side lengths. Special right triangles can replace longer calculations when the side pattern is recognizable.
- Pythagorean theorem: a² + b² = c²
- sin θ = opposite/hypotenuse
- cos θ = adjacent/hypotenuse
- tan θ = opposite/adjacent
- 45-45-90 sides: x, x, x√2
- 30-60-90 sides: x, x√3, 2x
Frequently asked questions
Clear answers before you begin.
Does the Digital SAT provide a Math formula sheet?+
Yes. Bluebook includes a reference sheet with common geometry formulas, but it does not replace knowing when and how to use them.
Do I need to memorize the quadratic formula?+
It is worth knowing because quadratic questions can require roots or solution analysis, even when another method such as factoring is faster.
Is a calculator allowed for all SAT Math questions?+
Yes. A calculator is allowed throughout the current Digital SAT Math section.
What formulas cause the most avoidable mistakes?+
Percent change, slope, circle radius versus diameter, and area or volume scale factors often produce preventable errors because students apply the right formula to the wrong quantity.
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