Math Flashcards by Kathryn Baker

median

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

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mode

that appears the most

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factors/GCF

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

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multiples/LCM

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

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absolute value

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

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Proportion

A C
- = -
B D

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Special linear equations

X + 1 = consecutive integers

X + 2 = even/odd integers

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Product property of exponents

X^m • x^n = x^m+n

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

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Factoring polynomials

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

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Factoring with prime numbers

Carry over, multiply, factor, divide, carry over

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Arithmetic sequence formula

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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Arithmetic series formula

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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Geometric sequence formula

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

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Geometric series formula

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

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Combinations

-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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Permutations

-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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Matrices

Multiply/divide/add/subtract with corresponding number

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Quotient rule of exponents

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

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Power rule of exponents

(x^m)^n = x^mn

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Logarithmic functions

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

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Product property of logs

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

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Quotient property of logs

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

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Power property of logs

Log(b) M^x = x • log(b) M

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Change of base formula

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

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Discriminant

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

Parabola formula

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

Circle equation

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

Ellipse equation

[(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

Hyperbola equation

Same for ellipse except minus sign

360 equals what in radians? 180? 90?

2pi Pi Pi/2

Complementary angles

Add up to 90

Supplementary angles

Add up to 180

Congruent triangles/similar triangles

Same/proportional

Area

1/2bh

How are triangles proportional?

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

Triangular congruence

SAS SSS ASA CPCTC - corresponding parts of triangles are congruent

45:45:90

1:1:square root of 2 | Square root of 2 times side length

Isosceles: equal sides and...

Corresponding equal angles

30:60:90

1:square root of 3:2 | Twice as long as shortest side

Equilateral triangle height

Square root of 3 • 1/2s

Sum of angles for triangles | For quadrilaterals

180/360

Parallelogram

Opposite angles are equal

Rhombus

All 4 sides are same length

Square

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

Rectangle

4 right angles, parallelogram

Diagonal of square

S•square root of 2

Rhombus/parallelogram area

S times h

Area of trapezoid

1/2(b1 + b2)h

Diagonal for rectangle

Square root of l^2 + w^2

Chord

Line that connects two points on circumference

Sector

2 radii and arc | Area = pi • r^2 • angle/360

Arch length

Arc around sector | Pi • r • angle/180

Central angle

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

Line tangent to circle = what angle

Volume of cylinder, cone, sphere, and pyramids

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

Linear equation

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

Perpendicular/parallel

-reciprocal/same

Graphing inequalities

= dashed line | Anything else solid

Midpoint formula

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

Slope

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

Point slope and standard form

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

Distance

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

VLT/HLT

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.

Rational and radical expression

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

Quadratic equations and parabolas

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

Cosecant, secant, and cots gent

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

Table of Common Values

``` 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 ```

Trig identities

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)

Double angle identity

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

Law of Sines

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

Period

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

Graphing trig functions

Sin = cos(x-pi/2) | Cos, sin

Complex numbers

``` i^2 = -1 i^3 = -i i^4 = 1 I^5 = i ```

Axis of symmetry and how to find vertex

x = -b/2a | Use axis to find x, then plug x into equation

- 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

Polygons

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

Diagonals of polygon

N(n-3)/2

Interior angles

180(n-2)/n

Exterior angles

360/n or 180 - interior angle

Math Flashcards

(79 cards)