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

Question 1: Writing with Symbols (2 points)

Write an inequality for each statement.

1. \(x\) is less than 8 (1 point)
2. \(y\) is at least 15 (1 point)

Question 2: Testing Solutions (2 points)

Decide whether the value is a solution of the inequality.

1. \(x > 5\); \(x = 5\) (1 point)
2. \(n \le 7.5\); \(n = 7.5\) (1 point)

Question 3: Listing Solutions (2 points)

Give three different solutions of \(x \ge 10\) (1 point) and one number that is not a solution (1 point).

Question 4: Graphing an Inequality (2 points)

Graph \(x < 4\) on the number line. Draw a circle and shade the solutions. (2 points)

Question 5: Reading a Graph (2 points)

Write the inequality shown by the graph. (2 points)

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

Compare the inequalities \(x > 3\) and \(x \ge 3\).

1. Is \(3\) a solution of \(x > 3\)? (1 point)
2. Is \(3\) a solution of \(x \ge 3\)? (1 point)
3. Explain how the graphs of the two inequalities differ. (1 point)

Question 7: Elevator Limit (3 points)

A sign in an elevator says that it holds at most \(12\) people. Let \(p\) be the number of people riding.

1. Write an inequality for \(p\). (1 point)
2. Is \(p = 12\) a solution? (1 point)
3. The value \(p = 12.5\) satisfies the inequality. Explain why it is not a reasonable answer in this situation. (1 point)

Question 8: Bake Sale Goal (2 points)

The school bake sale needs to raise at least $150. Let \(d\) be the total dollars raised.

1. Write an inequality for \(d\). (1 point)
2. Decide whether $150 and $149.99 meet the goal. (1 point)

Question 9: Game Rating (2 points)

A video game is rated for players older than \(9\) years. Let \(a\) be a player’s age. Write an inequality and graph it on the number line. (2 points)

See every chapter on the Grade 6 math page.