Grade 6: Expressions and Equations — Quiz

Multiple Choice

1. What does it mean for two expressions to be "equivalent"?
A) They both contain the same variable
B) They name the same number regardless of which value is substituted into them
C) They have the same number of terms
D) They both use addition

2. In the expression 2(8 + 7), how is (8 + 7) described?
A) A coefficient
B) A single entity and a sum of two terms
C) A quotient
D) A constant only

3. Which expresses 36 + 8 as a multiple of a sum of two whole numbers with no common factor, using the distributive property?
A) 4(9 + 2)
B) 2(18 + 4)
C) 8(4 + 1)
D) 6(6 + 2)

4. Using the formula V = s³, what is the volume of a cube with side length s = 1/2?
A) 1/2
B) 3/2
C) 1/8
D) 1/6

5. Which term refers to the number multiplying a variable, such as the 3 in 3y?
A) Constant
B) Term
C) Coefficient
D) Factor

6. According to the standards, an equation or inequality can be understood as a process of:
A) Memorizing facts
B) Answering which values from a specified set, if any, make it true
C) Always finding x = 1
D) Graphing a line only

7. Which is the correct form for a real-world equation described in the standards (with p, q, x as nonnegative rational numbers)?
A) x + p = q
B) x/p = q only
C) x – p = q only
D) p – x = q only

8. An inequality such as x > c has how many solutions?
A) Exactly one
B) Exactly two
C) Infinitely many
D) No solutions

Short Answer

9. Explain what it means to "evaluate" an algebraic expression, and describe what order of operations means in this process.

10. Using properties of operations, show why y + y + y is equivalent to 3y.

11. Write an inequality of the form x > c or x < c to represent a real-world constraint, and explain what "representing solutions on a number line diagram" would show for this inequality.

---

Answer Key

1. B — Equivalent expressions name the same number regardless of the value substituted.
2. B — (8 + 7) can be viewed as one entity or as a sum of two terms.
3. A — 4(9 + 2); 9 and 2 share no common factor.
4. C — (1/2)³ = 1/8.
5. C — Coefficient.
6. B — Solving means finding which values make the equation/inequality true.
7. A — x + p = q (and px = q) are the standard forms named in the resource.
8. C — Infinitely many solutions.
9. Evaluating means substituting specific values in for variables and performing the arithmetic operations (including whole-number exponents) in the conventional order (order of operations) when there are no parentheses specifying otherwise.
10. Applying properties of operations, y + y + y = 3y, since adding y three times is the same as multiplying y by 3 — both name the same number for any value of y.
11. Answers will vary; should include an inequality like x > c or x < c representing a real-world condition, with an explanation that the number line diagram would show all numbers greater than (or less than) c, indicating infinitely many solutions.