Formulas Flashcards by Gail I

Distance between a point with coordinates (x1, y1) and a line Ax + By + C = 0 is

|Ax1 + By1 + C| / √(A^2 + B^2)

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If θ is the angle between two lines, tanθ =

(m1 - m2) / (1 + m1m2), where m1 and m2 are the slopes of the two lines

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sum of roots of a quadratic equation =

-b/a

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product of roots of a quadratic equation =

c/a

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Area of a triangle ABC is

1/2bc * sinA

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(Pythagorean identities) sin²x + cos²x =

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(Pythagorean identities) sec²x =

tan²x + 1

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(Pythagorean identities) csc²x =

cot²x + 1

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(Double-angle formulas) sin2A =

2sinAcosA

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(double-angle formulas) cos2A= (both cos and sin)

cos²A - sin²A

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(double-angle formulas) cos2A= (just cos)

2cos²A - 1

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(double-angle formulas) cos2A= (just sin)

1 - 2sin²A

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(double-angle formulas) tan2A =

2tanA/ (1-tan²A)

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if x≥0, then |x| =

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if x

-x

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[x] =

I, where I is an integer and I≤ x

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(polar coordinates) x =

rcosθ

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(polar coordinates) y =

rsinθ

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(polar coordinates) r² =

x² + y²

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Distance between a point with coordinates (x1, y1, z1) and a plane with equation Ax + By + Cz + D= 0 is

(Ax1 + By1 + Cz1 + D)/ √(A² + B² + C²)

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volume of a cylinder

πr²h

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lateral surface area of a cylinder =

2πrh

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total surface area of a cylinder =

2πrh + 2πr²

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volume of a cone

1/3 * πr²h

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lateral surface area of a cone

πr√(r² + h²)

total surface area of a cone

πr√(r² + h²) + πr²

volume of a sphere

4/3 * πr³

surface area of a sphere

4πr²

nCr = (n/r)= | note: n/r is not actually a fraction

n!/ (n-r)!r! = nPr / r!

(arithmetic sequence) nth term =

tn = t1 + (n - 1)d

(arithmetic sequence) sum of n terms =

Sn= n/2 * (t1 + tn)

(geometric sequence) nth term =

tn= t1 * r^(n-1)

(geometric sequence) sum of n terms =

Sn = t1(1 - r^n) / (1 - r)

(geometric sequence) if |r|

lim as n→∞ of Sn = t1/ 1 - r

cofunctions of complementary angles are

equal

cofunction pairs:

sin & cos, sec & csc, tan & cot

the constant in a polynomial equation (e.g. x^4 + 15x^3 + x^2 + 2x + 1) is the

y-intercept

multiplication of matrices is possible only when the number of columns in the matrix on the left equals the number of ..... in that case, the product is a matrix with the number of rows equal to the number of rows in the .... and the number of columns equal to the number of columns in the ....

rows in the matrix on the right/ left-hand matrix; right-hand matrix

to find the inverse of a graph,

fold the graph about the line y = x

even function proof:

f(-x) = f(x)

odd function proof:

f(-x) = -f(x)

when equation is given in the form: Ax + By = C, the slope is... and the y-int is .... If B= 0 and A doesn't equal 0, then the equation is ...

-A/B; C/B; x = C/A, a vertical line

volume of a prism:

V = Bh

surface area of a prism:

SA = Ph + 2B (p is the base perimeter)

surface area of a rectangular solid:

SA = 2lw + 2lh + 2wh

surface area of a cube:

SA = 6s^2

volume of a pyramid:

V= 1/3 Bh

surface area of a pyramid:

SA = 1/2 PL + B (P is the base perimeter, L is the slant height)

diagonal of a rectangular solid:

D= √(l² + w² + h²)

length of diagonal of a cube:

e√3, where e is side length

|x| = b→

x = b or x = -b

|x|

-b

|x| > b→

x b

first few primes:

2, 3, 5, 7, 11, 13, 17, 19, 23

if ad > bc, then

a/b > c/d (this is true when the sign is changed to

is/ of =

% / 100

(x - y)(x + y) =

x² - y²

(x - y)² =

x² - 2xy + y²

(x + y)² =

x² + 2xy + y²

(for triangles) a² + b²

obtuse

(for triangles) a² + b² > c² if and only if angle C is

acute

area of equilateral triangle with side s,

A = (s²√3) / 4

if 2 triangles are similar and if k is the ratio of similitude, the ratio of their areas is

k²

in any polygon, the sum of the measures of the exterior angles, taking one at each vertex, is

360 degrees

(parallelograms) opposite sides are

parallel and congruent

(parallelograms) opposite angles are

congruent

(parallelograms) the sum of the measures of any pair of consecutive angles is

180 degrees

(parallelograms) a diagonal divides the parallelogram into

two congruent triangles

(parallelograms) the two diagonals

bisect each other

(rectangles) has all the properties of

parallelograms

(rectangles) the diagonals of a rectangle have the same

length

(rhombus) has all the properties of

parallelograms

(rhombus) the length of each side is

the same

(rhombus) the two diagonals are

perpendicular

(rhombus) the diagonals are angle

bisectors

squares have all the properties of

parallelograms, rectangles, and rhombi

area of a trapezoid:

A = 1/2 (b1 + b2)h

the measure of an inscribed angle of a circle is

1/2 the measure of its intercepted arc

the measure of the angle formed by 2 tangents drawn from the same point is

1/2 the difference of the two intercepted arcs

percentiles divide a set of data into

100 roughly equal groups

there are ... 4-digit integers

9000