Algebra II/Trig Review ;)

CHAPTER 6

100

Which expression is equivalent to 125^-1/3 

A. -5 

B. 1/5 

C. -1/5

D. 5

B, 1/5

200

Simplify 12/(2-√3)

12√3 + 24

300

Find the domain of f(x) if f(x) = √(2x+5)

{x | x ≥ -5/2} 

400

Find the inverse of f(x) = (x+12)/7

f^-1(x) = 7x-12

500

Given f(x) = 2x²+4x-3 and g(x) = 5x-2, find f(g(x))

f(g(x)) = 50x²-20x-3

CHAPTER 7

100

Write log₉(27) = 3/2 in exponential form.

9^3/2 = 27

200

Solve for x: 

4^3x-1 = 16^x

X = 1

300

What exponential function has a graph that passes through (0,125) and (3,1000)?

f(x) = 125(2)^x

400

What is the solution of: 

log₄(16) - log₄(x) = log₄(8)

X = 2

500

Write 2 ln(6) + 3 ln(4) - 5 ln(1/3) as a single logarithm

ln ((6²*4³)/(1/3)⁵) or ln (559,872)

CHAPTER 8

100

What is the LCM of x²-x and 3-3x?

-3x(x-1)

200

State the domain and range of f(x) = -5/(x-2) + 2

D: {x | x≠2}

R: {f(x) | f(x) ≠ -2}

300

If r ≠± 2, what is (r²+6r+8)/(r²-4) in its most simplified form? 

(r+4)/(r-2)

400

Determine the equation(s) of any vertical asymptotes and the values of x for any holes in the graph of: 

f(x) = (x²-9)/(x²-5x-24)

X = 8; hole at x = -3

500

Simplify: 

2/(x²-3x-10) - 6/(x²-8x+15)

(-4x-18)/(x-5)(x+2)(x-3)

CHAPTER 12

100

Write the degree measure in radians: 

215˚

(43π)/36

200

Find the exact value of Cos (3π/4)

-√2/2

300

Find the amplitude and period of y = 1/2 cos (2Ø)

A: 1/2

P: 180˚

400

What angle has a tangent and sine that are BOTH NEGATIVE?

A. 65˚

B. 120˚

C. 265˚

D. 310˚

D, 310˚

500

Find csc (Ø) when the terminal side of Ø in standard position contains the point (6,8)

10/8

CHAPTER 0

100

Permutation or combination? 

Choosing 3 people to each receive a “no homework” coupon. 

Combination

200

How many different ways can two students be assigned to five tutors if only one student is assigned to each tutor? 

20

300

If the occurrence of a first event does affect the probability of a second event occurring, then the events are? (Dependent or independent)

DEPENDENT 

400

There are 1400 students at a school. If 550 take Spanish, 700 take Biology, and 400 take both Spanish and biology, what is the probability that a randomly selected student takes Spanish or Biology? 

17/28

500

At a restaurant, 25% of customers order a hamburger. If 4% of customers order a hamburger AND a hotdog, find the probability that someone who orders a hamburger also orders a hotdog. 

16%, P(B|A) = P(A and B) / P(A)