Inequalities Test Answer Key with Scoring – Grade 6

Question 1 Writing inequalities (2 points)

(a) n ≥ 15. (b) k < −3.

Scoring: 1 point per part.

Question 2 Finding solutions (2 points)

3 − 2 = 1, 5 − 2 = 3, 8 − 2 = 6, 11 − 2 = 9. A value works when the result is at least 6, so 8 (6 ≥ 6) and 11 work.

8 and 11

Scoring: 1 point for the substitutions, 1 point for the two values.

Question 3 Reading a graph (2 points)

(a) Closed circle at 1 and shading left: x ≤ 1.

(b) For example, −4 is a solution and 2 is not; any number at most 1 works.

Scoring: 1 point per part.

Question 4 Graphing (3 points)

(a) Open circle at −2, shade right.

(b) Closed circle at 3, shade left.

(c) The open circle shows −2 is not a solution of x > −2. The closed circle shows 3 is a solution of x ≤ 3.

Scoring: 1 point per part.

Question 5 Real-world statements (2 points)

(a) p ≤ 48. (b) c > 12.5.

Scoring: 1 point per part.

Question 6 Trampoline weight limit (3 points)

(a) w ≤ 250.

(b) 180 ≤ 250 and 250 ≤ 250 are true; 251.5 ≤ 250 is false. 180 and 250.

(c) Yes: between any two weights, such as 249 and 250, there are more weights like 249.5 and 249.9.

Scoring: 1 point per part.

Question 7 Closed versus open (3 points)

(a) 4 ≥ 4 is true, so yes for x ≥ 4. 4 > 4 is false, so no for x > 4.

(b) x ≥ 4 has a closed circle at 4; x > 4 has an open circle. Both shade right.

(c) Any number above 4, such as 4.5.

Scoring: 1 point per part.

Question 8 Fundraiser goal (3 points)

(a) r ≥ 600.

(b) 610 ≥ 600 is true: yes.

(c) The smallest allowed total is 600, and 600 − 425 = $175.

Scoring: 1 point per part.