SAT Math Formulas: What's on the Reference Sheet and What to Memorize
6 min read · Updated
The Digital SAT gives you a reference sheet during Math, so you do not need to memorize area and volume formulas. But the reference sheet leaves out most of what the test actually asks about — lines, quadratics, exponents and circles in the coordinate plane — and those you must know.
On the reference sheet
- Circle: area πr², circumference 2πr
- Rectangle: area ℓw; triangle: area ½bh
- Pythagorean theorem: c² = a² + b²
- Special right triangles: 30°-60°-90° (x, x√3, 2x) and 45°-45°-90° (s, s, s√2)
- Volumes: box ℓwh, cylinder πr²h, sphere ⁴⁄₃πr³, cone ⅓πr²h, pyramid ⅓ℓwh
- A circle has 360 degrees and 2π radians; a triangle's angles sum to 180 degrees
Not on the sheet: lines
| Formula | Use |
|---|---|
| m = (y₂ − y₁) / (x₂ − x₁) | Slope from two points |
| y = mx + b | Slope-intercept form: m is the slope, b the y-intercept |
| y − y₁ = m(x − x₁) | A line through a known point |
| Parallel: equal slopes; perpendicular: slopes multiply to −1 | Comparing lines |
Not on the sheet: quadratics and exponents
| Formula | Use |
|---|---|
| x = [−b ± √(b² − 4ac)] / 2a | Quadratic formula |
| b² − 4ac > 0, = 0, < 0 | Two, one or no real solutions |
| x = −b / 2a | x-coordinate of the vertex |
| y = a(x − h)² + k | Vertex form: the vertex is (h, k) |
| a² − b² = (a + b)(a − b) | Difference of squares |
| xᵃ · xᵇ = xᵃ⁺ᵇ, (xᵃ)ᵇ = xᵃᵇ, x^(m/n) = ⁿ√xᵐ | Laws of exponents |
Not on the sheet: percentages and growth
| Formula | Use |
|---|---|
| (new − old) / old × 100 | Percent change |
| Increase by r%: multiply by (1 + r/100) | Successive changes multiply |
| A = P(1 + r)ᵗ | Exponential growth; use (1 − r) for decay |
Not on the sheet: circles and trig
| Formula | Use |
|---|---|
| (x − h)² + (y − k)² = r² | Circle with center (h, k) and radius r |
| Arc length = (θ / 360) · 2πr | Arc for a central angle θ in degrees |
| Sector area = (θ / 360) · πr² | Slice of a circle |
| sin = opp/hyp, cos = adj/hyp, tan = opp/adj | Right-triangle trig (SOH-CAH-TOA) |
| sin x° = cos(90 − x)° | Complementary angles |
Complete the square to find a circle's center
When a circle is given as x² + y² − 6x + 8y = 11, group and complete the square: (x − 3)² + (y + 4)² = 36. The center is (3, −4) and the radius is 6.
A circle in the xy-plane has equation (x + 2)² + (y − 5)² = 49. What is the radius of the circle?
- A5
- B7
- C24.5
- D49
Explanation
In (x − h)² + (y − k)² = r², the right side is r², so r² = 49 and r = 7. The trap is 49, the value of r² itself.