What the Test Gives You vs. What You Must Memorize
The SAT provides a reference sheet at the start of the Math section with certain geometric formulas. Knowing what's on that sheet saves you the mental energy of memorizing those — but it also means that everything not on the sheet is fair game to forget if you don't study it.
Formulas provided on the SAT reference sheet: Area of a circle (πr²), circumference (2πr), area of a rectangle (lw), area of a triangle (½bh), Pythagorean theorem (a² + b² = c²), special right triangles (30-60-90 and 45-45-90), volume of a box (lwh), volume of a cylinder (πr²h), volume of a sphere (4/3 πr³), volume of a cone (1/3 πr²h), volume of a pyramid (1/3 lwh).
Everything else in this article you must memorize. For each formula, we include what it means and when to use it.
Algebra and Linear Equations
| Formula | What It Means | When to Use It |
|---|---|---|
| y = mx + b | Slope-intercept form: m = slope, b = y-intercept | Any linear equation question; graphing lines; finding where a line crosses the y-axis |
| y − y₁ = m(x − x₁) | Point-slope form: build a line equation from one point and a slope | When given a point and slope but not the y-intercept |
| m = (y₂ − y₁)/(x₂ − x₁) | Slope formula: rise over run between two points | Any time you need the slope from two coordinate pairs |
| d = √[(x₂−x₁)² + (y₂−y₁)²] | Distance between two points in the coordinate plane | Geometry coordinate questions; circle radius problems |
| Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) | Average of the x-coordinates and y-coordinates | Finding the center of a segment; midpoint geometry questions |
| x = (−b ± √(b²−4ac)) / 2a | Quadratic formula: finds roots of ax² + bx + c = 0 | When a quadratic can't be factored easily; finding x-intercepts |
| b² − 4ac | Discriminant: positive = 2 real roots, zero = 1 root, negative = no real roots | Questions about number of solutions to a quadratic |
Geometry
| Shape / Concept | Formula | Notes |
|---|---|---|
| Circle — standard form | (x−h)² + (y−k)² = r² | Center is (h, k), radius is r |
| Arc length | L = (θ/360) × 2πr | θ is the central angle in degrees |
| Sector area | A = (θ/360) × πr² | Fraction of the full circle's area |
| Parallel lines cut by transversal | Alternate interior angles equal; co-interior angles supplementary | Identify angle pair type first |
| Triangle angle sum | ∠A + ∠B + ∠C = 180° | Also: exterior angle = sum of two non-adjacent interior angles |
| 45-45-90 triangle sides | x : x : x√2 | Legs are equal; hypotenuse = leg × √2 |
| 30-60-90 triangle sides | x : x√3 : 2x | Short leg : long leg : hypotenuse |
| SOHCAHTOA | sin = opp/hyp; cos = adj/hyp; tan = opp/adj | Right triangle trig; know these cold |
Statistics and Data Analysis
| Concept | Formula / Definition | When It Appears |
|---|---|---|
| Mean (average) | Mean = Sum of values / Number of values | Data set questions; combined averages |
| Median | Middle value when ordered; average of two middle values if even count | Comparing mean vs. median; skewed data sets |
| Mode | Most frequently occurring value | Frequency tables; bar chart questions |
| Standard deviation concept | Measures how spread out values are from the mean; larger SD = more spread | Comparing variability between two groups; no calculation required on SAT |
| Probability | P(event) = favorable outcomes / total outcomes | Probability questions; independent vs. dependent events |
| Percent change | % change = (new − old) / old × 100 | Word problems involving growth, decrease, or markups |
| Percent of a number | Part = Percent × Whole | Sales tax, discounts, commission problems |
Advanced Topics
| Topic | Key Rule or Formula | Notes |
|---|---|---|
| Exponent rules — product | aᵐ × aⁿ = aᵐ⁺ⁿ | Same base: add exponents |
| Exponent rules — quotient | aᵐ / aⁿ = aᵐ⁻ⁿ | Same base: subtract exponents |
| Exponent rules — power | (aᵐ)ⁿ = aᵐⁿ | Power to a power: multiply exponents |
| Negative exponents | a⁻ⁿ = 1/aⁿ | Negative exponent = reciprocal |
| Fractional exponents | a^(m/n) = ⁿ√(aᵐ) | a^(1/2) = √a; a^(1/3) = ∛a |
| Difference of squares | a² − b² = (a+b)(a−b) | Factor expressions quickly; appears frequently |
| Perfect square trinomial | a² ± 2ab + b² = (a ± b)² | Completing the square; vertex form of parabola |
| Direct variation | y = kx | k is the constant of proportionality |
| Inverse variation | y = k/x | As x increases, y decreases proportionally |
| Systems of equations | Substitution or elimination; solution is the intersection point | Parallel lines (same slope) = no solution; same line = infinite solutions |
| Vertex form of parabola | y = a(x−h)² + k | Vertex is (h, k); a determines direction and width |
| Function notation | f(a) = substitute a for x in the function | f(g(x)) means substitute g(x) as the input to f |
If you only have time to memorize five things: (1) slope-intercept form, (2) quadratic formula, (3) percent change formula, (4) difference of squares, and (5) SOHCAHTOA. These appear on virtually every SAT Math section.
Using Desmos Strategically
The digital SAT gives you access to the Desmos graphing calculator for the entire Math section. This changes your formula strategy: for anything involving graphing, intersections, or complex equations, type it into Desmos rather than solving algebraically. Desmos is fastest for:
- Finding the x-intercepts (roots) of quadratics and polynomials
- Solving a system of equations graphically (find the intersection point)
- Checking whether a parabola equation has 0, 1, or 2 x-intercepts
- Evaluating functions at specific values
Still memorize the formulas — many questions require conceptual understanding, and typing every problem into Desmos costs time. But use Desmos as your backup verification tool.
✅ Key Takeaways
- The SAT provides geometric formulas (circle, triangle, volume) on the reference sheet — you do not need to memorize those.
- Algebra and advanced math account for roughly 70% of Math questions — prioritize those formulas.
- The quadratic formula, slope-intercept form, and percent change formula appear on nearly every SAT.
- Desmos is available for the entire digital SAT Math section — use it strategically to verify answers and graph equations.
- Standard deviation is conceptual on the SAT — you'll never have to calculate it, just compare it between groups.