Praxis 5161 Review – Flashcards
101 test answers
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Permutation Clue Words
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Arrangement, schedule, order.
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Combination Clue Words
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Group, committee, set and sample.
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Combination
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Order does not matter!
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Permutation
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Order matters!
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Parabola
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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
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Circle
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r² =(x-h)²+(y-k)² -A circle is the locus of points equidistant from a center point. -Center:(h,k) -Radius:r
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Ellipse
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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.
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Hyperbola
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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
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Completing the Square (conic sections)
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x² -8x+_+y² +6y+_+24=0 x² -8x+16+y²+6y+9=-24+16+9 (x-4)²+(y+3)²=1
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locus
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the set of all points or lines that satisfy or are determined by specific conditions
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Rule for an arithmetic sequence
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an = a? + ( n - 1 )( d )
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Sum of a finite arithmetic sequence
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Sn = ( n ( a? + an ) ) / 2
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Rule for the nth term of a geometric sequence
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an = a?r^n-1
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Sum of the first n terms of a geometric series
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Sn = a? ( ( 1 - r^n ) / ( 1 - r ) )
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Sum of infinite geometric series with first term a? and a common ratio r (only when |r|<1)
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S = a? / ( 1 - r )
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1
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sin²x + cos²x
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sec²x
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tan²x + 1
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csc²x
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cot²x + 1
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tan x
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(sin x) / (cos x)
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cot x
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(cos x) / (sin x)
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csc x
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1 / sin x
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sec x
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1 / cos x
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cot x
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1 / tan x
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-sin x
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sin (-x)
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cos x
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cos (-x)
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-tan x
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tan (-x)
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sin 2x
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2 sin x cos x
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cos 2x
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cos²x - sin²x
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cos 2x
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2cos²x - 1
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cos 2x
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1 - 2sin²x
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tan 2x
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(2 tan x) / (1 - tan²x)
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sin (x + y)
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sin x cos y + sin y cos x
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sin (x - y)
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sin x cos y - sin y cos x
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cos (x + y)
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cos x cos y - sin x sin y
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cos (x - y)
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cos x cos y + sin x sin y
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tan (x + y)
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(tan x + tan y) / (1 - tan x tan y)
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tan (x - y)
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(tan x - tan y) / (1 + tan x tan y)
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sin²x
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(1 - cos 2x) / 2
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cos²x
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(1 + cos 2x) / 2
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tan²x
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(1 - cos 2x) / (1 + cos 2x)
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2?2
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a = ?
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4
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b = ?
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12
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a = ?
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6?3
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b = ?
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7
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a = ?
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8?2
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a = ?
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6
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a = ?
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6?3
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b = ?
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8
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a = ?
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10
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a = ?
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5?3
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b = ?
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8?3
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x = ?
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16
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y = ?
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(8?3)/3
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x = ?
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(16?3)/3
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y = ?
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28
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x = ?
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8?3
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y = ?
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3?3
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y = ?
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24
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x = ?
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12?3
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y = ?
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? du
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u +C
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? u^n du
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u^(n+1)/(n+1) +C
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? du/u
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ln|u| +C
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? e^u du
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e^u +C
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? a^u du
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(1/lna)a^u +C
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? sin u du
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-cos u +C
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? cos u du
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sin u +C
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? tan u du
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-ln|cos u| +C
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? cot u du
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ln|sin u| +C
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? sec u du
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ln|sec u + tan u| +C
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? csc u du
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-ln|csc u + cot u| +C
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? sec^2 u du
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tan u +C
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? csc^2 u du
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-cot u +C
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? sec u tan u du
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sec u +C
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? csc u cot u du
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-csc u +C
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? du/((a^2 - u^2)^(1/2))
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arcsin u/a +C
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? du/(a^2 + u^2)
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(1/a)arctan u/a +C
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? du/(u(a^2 - u^2)^(1/2))
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(1/a)arcsec |u|/a +C
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d/dx: sin(x)
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cos(x)
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d/dx: cos(x)
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-sin(x)
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d/dx: tan(x)
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sec^2(x)
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d/dx: sec(x)
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tan(x)sec(x)
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d/dx: csc(x)
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-cot(x)csc(x)
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d/dx: cot(x)
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-csc^2(x)
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d/dx: sin^-1(x)
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1/(sqrt(1-x^2))
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d/dx: cos^-1(x)
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-1/(sqrt(1-x^2))
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d/dx: tan^-1(x)
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1/(1+x^2)
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d/dx: sec^-1(x)
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1/(abs(x)sqrt(x^2-1))
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d/dx: cot^-1(x)
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-1/(x^2+1)
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d/dx: csc^-1(x)
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-1/(abs(x)sqrt(x^2-1))
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d/dx: e^u
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(e^u)(du/dx)
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d/du: a^u
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(a^u)(ln(a))(u')
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d/du: ln(u)
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u'/u
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d/du: loga(u)
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u'/(ulna)
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lim(x-;0) sin(x)/x
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1
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lim(x-;inf) (1 + 1/n)^n
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e
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lim(x-;0) (1+n) ^(1/n)
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e
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