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 $3x - 7 > 2x + 5$?

Accepted Answer

$x > 12$

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

Study Guide - Practice Questions

Study Guide - Flashcards