What is the slope of the line through (x1, y1) and (x2, y2)?

m = (y2 - y1) / (x2 - x1) — the change in y divided by the change in x. The slope is undefined when x1 = x2, which is a vertical line.

What is slope-intercept form, and what do the letters mean?

y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).

What is the quadratic formula?

For ax^2 + bx + c = 0 with a not equal to 0, x = (-b +/- sqrt(b^2 - 4ac)) / (2a).

What does the discriminant tell you?

The discriminant is b^2 - 4ac. If it is positive there are two distinct real solutions, if it is zero there is exactly one real solution, and if it is negative there are no real solutions.

What is vertex form of a parabola?

y = a(x - h)^2 + k, where (h, k) is the vertex. The parabola opens upward if a > 0 and downward if a < 0.

For y = ax^2 + bx + c, what is the x-coordinate of the vertex?

x = -b / (2a). The vertical line x = -b / (2a) is the axis of symmetry, and substituting that x back into the equation gives the y-coordinate of the vertex.

What is the distance between two points in the coordinate plane?

d = sqrt((x2 - x1)^2 + (y2 - y1)^2), which is the Pythagorean theorem applied to the horizontal and vertical differences.

What is the midpoint of the segment joining (x1, y1) and (x2, y2)?

((x1 + x2) / 2, (y1 + y2) / 2) — the average of the x-coordinates and the average of the y-coordinates.

What is the standard equation of a circle?

(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

What are the area and circumference of a circle?

Area = pi*r^2 and circumference = 2*pi*r, which equals pi*d since the diameter d = 2r.

How do you find arc length and sector area for a central angle of theta degrees?

Arc length = (theta / 360) * 2*pi*r and sector area = (theta / 360) * pi*r^2. Both are the fraction theta/360 of the whole circle.

What is the Pythagorean theorem?

In a right triangle, a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse, the side opposite the right angle.

What are the side ratios of a 30-60-90 triangle?

x : x*sqrt(3) : 2x. The shortest side faces the 30 degree angle, x*sqrt(3) faces the 60 degree angle, and the hypotenuse 2x faces the right angle.

What are the side ratios of a 45-45-90 triangle?

x : x : x*sqrt(2). The two legs are equal and the hypotenuse is a leg times sqrt(2).

What are the volumes of a rectangular prism, a cylinder, a cone and a sphere?

Prism V = lwh, cylinder V = pi*r^2*h, cone V = (1/3)*pi*r^2*h, sphere V = (4/3)*pi*r^3.

What do sine, cosine and tangent equal in a right triangle?

SOHCAHTOA: sine = opposite / hypotenuse, cosine = adjacent / hypotenuse, tangent = opposite / adjacent.

How are the sine and cosine of complementary angles related?

sin(x) = cos(90 - x) when angles are measured in degrees, so the sine of an acute angle equals the cosine of its complement.

What are the exponent rules for multiplying, dividing and raising powers?

x^a * x^b = x^(a + b), x^a / x^b = x^(a - b), and (x^a)^b = x^(a*b).

What do a negative exponent and a fractional exponent mean?

x^(-a) = 1 / x^a, and x^(1/n) is the nth root of x. Combining them, x^(m/n) is the nth root of x raised to the power m.

What is the formula for percent change?

Percent change = (new value - original value) / original value * 100. A negative result is a percent decrease.

How do you find an average, and how do you recover the total from one?

Average = sum of the values / number of values. Rearranged, sum = average * number of values, which is how most SAT average questions are actually solved.

What is the probability of an event with equally likely outcomes?

P(event) = number of favorable outcomes / total number of possible outcomes. The value is always between 0 and 1.

What is the sum of the interior angles of a polygon with n sides?

(n - 2) * 180 degrees. That gives 180 degrees for a triangle and 360 degrees for a quadrilateral.

What is the general form for exponential growth and decay?

y = a(1 + r)^t, where a is the initial amount, r is the growth rate per period (negative for decay) and t is the number of periods.

Which math formulas does the SAT give you?

The digital SAT provides a reference sheet with the area and circumference of a circle, the area of a rectangle and a triangle, the Pythagorean theorem, the 30-60-90 and 45-45-90 side ratios, volumes of a rectangular box, cylinder, sphere, cone and pyramid, and three bare facts: a circle has 360 degrees, a circle has 2*pi radians, and the angles of a triangle sum to 180 degrees. It is geometry only — everything algebraic or trigonometric in this deck you have to know yourself.

How many formulas do I need to memorize for SAT Math?

Fewer than most students expect. The genuinely must-know set is roughly the two dozen cards here — slope, the quadratic formula and discriminant, vertex form, the circle equation, exponent and radical rules, the trig ratios, averages, percent change and basic probability.

Are flashcards a good way to study SAT math?

Yes, for the recall layer. Formulas, identities and definitions are exactly the kind of material spaced repetition handles well, which leaves your practice-test time for reasoning and pacing. Cram can turn your own SAT prep notes into flashcards with AI and schedule the reviews for you.

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SAT Math Formulas flashcards

Q: Which math formulas does the SAT give you?

The digital SAT provides a reference sheet with the area and circumference of a circle, the area of a rectangle and a triangle, the Pythagorean theorem, the 30-60-90 and 45-45-90 side ratios, volumes of a rectangular box, cylinder, sphere, cone and pyramid, and three bare facts: a circle has 360 degrees, a circle has 2*pi radians, and the angles of a triangle sum to 180 degrees. It is geometry only — everything algebraic or trigonometric in this deck you have to know yourself.

Q: How many formulas do I need to memorize for SAT Math?

Fewer than most students expect. The genuinely must-know set is roughly the two dozen cards here — slope, the quadratic formula and discriminant, vertex form, the circle equation, exponent and radical rules, the trig ratios, averages, percent change and basic probability.

Q: Are flashcards a good way to study SAT math?

Yes, for the recall layer. Formulas, identities and definitions are exactly the kind of material spaced repetition handles well, which leaves your practice-test time for reasoning and pacing. Cram can turn your own SAT prep notes into flashcards with AI and schedule the reviews for you.

This deck holds the formulas and rules SAT Math assumes you already know: the slope and distance formulas, slope-intercept and vertex form, the quadratic formula and discriminant, circle area, circumference and the standard circle equation, volumes for prisms, cylinders, cones and spheres, the two special right triangles, the three basic trig ratios, exponent and radical rules, and the arithmetic behind averages, percent change and simple probability. Each card is one formula or one rule, with the meaning of every variable spelled out on the back.

The digital SAT gives you a reference sheet with common area, volume and special-right-triangle facts, but it does not give you slope, the quadratic formula, exponent rules, percent change or the trig ratios — those you supply from memory. The Math modules are timed tightly enough that re-deriving a formula, or scrolling to the reference sheet mid-question, costs you a question elsewhere. Knowing these cold turns a two-minute problem into a thirty-second one.

The deck

How to study this deck

Split the deck in two: formulas printed on the SAT reference sheet (circle area, volumes, 30-60-90 and 45-45-90) and formulas that are not (slope, quadratic formula, percent change, exponent rules, SOHCAHTOA). Drill the second group twice as often, because nothing on test day will supply them.
For every formula card, say what each letter stands for before you flip. Knowing y = a(x - h)^2 + k is useless if you cannot say that (h, k) is the vertex — the SAT tests the meaning far more often than the bare symbols.
After each pass, write the formulas out by hand on blank paper instead of only reading the backs. Recall you can produce with a pencil under time pressure is the only kind the Math modules reward.

SAT Math Formulas: FAQ

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