Combining Like Terms Quiz
Questions: 16 · 10 minutes
1. Three supply orders contain 2q + 4, 5q - 1, and q + 6 items. How many items do the orders contain altogether?
8q + 9
8q + 11
7q + 9
7q + 10
2. The expression kx + 5x simplifies to 12x. What value must k have?
17, from adding 12 and 5
60, from multiplying 12 by 5
-7, from subtracting in the opposite order
7, because 7 + 5 equals 12
3. A student rewrites 3(2a - 5) - 2(a + 1) as 6a - 15 - 2a - 2. Which final result correctly completes the work?
4a - 13
4a - 7
8a - 17
4a - 17
4. After all like terms are collected in 4x - 2y + 3 - x + 5y - 7, what remains?
3x + 3y - 4
3x + 7y - 4
3x + 3y + 10
5x + 3y - 4
5. A student combines 6y² + 3y - 2y² + 5y. Which result shows that terms with matching variable parts were grouped correctly?
8y² + 6y, from combining adjacent terms
12y, from removing the exponents
12y², from treating every term as quadratic
4y² + 8y, from combining each type separately
6. During a multi-step problem, you reach -4t + 7 + 9t - 2. What is the correctly reduced expression?
5t + 9, after adding rather than subtracting the constants
13t + 5, after ignoring the negative sign on 4t
5t + 5, after combining the variable terms and constants separately
-5t + 5, after reversing the subtraction of the coefficients
7. What does (1/2)x + (3/4)x - 2 become when the fractional coefficients are combined?
(4/6)x - 2, found by adding numerators and denominators
(5/4)x - 2, found by using a common denominator
(3/8)x - 2, found by multiplying the fractions
(5/4)x + 2, found after incorrectly changing the constant's sign
8. Which expression has the same value as 5x + 2x - 3 for every value of x?
7x + 3, with the constant sign changed
10x - 3, with the coefficients multiplied
7x - 3, with the coefficients added
7x² - 3, with the exponent increased
9. When -3 is distributed through -3(2x - 4) + x and the x-terms are combined, which expression results?
-5x + 12, because distribution gives -6x + 12 before adding x
-5x - 12, from failing to reverse the sign of negative 4
-6x + 4, from distributing only to the variable term
-7x + 12, from combining -6x and x as though x were negative
10. Subtract the second polynomial from the first: (8b² - 3b + 4) - (2b² + b - 5). What is the result?
6b² - 2b - 1
10b² - 4b + 9
6b² - 4b + 9
6b² - 4b - 1
11. Which pair can be combined directly as like terms?
3x² and 3x
5x and 5y
7x² and -2x²
4 and 4m
12. While simplifying 2(3x + 4) + 5x - 1, which final expression should appear after distributing and combining terms?
11x + 3
11x + 7
6x + 12
10x + 7
13. A club counts three groups containing 2n + 3, n - 5, and 4n items. Which expression gives the combined total?
7n + 8, obtained by adding the constant magnitudes
7n - 8, obtained by treating both constants as negative
6n - 2, obtained by omitting one n-term
7n - 2, obtained by combining all variable and constant terms correctly
14. Simplify the expression 7a + 4 - 2a + 9.
9a + 13
5a + 13
5a + 5
14a
15. A rectangle has length 3x + 2 and width x + 5. Which expression represents its perimeter?
8x + 14
4x + 7
6x + 14
8x + 7
16. Why can 4p and 3p² not be combined into one term?
Their coefficients have different signs.
Their variable parts have different exponents.
Only constant terms may be combined.
Terms containing the same letter must be multiplied.