Pre-Calculus Final Review

Trig

100

Write 210^o in radians.

7pie/6

200

Write 5pie/2 in degrees.

90^o

300

What is the exact value of cos(120^o)

-1/2

400

Find the exact value of tan(30^o)

sqrt(3)/3

500

What is the exact value of cot(240^o)

sqrt(3)/3

Conics

100

What type of conic is this?

x²+y²-4y+6x=1

Circle

200

What type of conic section is this?

x+3y²-4y+3x=0

Parabola

300

Write the standard form of a circle given the following:

Center:(-2,4)

Diameter: 6

(x+2)²+(y-4)²=9

400

Write the standard form of this parabola and label the vertex, focus, directrix, and axis of symmetry.

x²-18y+12x=126

(x+6)²=18(y+9)

Vertex:(-6,-9)

Focus:(-6,-4.5)

Directrix: y=-13.5

Symmetry: x=-6

500

Write this ellipse equation in standard form.

4x²+3y²+36y+60=0

x²/12 + (y+6)²/16 = 1

Matrices 1

100

Is this a square matrix?

[1   3

0   -3]

Yes

200

Add these matrices.

A=[3   2]

B=[5   -4]      

[8   -2]

300

Add the matrices.

A=  1   -2               B=  4     5    3

      0    -4                     -2    -1   0

Can not be added

Does not exist 

400

Use the information to determine the total amount of points scored by each player.

Rey: 44 FT, 32 2-pointers, and 25 3-pointers

Chris: 37 FT, 24 2-pointers, and 31 3-pointers

Jerry: 35 FT, 39 2-pointers, and 29 3-pointers

Rey: 183 points

Chris: 178 points

Jerry: 200 points

500

Solve the system of equations:

x+2y-3z=-28

3x-y+2z=3

-x+y-z=-5

(-4,-3,6)

Matrices 2

100

Simplify the matrix:

4A

A=[3,2]

[12,8]

200

Multiply:

AB

A=[1,3,4]

B=[-1

      -2

      1]

AB=[-3]

300

What is the determinant and inverse of matrix A?

A= 6   -5

     3     2

Det(A)=3

A^-1= -2/3     5/3

        -1         2

400

Find the determinant and inverse of matrix A:

A= 3   1   -2

     8   -5   2

     -4   3   -1

Det(A)=-11

A^-1=  1/11    5/11    8/11

         0           1          2

       -4/11     13/11    23/11

500

Determine if A and B are inverses of each other.

A=   12     -7

       -5       3

B=   3        7

       5       12

Yes

EXTRA

100

How many degrees and radians is a full circle?

360^o

2pie

200

What room are we in?

K-125

300

What day and time is your final?

Monday 5/21, second final, 10:21-12:16

400

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later.
What time is it now?

9 PM

500

A swimming pool has four faucets. The first can fill the entire pool with water in two days, the second - in three days, the third - in four days, and the last one can fill the pool in 6 hours.
How long will it take to fill the pool using all 4 faucets together?

Because there are 24 hours in one day, in one hour fills the first tap 1/48, the second tap 1/72, the third tap 1/96 and the fourth tap fills 1/6 of the reservoir. That is all together (6+4+3+48) / 288 = 61/288. The reservoir will be full in 288/61 hours, which is 4 hours 43 minutes and about 17 seconds.