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