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56 Cards in this Set
- Front
- Back
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nth term of an arithmetic sequence
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an = a1 + (n-1)d
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sum of first n terms of an arithmetic sequence
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[n(a1 + an)]/2
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nth term of a geometric sequence
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bn = b1*r^(n-1)
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sum of first n terms in a geometric sequence
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b1[(1-r^n)/(1-r)]
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sum of an infinite geometric series - how do we know a series is infinite?
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b1/(1-r); a series is infinite when r is between -1 and 1
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i
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sqrt(-1)
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complex number form
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a +bi
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i^2
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-1
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i^3
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-i
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i^4
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1
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i^n
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divide n by 4; remainder is exponent of i you should use to solve
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permutation (nPr)
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n!/(n-r)!
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combination (nCr) (n/r)
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n!/[(n-r)!r!] or nPr/r!
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mean
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sum of elements in a set/number of elements in the set
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probability
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number of times a certain event might occur/number of events that might occur
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multiple event probability
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P(event A)*P(event B)
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total elements of overlapping sets
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total = group A + group B + neither group A nor B - A and B overlaps
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union
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contains all elements of two original sets: A U B
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intersection
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set of overlapping elements: A (upside down U) B; if x is an element of intersection of A and B, then x must be an element of both A and B
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arc length
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rtheta
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arc segment area
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(1/2)r^2theta
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y = A*f(Bx+C) - identify parts!
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A = amplitude
-C/B = phase shift normal frequency/B = period |
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equation of a circle - identify parts!
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(x-h)h^2 + (y-k)^2 = r^2
(h,k) = coordinates of the center, r = radius of the circle |
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equation of an ellipse - identify parts!
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(x-h)^2/a^2 + (y-k)^2/b^2 = 1 if C>A
(x-h)^2/b^2) + (y-k)^2/a^2 = 1 if C(h,k) = coordinates of center, major axis is parallel to x-axis/y-axis depending on direction |
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WHICH CONIC SECTION:
B^2 - 4AC < 0 and A=C B^2 - 4AC < 0 and A/=C B^2 - 4AC = 0 B^2 - 4AC > 0 |
circle
ellipse parabola hyperbola |
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equation of a parabola - identify parts!
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(x-h)^2 = 4p(y-k) if C = 0
(y-k)^2 = 4p(x-h) if A = 0 (h,k) - vertex, p - distance from vertex to focus |
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equation of a hyperbola - identify parts!
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(x-h)^2/a^2 - (y-k)^2/b^2 = 1 when graph opens to the side
(y-k)^2/a^2 - (x-h)^2/b^2 = 1 when graph opens up and down |
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degrees to radians
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multiply by pi/180
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radians to degrees
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multiply by 180/pi
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domain/range of sin
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all real numbers/-1
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domain/range of cosine
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all real numbers/-1
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domain/range of tangent
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undefined every 180 degrees (x=n(180)+90)/all real numbers
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period of sinx
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2pi
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period of cosx
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2pi
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period of tanx
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pi
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period of a trigonometric function
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regular period of function/b if f(bx) = y
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diagonal of a cube
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s(sqrt(3))
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diagonal of a rectangular solid
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sqrt(l^2+w^2+h^2)
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surface area of a cube
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6s^2
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surface area of a rectangular solid
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2lw+2lh+2wh
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surface area of a cylinder
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2pir^2 + 2pirh
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surface area of a sphere
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4pir^2
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surface area of a cone
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pir^2 + pirl
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volume of a cube
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s^3
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volume of a rectangular solid
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lwh
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volume of a prism
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Bh
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volume of a cylinder
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pir^2h
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volume of a cone
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1/3pir^2h
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volume of a pyramid
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1/3Bh
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volume of a sphere
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4pir^3/3
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rule of cube inscribed in cylinder
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diagonal of cube face = diameter of cylinder
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rule of cylinder inscribed in sphere
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diameter of sphere = diagonal of cylinder's height and diameter
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rule of sphere inscribed in cube
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diameter of sphere = length of cube's edge
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rule of sphere inscribed in cylinder
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radius of cylinder = radius of sphere
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3 things to know about the binomial theorem!
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there are n+1 terms in the expansion, sum of exponents per term is n, coefficient = nCx (n!/(n-x)!(x)!)(x = power to which variable is raised in nth term)
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sum of interior angles in a polygon
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180(n-2)
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