Mistake Master
Digital SAT Math

Formulas and reference

The geometry sheet Bluebook gives you on every question — and the formulas it doesn't, organized by unit and linked to the lesson that drills each one. Printable.

Section 1

Given on test day

This exact sheet sits behind the reference button in Bluebook on every math question. Don't memorize it — but know what's on it, so you never burn time re-deriving a cone volume, and never expect it to hand you anything beyond geometry.

Circle

\(A = \pi r^2\)
\(C = 2\pi r\)

Rectangle

\(A = \ell w\)

Triangle

\(A = \tfrac{1}{2}bh\)

Right triangle

\(c^2 = a^2 + b^2\)

Special right · 30-60-90

hyp = 2 · short leg

Special right · 45-45-90

hyp = leg · √2

Rectangular solid

\(V = \ell wh\)

Cylinder

\(V = \pi r^2 h\)

Sphere

\(V = \tfrac{4}{3}\pi r^3\)

Cone

\(V = \tfrac{1}{3}\pi r^2 h\)

Pyramid

\(V = \tfrac{1}{3}\ell wh\)
Also stated on the sheet
  • The number of degrees of arc in a circle is 360.
  • The number of radians of arc in a circle is \(2\pi\).
  • The sum of the measures in degrees of the angles of a triangle is 180.
Section 2

Not on the sheet — know these cold

Everything below is fair game on test day and nowhere in Bluebook's reference. Each formula links to the lesson that drills it. If one looks unfamiliar, that link is your next stop.

Unit 1Linear Reasoning (Algebra)

Unit hub ›
\(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
Slope from any two points — rise over run. The single most-used formula on the test.
Lesson 1.3 ›
\(y = mx + b\)
Slope-intercept form: \(b\) is the starting value, \(m\) is the rate of change. Translate every linear word problem into this.
Lesson 1.3 ›
\(y - y_1 = m(x - x_1)\)
Point-slope form — fastest route to an equation when you have one point and a slope. No solving for \(b\).
Lesson 1.3 ›
\(m_1 = m_2 \quad\big/\quad m_1 m_2 = -1\)
Parallel lines share a slope; perpendicular slopes multiply to −1 (negative reciprocals).
Lesson 1.3 ›
\(Ax + By = C \;\Rightarrow\; m = -\dfrac{A}{B}\)
Read a slope straight off standard form without converting — the fast lane on "no solution" system questions.
Lesson 1.4 ›
same slope, different intercept → no solution
Systems: parallel lines never meet (zero solutions); identical lines overlap everywhere (infinitely many).
Lesson 1.4 ›

Unit 2Nonlinear Algebra (Advanced Math)

Unit hub ›
\(x^a x^b = x^{a+b},\;\; (x^a)^b = x^{ab}\)
Exponent rules — plus \(x^{-a} = \frac{1}{x^a}\) and \(x^{a/b} = \sqrt[b]{x^a}\). Fractional exponents are the SAT's favorite disguise.
Lesson 2.1 ›
\(a^2 - b^2 = (a+b)(a-b)\)
Difference of squares — and \((a+b)^2 = a^2 + 2ab + b^2\). Forgetting the middle term is a named mistake pattern for a reason.
Lesson 2.2 ›
\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
The quadratic formula. The discriminant \(b^2 - 4ac\) alone answers "how many real solutions": positive → 2, zero → 1, negative → 0.
Lesson 2.3 ›
\(y = a(x-h)^2 + k\)
Vertex form — vertex at \((h, k)\). From standard form, the vertex sits at \(x = -\frac{b}{2a}\). This is every max/min question.
Lesson 2.3 ›
\(x_1 + x_2 = -\dfrac{b}{a},\;\; x_1 x_2 = \dfrac{c}{a}\)
Sum and product of roots — the shortcut behind hard "sum of the solutions" questions that punish anyone who actually solves.
Lesson 2.3 ›
\(y = a(1+r)^t \;\;\text{vs.}\;\; y = a + rt\)
Exponential vs. linear growth: equal ratios per step vs. equal differences per step. Decay is \((1-r)^t\).
Lesson 2.5 ›

Unit 3Proportional Reasoning and Percentages

Unit hub ›
\(\%\,\Delta = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%\)
Percent change — always divided by the original. Using the new value instead is one of the test's most reliable traps.
Lesson 3.3 ›
\(\times(1+r_1)(1+r_2)\cdots\)
Successive percent changes multiply — a 20% increase then a 20% decrease is ×1.2 × 0.8 = ×0.96, not back to start.
Lesson 3.3 ›
\(A = P(1 + rt) \;\;/\;\; A = P(1+r)^t\)
Simple interest grows linearly; compound interest grows exponentially. Spot which one from the words "each year on the original" vs. "on the balance."
Lesson 3.3 ›
\(\dfrac{a}{b} = \dfrac{c}{d} \;\Leftrightarrow\; ad = bc\)
Proportions cross-multiply. Set the ratio up with matching units in matching positions before touching numbers.
Lesson 3.4 ›
\(\bar{x}_w = \dfrac{\sum (\text{value} \times \text{weight})}{\sum \text{weights}}\)
Weighted average — mixtures, class averages combined across sections, and concentration problems all run through this.
Lesson 3.5 ›

Unit 4Data, Statistics, and Probability

Unit hub ›
\(\text{mean} = \dfrac{\text{sum}}{\text{count}}\)
And the recovery move: sum = mean × count. Most "find the missing value" questions are this formula run backwards.
Lesson 4.2 ›
median = middle of the ordered list
Resistant to outliers; the mean is not. That asymmetry — which measure moves when an extreme value is added — is the question.
Lesson 4.2 ›
standard deviation = spread, never computed
The SAT never asks you to calculate it — only to compare: data bunched near the mean has a smaller SD than data spread out.
Lesson 4.2 ›
\(P = \dfrac{\text{favorable}}{\text{total}}\)
For conditional probability from a table, the condition shrinks the denominator to one row or column — not the grand total.
Lesson 4.4 ›

Unit 5Geometry and Trigonometry

Unit hub ›
triangle 180° · polygon (n−2)·180°
Angle sums, plus vertical angles equal and parallel-line angle pairs. Similar triangles: matching sides stay proportional.
Lesson 5.1 ›
\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
Distance formula — the Pythagorean theorem in disguise. Midpoint is just the average: \(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\).
Lesson 5.2 ›
\(\sin\theta = \dfrac{\text{opp}}{\text{hyp}},\; \cos\theta = \dfrac{\text{adj}}{\text{hyp}},\; \tan\theta = \dfrac{\text{opp}}{\text{adj}}\)
SOH-CAH-TOA. Not on the sheet, and roughly one question per test assumes you have it instantly.
Lesson 5.3 ›
\(\sin x = \cos(90° - x)\)
The cofunction identity — a favorite hard question. If \(\sin a = \cos b\), then \(a + b = 90°\).
Lesson 5.3 ›
\((x-h)^2 + (y-k)^2 = r^2\)
Equation of a circle: center \((h, k)\), radius \(r\). Expanded form? Complete the square to get back here.
Lesson 5.4 ›
\(\dfrac{\text{central angle}}{360°} \times C \;\;\text{or}\;\; \times A\)
Arc length and sector area are the same idea: the fraction of the circle the angle claims. Degrees ↔ radians: multiply by \(\frac{\pi}{180}\) or \(\frac{180}{\pi}\).
Lesson 5.4 ›
\(S_{\text{cyl}} = 2\pi rh + 2\pi r^2,\;\; S_{\text{sph}} = 4\pi r^2\)
Surface area — the sheet gives volumes only. For prisms, unfold and add the faces rather than memorizing.
Lesson 5.5 ›
Section 1 mirrors the reference sheet provided in the Bluebook testing app on the Digital SAT Math section. Reformatted as a study sheet, not an official College Board publication.