question

Combination

answer

Each choice or subset of r objects gives one ________. Order within the group does not matter.

question

Permutation

answer

Different orderings or arrangements of the r objects are different ________.

question

Combination Formula

answer

n!/(n-r)!r!

question

Permutation Formula

answer

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

question

Permutation Clue Words

answer

Arrangement, schedule, order.

question

Combination Clue Words

answer

Group, committee, set and sample.

question

Combination

answer

Order does not matter!

question

Permutation

answer

Order matters!

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Parabola

answer

Vertical: y-k=a*(x-h)² Horizontal: x-h=a*(y-k)² -A parabola is the locus of points equidistant from a point and a line. -Vertex:(h,k) Horizontal Parabola is not a function

question

Circle

answer

r² =(x-h)²+(y-k)² -A circle is the locus of points equidistant from a center point. -Center:(h,k) -Radius:r

question

Ellipse

answer

An ellipse is the locus of points around the two foci. The sum of the distances is constant. Standard form:(x-h)²/a²+(y-k)²/b²=1 c²=|a²-b²| Center:(h,k) Foci lie inside the rectangle, c units from the center.

question

Hyperbola

answer

A hyperbola is a locus of points around two foci. The difference of the distance is constant. Standard form:(x-h)²/a²-(y-k)²/b²=1 c²=a²+b² Center:(h,k) Foci lie outside the rectangle, c units from the center

question

Completing the Square (conic sections)

answer

x² -8x+_+y² +6y+_+24=0 x² -8x+16+y²+6y+9=-24+16+9 (x-4)²+(y+3)²=1

question

locus

answer

the set of all points or lines that satisfy or are determined by specific conditions

question

Rule for an arithmetic sequence

answer

an = a? + ( n - 1 )( d )

question

Sum of a finite arithmetic sequence

answer

Sn = ( n ( a? + an ) ) / 2

question

Rule for the nth term of a geometric sequence

answer

an = a?r^n-1

question

Sum of the first n terms of a geometric series

answer

Sn = a? ( ( 1 - r^n ) / ( 1 - r ) )

question

Sum of infinite geometric series with first term a? and a common ratio r (only when |r|<1)

answer

S = a? / ( 1 - r )

question

1

answer

sin²x + cos²x

question

sec²x

answer

tan²x + 1

question

csc²x

answer

cot²x + 1

question

tan x

answer

(sin x) / (cos x)

question

cot x

answer

(cos x) / (sin x)

question

csc x

answer

1 / sin x

question

sec x

answer

1 / cos x

question

cot x

answer

1 / tan x

question

-sin x

answer

sin (-x)

question

cos x

answer

cos (-x)

question

-tan x

answer

tan (-x)

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sin 2x

answer

2 sin x cos x

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cos 2x

answer

cos²x - sin²x

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cos 2x

answer

2cos²x - 1

question

cos 2x

answer

1 - 2sin²x

question

tan 2x

answer

(2 tan x) / (1 - tan²x)

question

sin (x + y)

answer

sin x cos y + sin y cos x

question

sin (x - y)

answer

sin x cos y - sin y cos x

question

cos (x + y)

answer

cos x cos y - sin x sin y

question

cos (x - y)

answer

cos x cos y + sin x sin y

question

tan (x + y)

answer

(tan x + tan y) / (1 - tan x tan y)

question

tan (x - y)

answer

(tan x - tan y) / (1 + tan x tan y)

question

sin²x

answer

(1 - cos 2x) / 2

question

cos²x

answer

(1 + cos 2x) / 2

question

tan²x

answer

(1 - cos 2x) / (1 + cos 2x)

question

2?2

answer

a = ?

question

4

answer

b = ?

question

12

answer

a = ?

question

6?3

answer

b = ?

question

7

answer

a = ?

question

8?2

answer

a = ?

question

6

answer

a = ?

question

6?3

answer

b = ?

question

8

answer

a = ?

question

10

answer

a = ?

question

5?3

answer

b = ?

question

8?3

answer

x = ?

question

16

answer

y = ?

question

(8?3)/3

answer

x = ?

question

(16?3)/3

answer

y = ?

question

28

answer

x = ?

question

8?3

answer

y = ?

question

3?3

answer

y = ?

question

24

answer

x = ?

question

12?3

answer

y = ?

question

? du

answer

u +C

question

? u^n du

answer

u^(n+1)/(n+1) +C

question

? du/u

answer

ln|u| +C

question

? e^u du

answer

e^u +C

question

? a^u du

answer

(1/lna)a^u +C

question

? sin u du

answer

-cos u +C

question

? cos u du

answer

sin u +C

question

? tan u du

answer

-ln|cos u| +C

question

? cot u du

answer

ln|sin u| +C

question

? sec u du

answer

ln|sec u + tan u| +C

question

? csc u du

answer

-ln|csc u + cot u| +C

question

? sec^2 u du

answer

tan u +C

question

? csc^2 u du

answer

-cot u +C

question

? sec u tan u du

answer

sec u +C

question

? csc u cot u du

answer

-csc u +C

question

? du/((a^2 - u^2)^(1/2))

answer

arcsin u/a +C

question

? du/(a^2 + u^2)

answer

(1/a)arctan u/a +C

question

? du/(u(a^2 - u^2)^(1/2))

answer

(1/a)arcsec |u|/a +C

question

d/dx: sin(x)

answer

cos(x)

question

d/dx: cos(x)

answer

-sin(x)

question

d/dx: tan(x)

answer

sec^2(x)

question

d/dx: sec(x)

answer

tan(x)sec(x)

question

d/dx: csc(x)

answer

-cot(x)csc(x)

question

d/dx: cot(x)

answer

-csc^2(x)

question

d/dx: sin^-1(x)

answer

1/(sqrt(1-x^2))

question

d/dx: cos^-1(x)

answer

-1/(sqrt(1-x^2))

question

d/dx: tan^-1(x)

answer

1/(1+x^2)

question

d/dx: sec^-1(x)

answer

1/(abs(x)sqrt(x^2-1))

question

d/dx: cot^-1(x)

answer

-1/(x^2+1)

question

d/dx: csc^-1(x)

answer

-1/(abs(x)sqrt(x^2-1))

question

d/dx: e^u

answer

(e^u)(du/dx)

question

d/du: a^u

answer

(a^u)(ln(a))(u')

question

d/du: ln(u)

answer

u'/u

question

d/du: loga(u)

answer

u'/(ulna)

question

lim(x-;0) sin(x)/x

answer

1

question

lim(x-;inf) (1 + 1/n)^n

answer

e

question

lim(x-;0) (1+n) ^(1/n)

answer

e

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