Algebra Problems

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Questions and Answers

Which of the following best describes the primary difference between algebra and arithmetic?

Algebra is limited to linear equations, while arithmetic handles all types of numerical problems.
Algebra deals with general relationships using variables, while arithmetic focuses on specific numerical calculations. (correct)
Arithmetic uses symbols, while algebra uses only numbers.
Arithmetic involves equations, while algebra involves only expressions.

In the expression $4x^2 + 7y - 9$, which term is the coefficient?

4 (correct)
x^2
y
7

What is the result of simplifying the expression $3(2x + 5) - 4x$?

$2x + 15$ (correct)
$2x + 5$
$10x + 5$
$10x + 15$

If $5x + 8 = 23$, what is the value of $x$?

3 (C) Signup and view all the answers

Which of the following equations is a linear equation?

$2x + 7 = 0$ (B) Signup and view all the answers

What is the solution set for the quadratic equation $x^2 - 5x + 6 = 0$?

{2, 3} (C) Signup and view all the answers

Using the quadratic formula, what is the solution for the equation $2x^2 + 5x - 3 = 0$?

{$1/2$, -3} (D) Signup and view all the answers

What is the value of $y$ in the following system of equations: $x + y = 5$ and $x - y = 1$?

2 (A) Signup and view all the answers

What is the solution to the inequality $3x - 2 < 7$?

$x < 3$ (D) Signup and view all the answers

Which of the following operations reverses the inequality sign when applied to both sides?

Dividing by a negative number (C) Signup and view all the answers

What is the solution set for the absolute value equation $|2x - 1| = 5$?

{-2, 3} (B) Signup and view all the answers

What is the solution to the absolute value inequality $|x + 3| < 2$?

$-5 < x < -1$ (B) Signup and view all the answers

Which of the following is a polynomial?

$4x^3 - x + 2$ (C) Signup and view all the answers

What is the degree of the polynomial $5x^4 - 3x^2 + 2x - 7$?

4 (D) Signup and view all the answers

What is the simplified form of the rational expression $\frac{x^2 - 4}{x + 2}$?

$x - 2$ (C) Signup and view all the answers

Simplify the expression: $\frac{a^5 \cdot a^{-2}}{a^2}$

$a$ (B) Signup and view all the answers

Simplify: $\sqrt{32}$

$4\sqrt{2}$ (B) Signup and view all the answers

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

10 (D) Signup and view all the answers

What is the domain of the function $f(x) = \frac{1}{x - 3}$?

All real numbers except $x = 3$ (A) Signup and view all the answers

How does the graph of $f(x) = x^2 + 3$ compare to the graph of $f(x) = x^2$?

Shifted 3 units upward (C) Signup and view all the answers

Flashcards

What is Algebra?

A branch of mathematics using symbols and rules to manipulate them.

What is a Variable?

A symbol representing a value that is unknown or can change.