Transcript Exam Review

Exam
Review
Chapters 7-13
Q1.
Expand:
4
(2 - 3y)
A1.
16 – 96y + 216y2 - 216y3 + 81y4
Q2.
ix x)
Find the coefficient
6
10
of a in (5 – 3a) .
A2.
95,681,250
Q3.
th
8
Find the
term
in the expansion
15
of (2x – 3) .
A3.
8
-3,602,776,320x
Q4.
State the
Law of Sines.
A4.
sinα = sinβ = sin γ
a
b
c
Q5.
State the
Law of Cosines.
A5.
a² = b² + c² - 2bccosα
Q6.
State the
Pythagorean
Identity.
A6.
cos²θ + sin²θ = 1
Q7.
A vector is a
quantity with
? and ?.
A7.
magnitude
and
direction
Q8.
A vector with a
magnitude of
one is called a
?.
A8.
unit vector
Q9.
A vector whose
initial point is
at the origin is
called a ?.
A9.
position vector
Q10.
If v = ai + bj,
then a and b
are called the
?.
A10.
components
Q11.
The set of all
points equidistant
from a point and a
line is called a(n)
?.
A11.
parabola
Q12.
The set of all points
such that the sum of
the distances from
two fixed points is a
constant is called
a(n) ?.
A12.
ellipse
Q13.
The set of all points
such that the
difference of the
distances from two
fixed points is a
constant is called a(n)
?.
A13.
hyperbola
Q14.
The line
associated
with a parabola
is called the ?.
A14.
directrix
Q15.
The two fixed
points of an
ellipse or
hyperbola are
called ?.
A15.
foci
Q16.
Which conic
has transverse
and conjugate
axes?
A16.
hyperbola
Q17.
What equation
will help you
find the foci for
a hyperbola?
A17.
b² = c² - a²
Q18.
Identify the conic:
7 y  8 x  24 xy
2
2
4 5 x  2 5 y  15  0
A18.
hyperbola
Q19.
A rectangular
array of
numbers is
called a(n) ?
A19.
matrix
Q20.
A triangular
display of
binomial
coefficients is
called ?
A20.
Pascal’s Triangle
Q21.
What are the dimensions
of the following matrix?
3
 1
 
 0 
A21.
3x1
Q22.
Write I3.
A22.
1 0 0 


0
1
0


0 0 1 
Q23.
A sequence is a
function whose ?
is the set of
positive integers.
A23.
domain
Q24.
A sequence whose
difference
between
successive terms
is a constant is ?.
A24.
arithmetic
Q25.
A sequence whose
ratio between
successive terms
is a constant is ?.
A25.
geometric
Q26.
Evaluate:
 11 
 
9
 
A26.
55
Q27.
A vector with a
magnitude of
zero is called a
?.
A27.
zero vector
Q28.
Evaluate:
a.) p(0)
b.) lim p(s)
x→0
A28.
a.) 0
b.) DNE
Q29.
Evaluate:
a.) G(2)
b.) lim G(x)
x→2
A29.
a.) 3
b.) 1
Q30.
Name another
polar
coordinate for
(-2, -π/3)
A30.
(-2, 5π/3)
(2, 2π/3)
(2, -4π/3)
Q31.
Convert to polar
coordinates:
(-4, 0)
A31.
(4, π)
(4, 180˚)
Q32.
Convert to
rectangular
coordinates:
(-2, 5π/6)
A32.
(√3, -1)
Q33.
Write the
rectangular form
of the equation:
r = 4sinθ
A33.
x² + (y-2)² = 4
Q34.
How many
petals does
r = 3cos5θ?
A34.
5
Q35.
In which
quadrant does
-1 – 5i fall?
A35.
III quadrant
Q36.
Identify the
graph:
r = 4 – 5cosθ
A36.
limaçon with
inner loop
Q37.
In which quadrant
does the point with
polar coordinates of
(-3,2π/3) fall?
A38.
IV quadrant
Q39.
Simplify:
2
cos 62˚
+
2
sin 62˚
A39.
1
Q40.
What is the length of
the hypotenuse in the
right triangle below?
43˚
7
A40.
10.26
Q41.
Find a:
14
38˚
8
a
A41.
no such triangle
Q42.
If v · w = 0, then
the two vectors
v and w are ?.
A42.
orthogonal
Q43.
If v x u = 2i + j – 3k,
then u x v =
A43.
-2i – j + 3k
Q44.
The following is the
standard equation
for which conic?
( y  2) ( x  1)

1
4
7
2
2
A44.
hyperbola
Q45.
Solve:
6x – 4y = 20
4x + y = 6
A45.
(2, -2)
Q46.
Solve:
x² – y = 4
2x + y = -1
A46.
(-3, 5)
(1, -3)
Q47.
Solve:
x+y+z=3
x-z=1
y – z = -4
A47.
(3, -2, 2)
Q48.
Solve:
x – √5y = 2.7
3.4x + 2y = 6.1
A48.
(1.983, -.321)
Q49.
Evaluate:
1
0
5
7
2 1
4 3
2 0
3 4
2
4
2
3
A49.
0
Q50.
Evaluate:
 6




k


k 8
11
A50.
-2.56
Q51.
Evaluate:
x 1
lim
x 1 x  1
4
A51.
4
Q52.
Evaluate:
lim  3 x  6
1/3
x 7
A52.
3