Quiz about Algebra 2 Honors Final Review 2025 Day 3-5

Question 1

Multiply and divide rational expressions. Simplify: 1. (4x + 6) / (2x + 3)

Accepted Answer

2

Answer

4x

Answer

x + 3

Answer

2x + 3

Question 2

Multiply and divide rational expressions. Simplify: 2. $$\frac{3x^2 - 12}{x^2 - x - 6}$$

Accepted Answer

3(x + 2)/(x - 3)

Answer

$$\frac{3x - 12}{x^2 - x - 6}$$

Answer

(x + 2)/(x - 3)

Answer

3(x - 2)/(x + 3)

Question 3

Multiply and divide rational expressions. Simplify: 3. $$\frac{x^2 + 13x + 40}{x^2 - 2x - 35}$$

Accepted Answer

(x + 8)/(x - 7)

Answer

(x + 5)/(x - 5)

Answer

(x + 10)/(x - 7)

Answer

(x + 8)/(x + 5)

Question 4

Simplify: $$\frac{3}{8x^3y^3} - \frac{1}{4xy}$$ Write your answer in simplest form.

Accepted Answer

$$\frac{3-2x^2y^2}{8x^3y^3}$$

Answer

$$\frac{3-2xy}{8x^3y^3}$$

Answer

$$\frac{3-2x^2y^2}{4x^3y^3}$$

Answer

$$\frac{3-2x^2y^2}{8xy}$$

Question 5

Simplify: $$\frac{y}{4y+8} - \frac{1}{y^2+2y}$$ Write your answer in simplest form.

Accepted Answer

$$\frac{y^2-4}{4y(y+2)}$$

Answer

$$\frac{y^2+4}{4y(y+2)}$$

Answer

$$\frac{y^2-4}{y(y+2)}$$

Answer

$$\frac{y^2-4}{4y^2+8y}$$

Question 6

Simplify: $$\frac{2}{x} + 6 \div \frac{1}{y}$$ Write your answer in simplest form.

Accepted Answer

$$\frac{2}{x} + 6y$$

Answer

$$\frac{2}{x} + \frac{6}{y}$$

Answer

$$\frac{2y}{x} + 6$$

Answer

$$\frac{2}{x} + \frac{1}{6y}$$

Question 7

Solve the equation: $$\frac{1}{x+4} = 5$$ Write your answer in simplest form.

Accepted Answer

$$x = -\frac{4}{5}$$

Answer

$ x = 5 $

Answer

$ x = 1 $

Answer

$ x = -9 $

Question 8

Solve the equation: $$\frac{1}{x-3} = 6$$ Write your answer in simplest form.

Accepted Answer

$$x = \frac{19}{6}$$

Answer

$$x = \frac{6}{19}$$

Answer

$$x = \frac{3}{6}$$

Answer

$$x = \frac{1}{6}$$

Question 9

Solve the equation: $$\frac{1}{x+2} = 5$$ Write your answer in simplest form.

Accepted Answer

x = $$-\frac{9}{5}$$

Answer

x = $$\frac{1}{5}$$

Answer

x = 3

Answer

x = -7

Question 10

Solve the equation: $$\frac{1}{2x-3} = \frac{1}{5-2x}$$ Write your answer in simplest form.

Accepted Answer

No solution (the denominators are negatives of each other, so the equation is never true).

Answer

x = 2

Answer

x = 1

Answer

x = 0

Question 11

Solve the equation: $$2 - \frac{1}{x+3} = \frac{1}{x+3}$$ Write your answer in simplest form.

Accepted Answer

x = -3 (but this makes the denominators zero, so no solution)

Answer

x = 0

Answer

x = 1

Answer

x = -2

Question 12

Solve the equation: $$\frac{2}{x-3} = \frac{3}{x}$$ Write your answer in simplest form.

Accepted Answer

x = 6

Answer

x = 0

Answer

x = -3

Answer

x = 3

Question 13

Solve the equation: $$\frac{1}{x+3} + \frac{1}{x-3} = \frac{6}{x^2-9}$$ Write your answer in simplest form.

Accepted Answer

$ x = 0 $

Answer

$ x = 3 $

Answer

$ x = -3 $

Answer

$ x = 6 $

Question 14

Solve the equation: $$\frac{4}{x+2} = \frac{x^2}{x+2}$$ Write your answer in simplest form.

Accepted Answer

x = 2

Answer

x = -2

Answer

x = 4

Answer

x = 0

Question 15

Solve the equation: $$\frac{x^2}{x+10} = \frac{100}{x+10}$$ Write your answer in simplest form.

Accepted Answer

x = 10

Answer

x = -10

Answer

x = 0

Answer

x = 5

Question 16

What are the real cube roots of 125?

Accepted Answer

5

Answer

-5

Answer

0

Answer

25

Question 17

What is the value of $$121^{(3/2)}$$ ?

Accepted Answer

1331

Answer

121

Answer

242

Answer

11

Question 18

What are the values of each expression? Round to the nearest hundredth. 5. What is the value of $$-(64)^{\frac{2}{3}}$$ ?

Accepted Answer

-16

Answer

16

Answer

-8

Answer

8

Question 19

Use composition to determine whether f and g are inverse functions. f(x) = (1/5)x - 3, g(x) = 5x + 15

Accepted Answer

Yes, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = x; g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = x. So, they are inverses.

Answer

No, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = x; but g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = 2x, so they are not inverses.

Answer

No, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = 2x; g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = x, so they are not inverses.

Answer

No, f(g(x)) = (1/5)(5x+15) - 3 = x + 3 - 3 = x; g(f(x)) = 5((1/5)x - 3) + 15 = x - 15 + 15 = 0, so they are not inverses.

Question 20

Write each equation in logarithmic form: c. $$36^{1/6} = 6$$

Accepted Answer

log_{36} 6 = 1/6

Answer

log_{6} 36 = 1/6

Answer

log_{6} 1/6 = 36

Answer

log_{1/6} 36 = 6

Question 21

Solve: 2log x = log(5x - 6)

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 3

Answer

x = 6

Question 22

In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student plays a sport given that they play an instrument? Write your answer as a fraction.

Accepted Answer

3/14

Answer

2/7

Answer

5/14

Answer

1/2

Question 23

What is the probability of drawing an ace from a standard deck of 52 cards?

Accepted Answer

4/52 or 1/13

Answer

1/52

Answer

1/4

Answer

13/52

Question 24

What is the probability that a student does not play on a sports team given they play an instrument?

Accepted Answer

3/11

Answer

5/11

Answer

8/11

Answer

1/3

Question 25

A basketball player has a 75% free throw success rate. If she takes 8 free throws in a game, what is the expected number of successful free throws?

Accepted Answer

6

Answer

4

Answer

8

Answer

5

Question 26

A coin is flipped 12 times. What is the expected number of heads?

Accepted Answer

6

Answer

5

Answer

8

Answer

4

Question 27

A bag contains 3 red balls and 2 blue balls. If two balls are drawn one after the other without replacement, what is the probability that both balls are red?

Accepted Answer

3/10

Answer

1/5

Answer

2/5

Answer

1/2

Question 28

A box contains 5 red, 4 green, and 3 blue marbles. If one marble is drawn at random, what is the probability that it is either red or green?

Accepted Answer

3/4

Answer

2/3

Answer

1/2

Answer

5/12

Algebra 2 Honors Final Review 2025 Day 3-5

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