Question 1

Which of the following best describes the solution set for a quadratic equation $$ax^2 + bx + c = 0$ where a$$ 
eq 0$$?

Accepted Answer

It may have two real solutions, one real solution, or two complex solutions depending on the discriminant $$b^2 - 4ac$.

Question 2

A system of equations is given by $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}. $$What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 3

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x + 3)(x - 3)$$

Question 4

If $$f(x) = 2x^2$ - 5x + 3$$, what is $$f(4)$$?

Accepted Answer

$$f(4) = 11$$

Question 5

Which of the following is the solution to the inequality $$3x - 7 \u003e 2x + 5$$?

Accepted Answer

$$x \u003e 12$$

Question 6

A student is solving the equation $$\frac{2x - 4}{x + 3} = 0. $$What is the solution?

Accepted Answer

$$x = 2$$

Question 7

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x - 2}$$?

Accepted Answer

$$x 
eq 2$$

Question 8

If the graph of $$y = x^2$ is shifted up by 5 units, what is the new equation?

Accepted Answer

$$y = x^2$ + 5$$

Question 9

Which of the following is the solution to the system $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 2)$$

Question 10

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the initial height of the ball?

Accepted Answer

$$1.5$$ meters

Question 11

Which of the following is the correct solution for $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 12

Which of the following is the correct solution to the equation $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 13

A chemical reaction is modeled by the exponential function $$N(t) = N_0$ e$$^{-kt}$$. If N_0$ = 100$$ and $$k = 0.2$$, what is $$N(5)$$?

Accepted Answer

$$N(5) = 100 e$$^{-1}$$

Question 14

Which of the following is the correct inverse of the function $$f(x) = 3x + 2$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 2}{3}$$

Question 15

A population grows according to $$P(t) = 500 \cdot 2^t. $$What is the population after 3 years?

Accepted Answer

$$P(3) = 4000$$

Question 16

Which of the following is the correct solution to $$\log_2$ x = 5$$?

Accepted Answer

$$x = 32$$

Question 17

If $$g(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 18

Which of the following is the correct solution to the equation $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 19

A medical dosage is modeled by $$D(t) = 50e$$^{-0.1t}$$. What is the dosage after 10 hours?

Accepted Answer

$$D(10) = 50e$$^{-1}$$

Algebra II Syllabus Overview and Course Structure

Guida di studio - Domande di pratica

Study guide - Flashcard