Practice Final Exam

12 114row

0) —2

/6

)-2-o) -2

/ -12)

Lf)

2.) Find the product ( 4)

/2.1+1.5(\J °O5&4)

“(-35o

(1—30

3.2+leO \—•o÷-’f).o) a-2o

-6+ON /7-6Nø*o)—2O o)

************************************************

Conics and other solutions of equations in two variables

3.) Give the ecluation for a line of slope 2 that passes through the origin.

4.) Give the equation for a line of slope 2 thatthe point (3,4).

Linear Algebra

1.) Give the vector written as a

(aN3O)

II

LI

2x

passes through

T2x(2(x-3)

3

5.) Give the equation for the unit circle.

—1

6.) Give the equation for the circle of radius 4 centered at the origin.

2 2

or

7.) Give the equation for the circle of radius 4 centered at the point (5, 7).

Oz a 2I1

7 L5

3

— 1

1 5 q

8.) Give the equation for the ellipse obtained by starting with the unitcircle, and then scaling the x-axis by 3, and the y-axis by 2.

F)

ci a)

9.) Give the equation for the ellipse from #8, shifted right by 4 and

2.upby5.-i-(R

Q317

rrsi3

10.) Draw the set of

11.) Draw the set of

12.) Draw the set of

13.) Draw the set of

14.) Draw the set of

1

15.) R_/4= 1 1

If H C 2 is the set of solutions of xy 1, then draw R_(H).

16.) Let P the set of solutions of y x2 from #13. Give the equationfor P shifted right by 2 and up by 3.

z

I

_

7

of the

of the

of the

of the

of the

equation xy = 1.

equation x2—

= 1.

equation y2 — 1.

equation y x2.

equation x = y2.

solutions

solutions

solutions

solutions

solutions

1

is the rotation of the plane by angle —.

3

2

Trigonometry

17.) What is the distance between the points (2, 5) and (3, 8)?

(3Z z

— 7282

For #21-29, graph cos(x), sin(x), tan(x), sec(x), csc(x), cot(x), arccos(x),arcsin(x), and arctan(x).

30.) What’s arccos (k)? COS (‘

31.) What’s arcsin(—1)? Sn (-)32.) What’s arctan(—1)?

1

arccos()

=-L aYcSiYi(...))

(23)Z

C

8

18.) Find the length of the unlabeled side of the triangle below.

71I3

c=flTh’19.) Find sin(O), cos(O), and tan(6) for the angle 6 given below. (3 points.)

srn(e)D _—

3tci(G) _

20.) What’s the Pythagorean Identity? os()Z

i(e’ I

5

Lf

t(-)sb1(-)

cos&) -z acton(-)

iViatch the functions with their graphs.

33.) sin(x)A 34.) sin (x + 35.) sin(2x) I36.) sin () 37.) sin(x) + 1 38.) sin(x) — 1 D39.) cos(x) 40.) sin (x

—41.) 2sin(x)C

42.) sin(x))_( 43.) —sin(x)E 44.) sin(—x)E

A

_B____

-7t -T

______

I I

G) H.) I.)

-2

-r

T-2

Match the functions with their graphs.

45.) f(x)

A.)

Jsin(x)

cos(x)

A.

if x E (—oo,O);

if x E [0,oo).

B.)

f cos(x)

sin(x)

if x (—oo,0);

if xE [O,oo).

47.) Find (2 + i3) + (4 + i5).

(24+ (3i.5) ÷iS48.) Find (2 + i3)(1 + i4)

(2+i3(4i 2(t)zj+3.

2÷i8÷3i2IZ

I (+49.) Whats the norm of 7 + i3.

Ij23•Lf

—iOIfl

I7I3l50.) Find 2(cos(3) +isin(3))4(cos(8) +isin(8)).

. 8(cos(II)+isi(Ii))

46.) g(x) =

C0S(t)

%

; (x);00,

Complex numbers

51.) Draw an X on your answer sheet on the number 3 ( cos () +i sin () ) z.(The number z is drawn on the answer sheet.)

52.) Find (+4)

So (± . (co5()+())“

CoS()+jsi., : ;‘53.) Find (+)

— ‘i.,‘ 2

Equations in one variable

Write the solutions of the following trigonometric equations.

54.) tan(x) —4

55.) cos(x)

56.) cos(x) = 7

57.) sin(x) =

58.) sin(x) = —2

See the answer sheet for #59-64.

Cl) z

z7

pP

C N) N

I)

Tj

Cl) z CD

I)

I)

N

ocN

I)

Ii11

1)

+

NII

/4

(p3’) (x-z)2************************************************

cos(e): n(O)::

21.) cos(x) 22.) sin(x) 23.) tan(x)

24.) sec(x) 25.) csc(x) 26.) cot(x)

15.)

4I

17.)r1

18.)

19.)

16.)

20.) cos (Z÷

2

I NM

2

I’

—I

-2

‘7W 21 /

I —I

-2-2

23

N 2

-ir-—l

-2

2

-7r2

VFfl\ir

41.)

42.)

___________________

43.)

A 44.)

45.)

I 46.)

____________________

47.)

B 48.)

0

____

49.)

EC—

A

13

4 ÷iS

—)04

-r150.) s (cos(ii)+s;(tnL

28.) arcsill(x)27.) arccos(x)

N

29.) arctan(x)

I

2

7

2.

—if

2.

—if

-

a

H

E

30.)

31.)

32.)

33.)

34.)

35.)

36.)

37.)

38.)

39.)

40.)

52.)

54.)

-i

acctov(Lt)+wir, n

/

ss.)x_accosQj)÷fl2?r, fl€

For the remaining questions, #59-64, give the solutions of the equations.If there is no solution, explain why there is no solution. For at least one ofthe remaining problems, the domain of the equation will play an important

51.) ct

x3(cos ()tj5))

1fo-tt’ts ‘y 2

L

53.)

56.) hO SOiL4f,Oyi

c&’rcsw(.i+ 2r,

or/2.\

57.)X4fc5bq (3)(n2t1ir /

58.) flO 5Olut3n

role in the solution.

o4-

I,

v’

1--

t40

At

V

iiN

SE‘0

1(c’

II

°•k

:1

-.

-I’

Lfl

1%N

Hv

I’

0A

—4

cY

Ii—

—U

+çF

______I

II

0cc

1-—

IT

T+

‘0

—0

___

+

Cc)

0o

cc—

cco

LCD

4I’

—+

—0

-

ii, S II

‘1

\V\v

oI II

0 -0

1’III

r ci EL