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Formulas Flashcards

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SAT® Prep flashcards
1
Q

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

A

|Ax1 + By1 + C| / √(A^2 + B^2)

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2
Q

If θ is the angle between two lines, tanθ =

A

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

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3
Q

sum of roots of a quadratic equation =

A

-b/a

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4
Q

product of roots of a quadratic equation =

A

c/a

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5
Q

Area of a triangle ABC is

A

1/2bc * sinA

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6
Q

(Pythagorean identities) sin²x + cos²x =

A

1

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7
Q

(Pythagorean identities) sec²x =

A

tan²x + 1

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8
Q

(Pythagorean identities) csc²x =

A

cot²x + 1

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9
Q

(Double-angle formulas) sin2A =

A

2sinAcosA

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10
Q

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

A

cos²A - sin²A

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11
Q

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

A

2cos²A - 1

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12
Q

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

A

1 - 2sin²A

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13
Q

(double-angle formulas) tan2A =

A

2tanA/ (1-tan²A)

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14
Q

if x≥0, then |x| =

A

x

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15
Q

if x

A

-x

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16
Q

[x] =

A

I, where I is an integer and I≤ x

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17
Q

(polar coordinates) x =

A

rcosθ

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18
Q

(polar coordinates) y =

A

rsinθ

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19
Q

(polar coordinates) r² =

A

x² + y²

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20
Q

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

A

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

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21
Q

volume of a cylinder

A

πr²h

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22
Q

lateral surface area of a cylinder =

A

2πrh

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23
Q

total surface area of a cylinder =

A

2πrh + 2πr²

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24
Q

volume of a cone

A

1/3 * πr²h

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25
Q

lateral surface area of a cone

A

πr√(r² + h²)

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26
Q

total surface area of a cone

A

πr√(r² + h²) + πr²

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27
Q

volume of a sphere

A

4/3 * πr³

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28
Q

surface area of a sphere

A

4πr²

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29
Q

nCr = (n/r)=

note: n/r is not actually a fraction

A

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

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30
Q

(arithmetic sequence) nth term =

A

tn = t1 + (n - 1)d

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31
Q

(arithmetic sequence) sum of n terms =

A

Sn= n/2 * (t1 + tn)

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32
Q

(geometric sequence) nth term =

A

tn= t1 * r^(n-1)

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33
Q

(geometric sequence) sum of n terms =

A

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

34
Q

(geometric sequence) if |r|

A

lim as n→∞ of Sn = t1/ 1 - r

35
Q

cofunctions of complementary angles are

A

equal

36
Q

cofunction pairs:

A

sin & cos, sec & csc, tan & cot

37
Q

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

A

y-intercept

38
Q

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 ….

A

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

39
Q

to find the inverse of a graph,

A

fold the graph about the line y = x

40
Q

even function proof:

A

f(-x) = f(x)

41
Q

odd function proof:

A

f(-x) = -f(x)

42
Q

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

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

43
Q

volume of a prism:

A

V = Bh

44
Q

surface area of a prism:

A

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

45
Q

surface area of a rectangular solid:

A

SA = 2lw + 2lh + 2wh

46
Q

surface area of a cube:

A

SA = 6s^2

47
Q

volume of a pyramid:

A

V= 1/3 Bh

48
Q

surface area of a pyramid:

A

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

49
Q

diagonal of a rectangular solid:

A

D= √(l² + w² + h²)

50
Q

length of diagonal of a cube:

A

e√3, where e is side length

51
Q

|x| = b→

A

x = b or x = -b

52
Q

|x|

A

-b

53
Q

|x| > b→

A

x b

54
Q

first few primes:

A

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

55
Q

if ad > bc, then

A

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

56
Q

is/ of =

A

% / 100

57
Q

(x - y)(x + y) =

A

x² - y²

58
Q

(x - y)² =

A

x² - 2xy + y²

59
Q

(x + y)² =

A

x² + 2xy + y²

60
Q

(for triangles) a² + b²

A

obtuse

61
Q

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

A

acute

62
Q

area of equilateral triangle with side s,

A

A = (s²√3) / 4

63
Q

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

A

k²

64
Q

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

A

360 degrees

65
Q

(parallelograms) opposite sides are

A

parallel and congruent

66
Q

(parallelograms) opposite angles are

A

congruent

67
Q

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

A

180 degrees

68
Q

(parallelograms) a diagonal divides the parallelogram into

A

two congruent triangles

69
Q

(parallelograms) the two diagonals

A

bisect each other

70
Q

(rectangles) has all the properties of

A

parallelograms

71
Q

(rectangles) the diagonals of a rectangle have the same

A

length

72
Q

(rhombus) has all the properties of

A

parallelograms

73
Q

(rhombus) the length of each side is

A

the same

74
Q

(rhombus) the two diagonals are

A

perpendicular

75
Q

(rhombus) the diagonals are angle

A

bisectors

76
Q

squares have all the properties of

A

parallelograms, rectangles, and rhombi

77
Q

area of a trapezoid:

A

A = 1/2 (b1 + b2)h

78
Q

the measure of an inscribed angle of a circle is

A

1/2 the measure of its intercepted arc

79
Q

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

A

1/2 the difference of the two intercepted arcs

80
Q

percentiles divide a set of data into

A

100 roughly equal groups

81
Q

there are … 4-digit integers

A

9000

SAT & subject tests (30 decks)

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