Algebra II Finals Review

Radical Functions

100

Find the simplified square root of 500 

10 root 5 

200

Simplify (7 divided by the square root of 7) 

(Square root 7) / 1 

300

Cube root of (x¹¹y⁶z³⁰) 

x³y²z¹⁰ * Cube root (x²)

400

5 * square root 2 + 7 * square root 8 

19 root 2 

500

5 square root 2 - (2 square root 3 + 4 square root 8) 

- 3 square root 2 - 2 square root 3 

Logs / Exponentials

100

Log 10 

1 

200

Solve for x: 

3^x = 729

x = 6 

300

solve for x 

4^x = 1076

x = 5.036

(use power property and log both sides) 

400

Find the solution! 

log (3x + 4 ) = log (-71) 

X = -25 

TRICK  QUESTION - EXTRANEOUS SOLUTION 

500

solve for x: 

e^3x+5 = 47,000

x = 1.919

Simplify Rationals

100

(x²+4x+3) / (x+1)

STATE RESTRICTIONS

(x+3)

x cannot = -1

200

If X varies directly with Y, and x = 5 when

y = 1, what is the k value? 

k = 5

300

X varies jointly with Y and Z. When X = 20, Y = 2 and Z = 5 

What does x = when Y = 10 and Z = 25? 

Hint (Write equation then find k value)

K = 2 

X = 500 

400

((x+8) / (x²-64)) DIVIDED BY ((x-4) / (x² + x - 72))

INCLUDE RESTRICTED VALUES 

(x+9) / (x-4) 

x cannot = 4,8,-8,-9

500

(3/7x) + (2x/3x³)

(9x+14) / 21x²

Trigonometry

100

Find a positive and negative coterminal angle for 35 degrees 

395 and -325 (and many others) 

200

What is the reference angle for 113 degree? 

67 degrees 

300

What is the reference angle for 1521 degrees 

61 degrees (Must be positive) 

400

In a 45-45-90 triangle, if one of the legs is 19 inches, what are the other 2 side lengths? Draw a picture

In a 30-60-90 triangle, the shortest leg is 10 kilometers. How long are the other side lengths? 

19 inches & 19 * sqrt (2) inches. 

10 * Sqrt (3) kilometers and 20 kilometers 

500

For a right triangle with a hypotnuse length of 34 units and a leg length of 16 units: 

1. Draw the triangle 

2. Find the missing side length 

3. Find all 6 trig functions from either angle of your choice! 

x = 30 

ratios: 15/17, 8/17 and 8/15 (And their reciprocals) 

MISC / Word Problems

100

A farmer is standing 17 meters away from his Cilo. He is looking up at a 37 degree angle. How tall is his cilo?

HINT: Draw a picture!  

Hi Cilo is 12.81 meters high!

Tangent = x / 17 

200

A person skis down a slope and travels 450 meters in total. If the person covers 300 meters in horizontal distance: 

1. How much vertical feet did they drop? 

2. What is the angle of depression? 

335.41 meters vertical 

COS (angle) = 48.19 degrees is the angle of depression 

300

Draw the angle for -777 degrees

Answers will vary (Must be clockwise and in quadrant 4) 

400

A scientist is studying the growth of a certain type of bacteria in a petri dish. The number of bacteria grows continuously and can be modeled by the equation: y=A(e)^0.4t, where A is the initial amount and t is time in hours. At 1:00 PM, there are 700 bacteria in the dish.

Assuming the bacteria grows using the equation above, how many bacteria would be in the dish at 10:00 PM? 

25,618.76 Bacteria

500

Solve for x:

3/x - 1/2 = 12/x

x = -18