Adv. Math Sem 1

Exponents

100

Simplify:

8⁰

1

200

Simplify:

4^3/2  +   3^-3

8/27

300

Simplify:

(3^-3 + 9^-2)/(3^-3)

1 and 1/3

400

Solve: 

2^6-x = 4^2+x

x = 2/3

500

Solve:

3sqrt(27) = 9^2x

x = 5/4

Logarithms

100

Rewrite as a logarithm:

2³ = 8

log₂8 = 3

200

Find the exact value of:

log₈2

1/3

300

Find the exact value of:

2^log4(64)

8

400

Expand:

log_bM²N³

2log_bM + 3log_bN

500

Solve:

log₅x + log₅(x-4) = 1

x = 4.24

x = -.24

Circles and Ellipses

100

Where is the center of the circle?

(x - 2)² + y² = 9

(2, 0)

200

What is the radius of the circle?

(x - 2)² + y² = 9

3

300

Find the equation of the circle where the endpoints of the diameter are at (2,5) and (-2,-1).

x² + (y-2)² = 3.6²​​​​

400

Write the equation of the circle in standard form:

4x² + 4y² - 8x + 24y + 15 = 0

(x-1)² + (y+3)² = 25

500

Find where the line and the ellipse intersect:

2x + 3y = 6

4x² + 9y² = 36

(0,2)

(3,0)

Trig

100

Convert 5pi/6 radians to degrees.

150 degrees

200

Convert 186 degrees to radians

3.25 radians

300

Find the exact value of:

cos (-90 degrees)

0

400

Find the exact value of:

tan (120 degrees)

-sqrt3

500

Find the exact value of:

sec(Cos^-1(-3/5))

-5/3