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Digital SAT Math Formula Sheet

Every formula you need for SAT Math: the ones on the official reference sheet, and the ones you have to memorize because the test will not give them to you.

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Formulas given on the Digital SAT reference sheet

Provided

These appear on the built-in reference sheet in Bluebook. You can look them up during the test, but knowing them cold saves time.

Area of a circle

A=πr2A = \pi r^2

Circumference of a circle

C=2πrC = 2\pi r

Area of a rectangle

A=ℓwA = \ell w

Area of a triangle

A=12bhA = \tfrac{1}{2}bh

Pythagorean theorem

a2+b2=c2a^2 + b^2 = c^2

30-60-90 triangle

sides x, x3, 2xx,\ x\sqrt{3},\ 2x

45-45-90 triangle

sides s, s, s2s,\ s,\ s\sqrt{2}

Volume of a rectangular prism

V=ℓwhV = \ell wh

Volume of a cylinder

V=πr2hV = \pi r^2 h

Volume of a sphere

V=43πr3V = \tfrac{4}{3}\pi r^3

Volume of a cone

V=13πr2hV = \tfrac{1}{3}\pi r^2 h

Volume of a pyramid

V=13ℓwhV = \tfrac{1}{3}\ell wh

Angles in a circle

360∘360^\circ or 2π2\pi radians
Angles in a triangle sum to 180∘180^\circ.

Algebra and linear equations

Memorize

Not on the reference sheet. Algebra is about 35% of SAT Math, so these come up constantly.

Slope

m=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}

Slope-intercept form

y=mx+by = mx + b

Point-slope form

y−y1=m(x−x1)y - y_1 = m(x - x_1)

Standard form

Ax+By=CAx + By = C
Slope is −AB-\tfrac{A}{B}.

Parallel and perpendicular lines

parallel: m1=m2m_1 = m_2, perpendicular: m1m2=−1m_1 m_2 = -1

System with no solution

same slope, different intercept

System with infinitely many solutions

same slope, same intercept

Quadratics and advanced math

Memorize

The Advanced Math domain is heavy on quadratics and exponentials. None of these are provided.

Quadratic formula

x=−b±b2−4ac2ax = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Discriminant

b2−4acb^2 - 4ac
Positive: 2 real roots. Zero: 1. Negative: none.

Vertex form

y=a(x−h)2+ky = a(x - h)^2 + k
Vertex is (h,k)(h, k).

Vertex x-coordinate

x=−b2ax = -\dfrac{b}{2a}

Sum and product of roots

sum =−ba= -\tfrac{b}{a}, product =ca= \tfrac{c}{a}

Difference of squares

a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)

Exponential growth or decay

y=a(1±r)ty = a(1 \pm r)^t

Exponent rules

xaxb=xa+bx^a x^b = x^{a+b}, (xa)b=xab(x^a)^b = x^{ab}, x−a=1xax^{-a} = \tfrac{1}{x^a}, xmn=xmnx^{\frac{m}{n}} = \sqrt[n]{x^m}

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Geometry and trigonometry

Memorize

Circles and right triangle trig are tested every time, and these are the ones students forget.

Equation of a circle

(x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2

Distance formula

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Midpoint formula

(x1+x22, y1+y22)\left(\dfrac{x_1 + x_2}{2},\ \dfrac{y_1 + y_2}{2}\right)

Arc length

θ360⋅2πr\dfrac{\theta}{360} \cdot 2\pi r

Sector area

θ360⋅πr2\dfrac{\theta}{360} \cdot \pi r^2

Degrees to radians

radians=degrees⋅π180\text{radians} = \text{degrees} \cdot \dfrac{\pi}{180}

SOH CAH TOA

sin⁡θ=opphyp\sin\theta = \tfrac{\text{opp}}{\text{hyp}}, cos⁡θ=adjhyp\cos\theta = \tfrac{\text{adj}}{\text{hyp}}, tan⁡θ=oppadj\tan\theta = \tfrac{\text{opp}}{\text{adj}}

Complementary angles

sin⁡x∘=cos⁡(90−x)∘\sin x^\circ = \cos(90 - x)^\circ

Interior angles of a polygon

(n−2)⋅180∘(n - 2) \cdot 180^\circ

Problem solving and data analysis

Memorize

Percent, rate, and statistics questions reward knowing these by heart.

Percent change

new−oldold×100\dfrac{\text{new} - \text{old}}{\text{old}} \times 100

Mean

sum of valuesnumber of values\dfrac{\text{sum of values}}{\text{number of values}}

Median

middle value of the ordered list

Distance, rate, time

d=rtd = rt

Probability

P=favorable outcomestotal outcomesP = \dfrac{\text{favorable outcomes}}{\text{total outcomes}}

Margin of error

estimate ±\pm margin gives the plausible range

Common questions

Does the Digital SAT give you a formula sheet?

Yes. Bluebook includes a reference sheet with area, volume, Pythagorean theorem, and special right triangle formulas. It does not include slope, the quadratic formula, the circle equation, or trig ratios.

Which SAT Math formulas do I need to memorize?

Memorize slope, the forms of a line, the quadratic formula, the discriminant, vertex form, the equation of a circle, distance and midpoint, arc length, SOH CAH TOA, and percent change.

Can Desmos replace memorizing formulas?

Desmos helps you graph and solve quickly, but you still need to know the formula to set up the problem. The fastest students combine both.

More free resources

Desmos SAT Math Guide: 8 calculator tricks that save points1-on-1 SAT Math tutoring

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