Trig Equations
Polar and Probability
Matrices
Conics
Sequences
100
Solve give the general solution:
2cos^2x-cosx=0
x={+-pi/3+2pin,+-pi/2+2pin}
100
How many petals does the following rose graph have?
r = 2sin3theta
3
100
What are the dimensions of the following matrix?
3 x 2
100
What type of conic section is this?
Ellipse
100
Write an explicit formula for the following sequence:
2, 6, 18, 54, ...
a_n=2(3)^(n-1)
200
Solve for the general solution:
4sin^2x=3
x={pi/3+2pin, (2pi)/3+2pin, (4pi)/3+2pin, (5pi)/3+2pin}
200
What is the name of this type of polar graph?
limacon
200
If A is an invertible 3x3 matrix, then
A A^-1 =
[[100],[010],[001]]
200
What number must be added to complete the square?
x^2+3x
9/4
200
Find the 20th term of the sequence:
50, 45, 40, 35, ...
-45
300
Solve for the given domain of
[0,2pi]
2csc^2x-3cscx-2=0
x={pi/6, (5pi)/6}
300
What is the polar form of this equation?
x^2+y^2=3
r^2=3
300
What is the determinant of matrix C?
-16
300
In which direction does this parabola open?
y^2=6x
right
300
What is the coefficient of the term containing
a^6
in the expansion of
(a+3b)^10?
17010
400
Solve for the domain of
[-pi,pi]
cos(2x)=cosx
x={-2pi/3, 0, (2pi)/3}
400
There are 10 different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast?
720
400
lim_(x->2) 1/(x-2)^2
oo
400
Write the equation of this hyperbola:
x^2/16-y^2/9=1
400
What is the sum of the series?
sum_(n=1)^oo 2(1/3)^(n-1)
3
500
Solve for the given domain:
(-pi,pi)
1-cos x=-sin x
x={-pi/2, 0}
500
What is the probability that the first three cards you draw out of a standard deck are all aces? Give the answer as a percent with 2 significant digits.
0.00018%
500
What is the inverse of matrix B?
[[2/5 -1/5], [3/10 1/10]]
500
What are the coordinates of the foci for this ellipse?
(0, 2sqrt5)
(0, -2sqrt5)
500
Find the sum of the first 100 terms of an arithmetic series if the first 3 terms of the series are 1, 4, 7.
14,950