Algebraic Expressions Test Answer Key with Scoring – Grade 6

Question 1 Parts of an expression (2 points)

(a) 8. (b) 5.

Scoring: 1 point per part.

Question 2 Writing expressions (2 points)

(a) 4 times n is 4n, and 6 less is 4n − 6.

(b) w9 (that is, w ÷ 9).

Scoring: 1 point per part.

Question 3 Evaluate with a power (2 points)

2 × 6² − 9 = 2 × 36 − 9 = 72 − 9 = 63.

Scoring: 1 point for 36, 1 point for 63.

Question 4 Two variables (2 points)

5 × 6 − 2 × 7 = 30 − 14 = 16.

Scoring: 1 point for the substitution, 1 point for 16.

Question 5 Cube formulas (3 points)

(a) 7 × 7 × 7 = 343 cubic centimeters.

(b) 7² = 49, and 6 × 49 = 294 square centimeters.

Scoring: 1 point for (a); 1 point for 49 and 1 point for 294.

Question 6 Distributive property (2 points)

(a) 5x + 30.

(b) 7a + 2a = 9a and 3 − 1 = 2: 9a + 2.

Scoring: 1 point per part.

Question 7 Factoring (2 points)

GCF(18, 24) = 6; 18x = 6 × 3x and 24 = 6 × 4.

18x + 24 = 6(3x + 4).

Scoring: 1 point for the GCF 6, 1 point for the factored form.

Question 8 Scooter rental (3 points)

(a) 5 + 0.75m.

(b) 5 + 0.75 × 20 = 5 + 15 = $20.

(c) 5 + 0.75 × 12 = 5 + 9 = $14.

Scoring: 1 point per part.

Question 9 Equivalent or not (2 points)

(a) 2(4 + 5) = 18, but 2 × 4 + 5 = 13.

(b) No. The 2 must multiply both terms: 2(n + 5) = 2n + 10.

Scoring: 1 point per part.