Exam Review Chapters 7-13. Q1. Expand: (2 - 3y) 4.
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Transcript of Exam Review Chapters 7-13. Q1. Expand: (2 - 3y) 4.
Exam
Review
Chapters 7-13
Q1.
Expand:
(2 - 3y)4
A1.
16 – 96y + 216y2 - 216y3 + 81y4
Q2.
Find the coefficient of a6 in (5 – 3a)10.
ix x)
A2.
95,681,250
Q3.
Find the 8th term in the expansion
of (2x – 3)15.
A3.
-3,602,776,320x8
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:
2 27 8 24
4 5 2 5 15 0
y x xy
x y
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.
3 x 1
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: cos262˚ + sin262˚
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?
2 2( 2) ( 1)1
4 7y x
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 = 3x - z = 1y – z = -4
A47.
(3, -2, 2)
Q48.
Solve:
x – √5y = 2.7
3.4x + 2y = 6.1
A48.
(1.983, -.321)
Q49.
Evaluate:1 2 1 2
0 4 3 4
5 2 0 2
7 3 4 3
A49.
0
Q50.
Evaluate: 11
8
6
k k
A50.
-2.56
Q51.
Evaluate:
4
1
1
1limx
x
x
A51.
4
Q52.
Evaluate:
1/37
lim 3 6x
x
A52.
3