Algebra Quiz
Questions: 16 · 10 minutes
1. A rectangle has width w and length w + 3. Its perimeter is 30. Which equation correctly models the situation?
w(w + 3) = 30, which models area
w + (w + 3) = 30, which counts only two sides
2w + 2(w + 3) = 30, which counts all four sides
2w(w + 3) = 30, which doubles the area expression
2. A taxi ride costs a $4 base fee plus $2 for each mile traveled. Which expression represents the total cost for m miles?
4m + 2
4 + 2m
6m
2(m + 4)
3. The numerator x² − 9 factors as (x − 3)(x + 3). For x ≠ 3, what remains after the common factor in (x² − 9)/(x − 3) is canceled?
x − 3, the factor that was canceled
x + 3, the uncanceled factor
x² − 6, obtained by subtracting the constants
The constant 1, obtained by canceling the entire numerator
4. Which option gives the complete factorization of x² + 5x + 6?
(x + 1)(x + 6), whose middle coefficient would be 7
(x − 2)(x − 3), which produces negative middle terms
(x + 2)(x + 3), whose factors multiply to 6 and add to 5
(x − 1)(x − 6), whose constant is positive but middle coefficient is negative
5. When 3 is distributed across x − 4, what result is obtained?
3x − 4, because only x is multiplied by 3
3x − 12, because both terms are multiplied by 3
3x + 12, because subtraction changes to addition
x − 12, because only the constant is multiplied by 3
6. If f(x) = 2x² − 1, what is f(3)?
5
11
35
17
7. In the term −7x, what is the coefficient of x?
The coefficient is −7.
The coefficient is positive 7.
The coefficient is the variable x.
The entire term −7x is the coefficient.
8. The arithmetic sequence 5, 9, 13, 17, … uses n = 1 for its first term. Which expression gives its nth term?
4n + 1
5n − 1
4n + 5
5n
9. Apply the product rule for exponents to x³ · x⁴.
x⁷, found by adding the exponents
2x⁷, found by adding an unnecessary coefficient
x, found by subtracting the exponents
x¹², found by multiplying the exponents
10. Solve the equation 2x + 5 = 17.
x = 6
x = 7
x = 11
x = 5
11. After solving −2x > 8 and accounting for division by a negative number, which inequality results?
x > −4, with the original inequality direction retained
x > 4, using a positive boundary value
x < 4, reversing the sign but using the wrong boundary
x < −4, reversing the inequality direction correctly
12. A line passes through (2, 3) and (6, 11). What is its slope?
A slope of −2, indicating a decreasing line
A slope of 1/2, from dividing the horizontal change by the vertical change
A slope of 2, from dividing the vertical change by the horizontal change
A slope of 8, using only the change in y
13. Which algebraic statement is an equation?
The expression 4x + 9
The equality 4x + 9 = 21
The inequality 4x + 9 > 21
The two-variable expression 4x + 9y
14. Which ordered pair solves both x + y = 10 and x − y = 2?
(4, 6)
(5, 5)
(8, 2)
(6, 4)
15. Where does the line y = −3x + 7 cross the y-axis?
At y = −7, the opposite of the constant term
At y = −3, the value of the slope
At y = 3, the opposite of the slope
At y = 7, the value of the constant term
16. Which pair consists of like terms?
3x and 3y
3x and 3x²
3x and −5x
3x and 3