Logarithms
Series and Sequences
Conic Sections
Polar coordinates
Vectors
100
Rewrite 3x=8 in logarithmic form
Log38 = x
100
What is the algebraic formula for the nth term of the sequence
4, 12, 20, 28 ....
an= 8n - 4
100
What type of conic section is
r = 4/(3-5sinθ)
Hyperbola
100
Convert (0, -2) in (x, y) to polar coordinates
(2, 3pi/2)
100
What is the dot product of 4i + 2j + 3k and i - 2k ?
-2
200
Simplify Ln e5
5
200
What is the algebraic formula for the nth term of the sequence
20, 10 ,5, 2.5, 1.25 ....
an=20(0.5)n-1
200
For an ellipse, the formula to determine c is
c2=a2- b2
200
What is another set of coordinates for (6, pi/6)
(6, -11pi/6) or (-6, 7pi/6) or (-6, -5pi/6)
200
What is the magnitude of 3i-j + 2k ?
√14
300
Rewite as a logarithm of a single quantity
Log x + 2Log (3+x)
Log x(3+x)2
300
What type of sequence is
-7, -4, -1, 2, 5, 8 ....
arithmetic
300
Eccentricity =
c / a
300
What quadrant is the polar coordinate point (-6, -5pi/4) in?
4th
300
How do you determine that 2 vectors are orthogonal?
Their dot product is zero.
400
Solve: Log 4x = 2
25
400
What is the sum of the first 50 terms of the sequence
3, 9, 15, 21, 27 ....
7,500
400
What is the equation for the ellipse with
center (0, 2) vertex (0, 8) and
minor axis endpoint (4, 2)
x2/16 + (y-2)2/36 = 1
400
Convert (6, pi/3) to (x, y)
(3, 3√3)
400
The parametric equations for a line through
pointt (1, 5, 6) and parallel to vector <4, 8, -3> is
x = 1 + 4t,
y = 5 + 8t,
z = 6 - 3t
500
2ex+1=14
ex+1=7
ln ex+1=ln 7
x +1 = ln 7
x = ln 7 - 1
x = 0.9459101491
500
What is the sum of the infinite series
24, 6, 1.5, 0.375, 0.9375....
32
500
What is the equation of the ellipse (in standard rectangular form)
with center at (4, 0), vertex at (10,0)
and focus at (8,0)?
(x-4)2/36 + y2/20 = 1
500
What is the equation of the directrix for the polar equation
r = 3/(2+sinθ)
y = 3
500
What is the equation of the plane that passes through
point (4, 6, -1) and is parallel to 6x-2y+z=4
6x - 2y + z - 11 = 0
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