Algebra 2 Spring EOC Exam Review

Inverses

100

What is the inverse of f(x)=2x+3 ?

f^-1(x)=(x-3)/2

200

What is the inverse of  f(x)=x²-4 ?

f^-1(x) = sqrt(x+4)

300

What are the steps to find the inverse of a graph?

1. Identify two points

2. Switch x and y values

3. Graph new points and draw line

400

What is the inverse of f(x) = 3(x-2)² ?   

f^-1(x)= sqrt(x/3) + 2

500

What is the inverse operation of cubing something?

cube root

Logarithms

100

Expand the logarithm: log (2x/3)

(log 2 + log x) - log 3

200

Condense the logarithm: 3log 3 + 4 log x

log(3³x⁴)

300

Rewrite the log as an exponent: log₃x=123

3¹²³=x

400

Rewrite the exponent as a logarithm: m^w = 123

log_m 123 = w

500

What is the standard base for a logarithm?

10

Polynomials

100

Subtract the polynomials: (3x² + 4x - 7) - (12x² - 9x +1)

-9x² + 13x - 8

200

What is the degree of 6x⁴+9x²+12x⁶

6

300

Factor the quadratic: x²-2x-15

(x-5)(x+3)

400

Multiply the polynomials (3x³ - 2x² + 5x + 8)(2x+3)

6x⁴+5x³+4x²+31x+24

500

Factor: 2x³+6x² - 3x -9

(2x²-3)(x+3)

Complex Numbers

100

What is the squareroot of negative 1?

i

200

Add the complex numbers (3i-12) + (-9i +7)

-6i -5

300

Simplify squareroot of -48

4i sqrt(3)

400

Multiply the complex numbers (12i-8)(3i-7)

60i+20

500

Simplify i sqrt(-5)

- sqrt(5)

Trig

100

If the hypotenuse is 5, opposite is 4, and the adjacent is 3, what is tangent?

4/3

200

If the hypotenuse is 5, opposite is 4, and the adjacent is 3, what is secant?

5/3

300

What is the formula to get from polar coordinates to cartesian coordinates?

x = r cos (theta)

y = r sin (theta)

400

If I have two sides and need to find the angle, what do I do?

use inverse trig

500

What is the formula to go from cartesian to polar coordinates?

r = sqrt(x²+y²)

theta = tan^-1(y/x)