Second Semester Final Exam Review (Algebra II Trig)

Exponentials and Logarithms (Ch 6)

200

Evaluate log(1/100)

-2

300

Expand completely: ln(5x³/y⁴)

ln5+3lnx-4lny

400

Solve log₃(5x+9)=3

18/5

500

Solve: 16^x+2=8^x-1

-11

Trigonometry (Ch 9)

200

Determine the period AND amplitude of 

y=5sin(4x)

Period: pi/2

Amplitude: 5

300

Give the exact value of sin (300) degrees.

-sqr(3)/2

400

Give the exact value tan(2pi/3)

- sqr(3)

500

A 20 foot ladder is placed against a wall at an angle of 72 degrees with the ground. How far from the base of the wall is the bottom of the ladder? Leave answers EXACT (no calculators)

20cos(72)

Rational Exponents and Radicals (Ch 5)

200

Rationalize:

6/sqrt(3)

2sqrt(3)

300

Simplify completely:

a) 16^3/4

b) (x³)^-3(3x)³

a)8

b)27/x³

400

Find the inverse of f(x)=4x³-2

cuberoot((x+2)/4)

500

Solve. Check for Extraneous solutions!

Sqr(x)=x-2

4 only (1 is extraneous)

Transformations, Factoring and Graphing Polynomials (Ch 4)

200

Graph the transformed the function. Identity the domain and range.

f(x)=sqr(x+7)-5

graph is radical that goes left 7 and down 5. 

Domain: [-7,infinity)

Range: [-5, infinity)

300

Factor and solve 5x² + 8x - 4=0

(5x-2)(x+2), 2/5, -2

400

Solve and graph, keeping multiplicity and end behavior in mind. 5x⁴-45x²=0

0 m2, 3 m1, -3 m1 (teacher draws graph on board)

500

Use the rational root theorem to solve. Write your answers with multiplicity. 

x³-5x²+3x+9

-1 m1, 3 m2