math GRE

Question 0

Product of Polynomial Roots

Answer 0

(-1)^n a_0/n

Question 1

Sum of Polynomial Roots

Answer 1

(-a_n-1)/(a_n)

Question 2

Root Location Theorem

Answer 2

For real Polynomial p(x) where a,b exist st p(a)<0 and p(b)>0, then there exists a<x<b st p(x) = 0

Question 3

Rational Roots Theorem

Answer 3

If p(x)=0 has any rational roots, then they must be of the form x=s/t where s is a factor of the constant and t is a factor of the leading coefficient

Question 4

Complex Radical Roots Theorem

Answer 4

If p(x) has a root of the form x = s + tsqrt(u) where u is not a perfect square, then the conjugate is also a root

Question 5

Complex Conjugate Roots Theorem

Answer 5

If a complex number is a root, it’s conjugate must be as well

Question 6

Change of Base Formula

Answer 6

Log_b(a) * log_a(x) = log_b(x)

Question 7

Tan(a+b)

Answer 7

(tana + tanb) / (1 - tanatanb)

Question 8

Tan(a-b)

Answer 8

(Tana - tanb)/(1 + tanatanb)

Question 9

Sin2x

Answer 9

2sinxcosx

Question 10

Cos2x

Answer 10

Cos^2x - sin^2x

Question 11

Tan2x

Answer 11

(2tanx) / (1-tan^2x)

Question 12

Focus of a Parabola

Answer 12

p where y=1/(4p) * x^2

Question 13

Area of an Ellipse

Answer 13

Piab where x^2/a^2 + y^2/b^2 = 1

Question 14

Inverse function rule

Answer 14

Derivative of the inverse of f is one over derivative of f

Question 15

D(Tanx)

Answer 15

Sec^2 x

Question 16

D(cot x)

Answer 16

-csc^2 x

Question 17

d(secx)

Answer 17

Secxtanx

Question 18

D(cscx)

Answer 18

-cscxcotx

Question 19

d(arcsin)

Answer 19

1/sqrt(1-x^2)

Question 20

d(arc tan)

Answer 20

1/(1+x^2)

Question 21

Dot Product

Answer 21

AdotB = ABcostheta

Question 22

Cross Product

Answer 22

ABsintheta

Question 23

Find the vector perpendicular to the plane created by vectors A and B

Answer 23

Take the cross product

Question 24

Find the volume of the parallelepiped created by A B and C.

Answer 24

Triple Scalar product, (AxB)dotC= det(a,b,c)