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Math Flashcards

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1
Q

median

A

middle # of a series if odd, take average of two middle digits if even

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2
Q

mode

A

that appears the most

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3
Q

factors/GCF

A

71 = 2^3 x 3^3 - GCF between two #s is the repeated factors in each number

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4
Q

multiples/LCM

A

9, 18, 27, 36, etc. LCM = take factors of each number, multiple the greatest number of each factor

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5
Q

absolute value

A

can NEVER equal a negative number, |x-7| = both -5 and 5, if inequality, change sign AND -/+

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6
Q

Proportion

A

A C
- = -
B D

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7
Q

Special linear equations

A

X + 1 = consecutive integers

X + 2 = even/odd integers

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8
Q

Product property of exponents

A

X^m • x^n = x^m+n

Ex) (3m^5)(-4m^3) = -12m^8

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9
Q

Factoring polynomials

A

If c is negative, then signs will be different. If c is positive, then signs will be the same.

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10
Q

Factoring with prime numbers

A

Carry over, multiply, factor, divide, carry over

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11
Q

Arithmetic sequence formula

A 
A(n) = a(1) + (n-1)d
Where...
A(n) is nth term
A(1) is first term
N is number of terms
D is common difference
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12
Q

Arithmetic series formula

A 
S(n) = n/2(a(1) + a(n))
Where...
S(n) is sum of sequence
N is number of terms
A(1) is first term
A(n) is nth term
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13
Q

Geometric sequence formula

A

A(n) = a(1) • r^(n-1)
Where…
R is common ratio

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14
Q

Geometric series formula

A

S(n) = [a(1)(1-r^n)]/1-r

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15
Q

Combinations

A 
-order doesn't matter
nCr = [n!]/[r!(n-r)!]
Where...
R is number you're selecting
N is total number of choice
Ex) 15 children in class, 5 needed for chores, possible combos
-Calculator: 15, MATH, PRB, 3: nCr, 5
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16
Q

Permutations

A

-order does matter
nPr = [n!]/[(n-r)!]
-Ex) 10 horses running, possible combos for 1st, 2nd, and 3rd
Calculator: 2 instead of 3

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17
Q

Matrices

A

Multiply/divide/add/subtract with corresponding number

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18
Q

Quotient rule of exponents

A

X^m/x^n = x^(m-n)

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19
Q

Power rule of exponents

A

(x^m)^n = x^mn

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20
Q

Logarithmic functions

A

If b^x = y, then log(b)Y = x

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21
Q

Product property of logs

A

Log(b)MN = log(b) M + log(b) N

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22
Q

Quotient property of logs

A

Log(b) M/N = log(b) M - log(b) N

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23
Q

Power property of logs

A

Log(b) M^x = x • log(b) M

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24
Q

Change of base formula

A

Log(b) M = log(c) M / log(c) b

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25
Q

Discriminant

A

B^2 - 4ac
If 0, 1 real solution
If negative, non-real.
If positive, 2 real.

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26
Q

Parabola formula

A

Y=a(x-h)^2+k
Where…
(H,k) = vertex
A determines orientation and width

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27
Q

Circle equation

A

(X-h)^2 + (y-k)^2=r^2
(H,k) is center point
R is radius

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28
Q

Ellipse equation

A

[(x-h)^2]/a^2 + (y-k)^2/b^2 = 1
(H,k) center point equidistant from extremes on x and y
A is distance from center on x
B is distance from center on y

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29
Q

Hyperbola equation

A

Same for ellipse except minus sign

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30
Q

360 equals what in radians?
180?
90?

A

2pi
Pi
Pi/2

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31
Q

Complementary angles

A

Add up to 90

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32
Q

Supplementary angles

A

Add up to 180

33
Q

Congruent triangles/similar triangles

A

Same/proportional

34
Q

Area

A

1/2bh

35
Q

How are triangles proportional?

A

Shortest side = shortest angle
Same length = sam angle
Longest side = longest angle

36
Q

Triangular congruence

A

SAS
SSS
ASA
CPCTC - corresponding parts of triangles are congruent

37
Q

45:45:90

A

1:1:square root of 2

Square root of 2 times side length

38
Q

Isosceles: equal sides and…

A

Corresponding equal angles

39
Q

30:60:90

A

1:square root of 3:2

Twice as long as shortest side

40
Q

Equilateral triangle height

A

Square root of 3 • 1/2s

41
Q

Sum of angles for triangles

For quadrilaterals

A

180/360

42
Q

Parallelogram

A

Opposite angles are equal

43
Q

Rhombus

A

All 4 sides are same length

44
Q

Square

A

4 right angles and 4 congruent sides (rectangle, rhombus, and parallelogram)

45
Q

Rectangle

A

4 right angles, parallelogram

46
Q

Diagonal of square

A

S•square root of 2

47
Q

Rhombus/parallelogram area

A

S times h

48
Q

Area of trapezoid

A

1/2(b1 + b2)h

49
Q

Diagonal for rectangle

A

Square root of l^2 + w^2

50
Q

Chord

A

Line that connects two points on circumference

51
Q

Sector

A

2 radii and arc

Area = pi • r^2 • angle/360

52
Q

Arch length

A

Arc around sector

Pi • r • angle/180

53
Q

Central angle

A

Angle between 2 radii
Arc measure same as central angle
Arc measure/2 = inscribed angle

54
Q

Line tangent to circle = what angle

A

90

55
Q

Volume of cylinder, cone, sphere, and pyramids

A

Cy: pi•r^2h
Co: 1/3•pi•r^2h
Sphere: 4/3•pi•r^3
Pyramids: 1/3bh

56
Q

Linear equation

A

Y=mx+b
B is y intercept
M is slope

57
Q

Perpendicular/parallel

A

-reciprocal/same

58
Q

Graphing inequalities

A

= dashed line

Anything else solid

59
Q

Midpoint formula

A

(X+x/2,y+y/2)

60
Q

Slope

A

-\ +/
Y=2 (-)
X=2 (|)
Formula: y-y/x-x

61
Q

Point slope and standard form

A

Y-y(1) = m(x-x(1))
Finding y intercept
Ax+By = C

62
Q

Distance

A

Square root of (x(1)-x(2))^2 + [y(1)-y(2)]^2

63
Q

VLT/HLT

A

If a vertical line intersects the graph twice, then it is not a function. If a horizontal line intersects the graph twice, then the inverse is not a function.

64
Q

Rational and radical expression

A

Can be written as a fraction
Contains radicals/roots
Can only multiply radicals with same degree

65
Q

Quadratic equations and parabolas

A

If parabola is completely above the line, no solutions
If parabola is on the x axis, one solution
If parabola crosses x axis with both arms, 2 solutions

66
Q

Cosecant, secant, and cots gent

A
  1. Reciprocal of sin (h/o)
  2. Reciprocal of cos (h/a)
  3. Reciprocal of tan (a/o)
67
Q

Table of Common Values

A 
Radian 0 pi/6 pi/4 pi/3 pi/2
Angle 0   30   45   60   90
Sin     0  1/2 (2)/2 (3)/2  1
Cos    0 (3)/2 (2)/2 1/2   0
Tan     0 (3)/3   1    (3)  undefined
68
Q

Trig identities

A

Sin^2(x) + cos^2(x) = 1
Divide by cos^2(x): tan^2(x) + 1 = sec^2(x)
Divide by sin^2(x): cot^2(x) + 1 = csc^2(x)

69
Q

Double angle identity

A

Sin(2x) = 2sin(x)cos(x)

70
Q

Law of Sines

A

A/sin(a) = B/sin(b) = C/sin(c)

71
Q

Period

A
  • The distance along the x axis that it takes for the function to repeat itself (2pi)
  • 2pi/b
72
Q

Graphing trig functions

A

Sin = cos(x-pi/2)

Cos, sin

73
Q

Complex numbers

A 
i^2 = -1
i^3 = -i
i^4 = 1
I^5 = i
74
Q

Axis of symmetry and how to find vertex

A

x = -b/2a

Use axis to find x, then plug x into equation

75
Q

SA

A
  • area of the sides of the box
  • cylindrical surface area: 2•pi•r(h+r)
  • rectangular SA: 2(lw + lh + wh)
  • LSA: SA without the bases
  • spherical SA: 4•pi•r^2
76
Q

Polygons

A

Straight lines, enclosed area, regular is all sides the same

77
Q

Diagonals of polygon

A

N(n-3)/2

78
Q

Interior angles

A

180(n-2)/n

79
Q

Exterior angles

A

360/n or 180 - interior angle

ACT (2 decks)

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