SAT formula sheet, one card each

The formulas the test expects you to know, including the ones its reference sheet leaves out.

Free on the 3-day trial. No card.

What students are saying

Algebra

Linear equation in one variable

General form

ax + b = c

Solve for x

x = \dfrac{c - b}{a}

No solutionsame

x

-coefficient on both sides, different constants — e.g.

4x + 3 = 4x + 7

Infinite solutionsboth sides simplify to the identical expression — every

x

works

RememberUndo operations in reverse to isolate

x

, then plug your answer back into the original equation to check it. For “what value of

k

gives infinitely many solutions”: pick

k

so the two sides match term for term.

Slope

m = \dfrac{\text{rise}}{\text{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}

Forms of a line

Slope-intercept

y = mx + b

m

= slope,

b

y

-intercept

Point-slope

y - y_1 = m(x - x_1)

Standard form

Ax + By = C

slope

= -\tfrac{A}{B}

Remember

x

-intercept: set

y = 0

and solve.

y

-intercept: set

x = 0

and solve.

Advanced Math

Exponent rules — combining

Multiply (same base)

a^b \cdot a^c = a^{\,b+c}

Divide (same base)

\dfrac{a^b}{a^c} = a^{\,b-c}

Power of a power

(a^b)^c = a^{\,bc}

RememberMultiplying adds exponents, dividing subtracts them, and a power of a power multiplies them.

Quadratic forms

Standard

f(x) = ax^2 + bx + c

y

-intercept

= c

Factored

f(x) = a(x-m)(x-n)

x

-intercepts

= m, n

Vertex

f(x) = a(x-h)^2 + k

vertex

= (h, k)

Upward parabola — roots m, n; vertex (h, k) on the axis of symmetry

RememberOpens up if

a > 0

, down if

a < 0

Percent increase & decrease

Increase by

r

multiply by

(1 + r)

Decrease by

r

multiply by

(1 - r)

Remember

r

is the rate as a decimal (5% → 0.05). A 20% rise then a 20% fall does not return to the start.

Parent graphs

y = x

straight line

y = |x|

V-shape

y = x^2

parabola

y = x^3

cubic (S-curve through origin)

y = a^{x}

exponential curve

y = \sqrt{x}

half sideways-parabola

Data Analysis

Ratios, rates & proportions

Ratio of

a

b

a:b = \dfrac{a}{b}

Proportion

\dfrac{a}{b} = \dfrac{c}{d} \Rightarrow ad = bc

cross-multiply

Distance

d = rt

distance = rate × time

Unit conversion

\left( \dfrac{\text{ending units}}{\text{starting units}} \right)

e.g.

10\,\text{ft} \times \tfrac{12\,\text{in}}{1\,\text{ft}} = 120\,\text{in}

RememberSet up the fraction so the unit you're leaving cancels — the starting unit always goes on the bottom.

Percentages

Part

\text{Part} = \text{Whole} \times \dfrac{\%}{100}

Percent

\% = \dfrac{\text{Part}}{\text{Whole}} \times 100

Whole

\text{Whole} = \dfrac{\text{Part}}{\%} \times 100

Percent change

\dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%

RememberPercent change is always “change over the original” — the denominator is the old value, never the new one.

Measures of center

Mean

\dfrac{\sum x}{n}

sum of values ÷ how many

Medianmiddle value when data is ordered

Modemost frequently occurring value

RememberOutliers drag the mean toward them but barely move the median — so the median is the more robust center for skewed data.

Geometry & Trig

Angle pairs

Complementarytwo angles that sum to

90^\circ

Supplementarytwo angles that sum to

180^\circ

(e.g. a linear pair)

Around a pointadd to

360^\circ

Vertical anglesequal

RememberComplementary = Corner (90°); Supplementary = Straight line (180°). C before S, 90 before 180.

Triangles

Interior anglessum to

180^\circ

Exterior angleequals the sum of the two remote interior angles

Typesscalene (none equal), isosceles (two equal), equilateral (all equal, each

60^\circ

)

Triangle inequalityany two sides must sum to more than the third; the longest side faces the largest angle

RememberTriangle inequality quick check: if the two shorter sides don't out-total the longest, no triangle exists. With sides

a \le b \le c

, you only need

a + b > c

Pythagorean theorem

a^2 + b^2 = c^2

right triangles only;

c

is the hypotenuse

Triples3-4-5 · 6-8-10 · 5-12-13 · 7-24-25 · 8-15-17

Right triangle: a² + b² = c²

Area of polygons

Square

A = s^2

Rectangle

A = lw,\quad P = 2l + 2w

Parallelogram

A = bh

Triangle

A = \tfrac{1}{2}bh

Trapezoid

A = \tfrac{1}{2}(b_1 + b_2)h

Rhombus

A = \tfrac{1}{2} d_1 d_2

RememberMost of these are just base × height — halved for the triangle. The rhombus is the odd one out: half the product of its diagonals

\left(\tfrac{1}{2} d_1 d_2\right)

Area of circles & ellipses

Circle

A = \pi r^2,\quad C = 2\pi r

Ellipse

A = \pi a b

RememberAn ellipse is a stretched circle: with semi-axes

a

and

b

, its area

\pi a b

collapses to

\pi r^2

when

a = b = r

Frequently Asked Questions

Does the SAT give you a formula sheet?

Yes. Bluebook has a reference sheet you can open during Math: areas and circumference, the Pythagorean theorem, special right triangles, the volume of common solids, and that a circle has 360 degrees (2π radians) and a triangle's angles add to 180.

Which SAT formulas should I memorize?

The ones the reference sheet leaves out: slope and the forms of a line, the quadratic formula and vertex form, exponent rules, percent change, and the equation of a circle. Those come up every test and nobody hands them to you.

Can you bring a cheat sheet to the SAT?

No. The only formulas you get on test day are the ones on the built-in reference sheet.

How many formulas are on CuePrep's SAT formula sheet?

58 formula cards across Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. The whole sheet is open on the 3-day trial, with practice questions on each formula.

Know every formula cold

Free on the 3-day trial. No card.