Writing and Graphing Inequalities: Grade 6 Math Test Answer Key – PDF Download

Question 1: Writing with Symbols (2 points)

1. \(x < 8\)
2. \(y \ge 15\)

Scoring: 1 point for each correct inequality.

Question 2: Testing Solutions (2 points)

1. \(5 > 5\) is false. Not a solution
2. \(7.5 \le 7.5\) is true. A solution

Scoring: 1 point for each correct decision with a valid reason.

Question 3: Listing Solutions (2 points)

Any three numbers that are at least \(10\) work, for example 10, 12, and 25.5. Any number below \(10\) is not a solution, for example 9.9, because \(9.9 \ge 10\) is false.

Scoring: 1 point for three valid solutions (10 counts); 1 point for a valid non-solution.

Question 4: Graphing an Inequality (2 points)

Open circle at \(4\), because \(4 < 4\) is false, and shading to the left.

Scoring: 1 point for an open circle at 4; 1 point for shading to the left.

Question 5: Reading a Graph (2 points)

The closed circle at \(2\) means \(2\) is included, and the shading goes right: \(x \ge 2\).

Scoring: 1 point for the correct symbol; 1 point for the correct number.

Question 6: Greater Than or Equal To (3 points)

1. \(3 > 3\) is false. No
2. \(3 \ge 3\) is true. Yes
3. The graph of \(x > 3\) has an open circle at \(3\); the graph of \(x \ge 3\) has a closed circle at \(3\). Both are shaded to the right.

Scoring: 1 point for each part.

Question 7: Elevator Limit (3 points)

1. \(p \le 12\)
2. \(12 \le 12\) is true. Yes
3. People are counted in whole numbers, so half a person makes no sense. \(p\) must be a whole number.

Scoring: 1 point for each part.

Question 8: Bake Sale Goal (2 points)

1. \(d \ge 150\)
2. \(150 \ge 150\) is true, so $150 meets the goal. \(149.99 \ge 150\) is false, so $149.99 does not.

Scoring: 1 point for the inequality; 1 point for both decisions.

Question 9: Game Rating (2 points)

Older than \(9\) does not include \(9\): \(a > 9\). Open circle at \(9\) with shading to the right.

Scoring: 1 point for the inequality; 1 point for the correct graph.

See every chapter on the Grade 6 math page.