Writing and Evaluating Algebraic Expressions: Grade 6 Math Test Answer Key – PDF Download

Question 1: Parts of an Expression (2 points)

1. The coefficient of \(y\) is \(11\)
2. The terms are \(6x\), \(11y\), and \(4\): 3 terms

Scoring: 1 point for each correct part.

Question 2: Translating Phrases (2 points)

1. \(12 + k\) (or \(k + 12\))
2. \(\frac{w}{5}\) (or \(w: 5\))

Scoring: 1 point for each correct expression.

Question 3: Translating Longer Phrases (2 points)

1. Twice \(n\) is \(2n\); 3 less is \(2n – 3\)
2. The sum is \(x + 9\); 4 times it is \(4(x + 9)\)

Scoring: 1 point for each correct expression. Award 0 for \(3 – 2n\) in (a) or \(4x + 9\) in (b).

Question 4: Evaluating with One Variable (2 points)

1. \(5\times 8 – 12 = 40 – 12 = \) \(28\)
2. \(\frac{64}{8} + 8^2 = 8 + 64 = \) \(72\)

Scoring: 1 point for each correct value.

Question 5: Evaluating with Two Variables (2 points)

1. \(2\times 3^2 + 4 = 2\times 9 + 4 = 18 + 4 = \) \(22\)
2. \((3 + 4)^2 – 10 = 7^2 – 10 = 49 – 10 = \) \(39\)

Scoring: 1 point for each correct value.

Question 6: Cube Formulas (3 points)

1. \(V = 5^3 = \) \(125\text{ in}^3\)
2. \(A = 6\times 5^2 = 6\times 25 = \) \(150\text{ in}^2\)
3. \(V = (\frac{1}{2})^3 = \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} = \) \(\frac{1}{8}\text{ in}^3\)

Scoring: 1 point for each correct value with units.

Question 7: Equivalent Expressions (3 points)

1. \(7\times 3x + 7\times 2 = \) \(21x + 14\)
2. The greatest common factor is \(6\): \(6(2y + 3)\)
3. \(5a + 3a = 8a\) and \(2 + 9 = 11\): \(8a + 11\)

Scoring: 1 point for each correct expression.

Question 8: Testing Equivalence (2 points)

Substitute \(x = 1\). First expression: \(4(1 + 2) = 12\). Second expression: \(4(1) + 2 = 6\). The values differ, so the expressions are not equivalent. Correctly, \(4(x + 2) = 4x + 8\).

Maya is not correct.

Scoring: 1 point for a valid substitution showing different values; 1 point for the correct conclusion.

Question 9: Movie Night (2 points)

1. Tickets cost \(3\times 9 = 27\) and popcorn costs \(6b\): \(27 + 6b\)
2. \(27 + 6\times 2 = 27 + 12 = \) \(\$39\)

Scoring: 1 point for a correct expression; 1 point for the correct total.

See every chapter on the Grade 6 math page.