Algebra 2 Final Review

Radicals and Rational Exponents

100

What equation is equivalent to P = 210 x^4/3y^7/3?

1) P = ∛210x⁴y⁷

2) P =70xy² ∛xy

3) P = 210xy²∛xy

4) P = 210xy²∛x³y⁵

3) P = 210xy²∛xy

200

Given y >0, the expression  √3x²y  ⋅  ∛27x³y² is equivalent to: 

1) 81x⁵y³

2) 3^1.5x²y

3) 3^5/2x²y^5/3

4) 3^3/2x²y^7/6

4) 3^3/2x²y^7/6

300

The product of (3 + √5) ( 3 - √5) is:

1) 4 - 6√5

2) 14 - 6√5

3) 14

4) 4

4) 4

400

Rationalize: 3 / 2√6

(1√6) / 4

500

Given x >0, the expression x^1/5 / x^1/2 can be rewritten as:

1) ∛x

2)-¹⁰√x³

3) 1 / ¹⁰√x³

4) ∛x¹⁰

3) 1 / ¹⁰√x³

Logarithms and Exponential Equations

100

Given p does not equal q, p= (1/2)^q, expressed in logarithmic form, is equivalent to: 

1) log_p(1/2) = q

2) log_q(p) = 1/2

3) log_1/2(p) = q

4)  log_1/2(q) = p

3) log_1/2(p) = q

200

Which expression is not a solution to the equation

2^t = √10?

1) 1/2 log₂10

2) log₂√10

3) log₄10

4) log₁₀4

4) log₁₀4

300

Solve 3.8e^1.5t = 16 algebraically for t to the nearest hundredth.

t = 0.96

400

Which expression is not equivalent to log_b36? 

1) 6log_b2

2) log_b9 + log_b4

3) 2log_b6

4) log_b72- log_b2

1) 6log_b2

500

If L = x²/ k, then logL is equal to:

1) 2log (x/k)

2) 2(logx - logk)

3) 2logx - logk

4) (2logx) / logk 

3) 2logx - logk

Trigonometric Functions

100

Expressed as a function of a positive acute angle, cot (-120)° is equivalent to:

1) -tan60°

2) cot60°

3) -cot30°

4) cot30°

2) cot60°

200

Which expression is equivalent to sin(-120°)?

1) sin60°

2) -sin60°

3) cos30°

4) -cos60°

2) -sin60°

300

The exact value of sin (8π/3) is:

1) 1/2

2) -1/2

3) - √3/2

4) √3/2

4) √3/2

400

As θ increases from -π/2 to 0 radians, the value of cosθ will:

1) decrease from 1 to 0

2) decrease from 0 to -1

3) increase from -1 to 0 

4) increase from 0 to 1

4) increase from 0 to 1 

500

Given tan θ =-4/3 where π/2 < θ< π, what is the value of sec θ?

1) -5/3

2) -3/5

3) 4/5

4) 5/3

1) -5/3

More Trig!

100

Which quadrants are where sin is negative? 

Quadrant III and quadrant IV

200

Given cos θ = 7/25, where is an angle in standard position terminating in quadrant IV, sin²θ  + cos²θ  = 1, what is the value of tan θ?

1) -24/25

2) -24/7

3) 24/25

4) 24/7

2) -24/7

300

If cos θ = -3/4 and θ is in Quadrant III, then sin θ  is equivalent to:

1) -√7/4

2) √7/4

3) -5/4

4) 5/4

1) -√7/4

400

If θ is an angle in standard position whose terminal side passes through the point (-2, -3), what is the numerical value of tan θ?

1) 2/3

2) 3/2

3) -2/√13

4) -3/√13

2) 3/2

500

Given sin θ =7/25 and θ terminates in Quadrant II, what is the value of tan θ?

1) -7/24

2) -24/7

3) 7/24

4) 24/7

1) -7/24