study for shaun final

Question 1

descartes’ law of signs

Answer 1

replace x with 1. number of sign switches between terms is max number of positive real roots, other options are that number -2 down to zero. replace x with 1, number of sign switches is max number of negative real roots, -2 down to zero

Question 2

vieta’s formula for sum of roots

Answer 2

-(an-1)/an or -b/a

Question 3

vieta’s formula for product of roots

Answer 3

(-1)^n * a0/an or c/a

Question 4

heron’s formula

Answer 4

sqrt(s(s-a)(s-b)(s-c))

Question 5

eccentricity of ellipse

Answer 5

major axis / focal distance – higher number for flatter ellipse, 0<x<1

Question 6

area formula with sine

Answer 6

1/2 * absinC

Question 7

eccentricity of parabola

Answer 7

1– equal distance from focus and directrix

Question 8

eccentricity of hyperbola

Answer 8

focal length / major axis, x>1

Question 9

eccentricity of circle

Question 10

finding the foci of an ellipse

Answer 10

focal distance = sqrt(major axis^2 - minor axis^2)

Question 11

finding the foci of a hyperbola

Answer 11

focal distance = sqrt(major axis^2 + minor axis^2)

Question 12

sum of arithmetic sequence

Answer 12

(a1 + an) * n / 2

Question 13

sum of geometric sequence

Answer 13

a1 * (1 - r^n) / (1 - r)

Question 14

infinite geometric series

Answer 14

a1 / (1-r)

Question 15

an of arithmetic sequence

Answer 15

a1 + d*n

Question 16

an of geometric sequence

Answer 16

a1 * r^n

Question 17

pythagorean identities

Answer 17

sin^2 + cos^2 = 1

Question 18

sine addition

Answer 18

sin(a + b) = sinacosb + cosasinb

Question 19

cosine addition

Answer 19

cos(a + b) = cosacosb - sinasinb

Question 20

equation of parabola in focus/directrix form

Answer 20

(x-h)^2 = 4p(y-k) – p is distance between vertex and focus or vertex and directrix