Inequalities Test – Grade 6 Math (Printable PDF)

Question 1 Writing inequalities (2 points)

Write an inequality for each statement.

1. n is at least 15. (1 point)
2. k is less than −3. (1 point)

Question 2 Finding solutions (2 points)

Which of the values 3, 5, 8 and 11 are solutions of x − 2 ≥ 6? Show the substitutions.

Question 3 Reading a graph (2 points)

Use the graph.

1. Write the inequality shown. (1 point)
2. Name one solution and one number that is not a solution. (1 point)

Question 4 Graphing (3 points)

Use number lines like the one below.

1. Graph x > −2. (1 point)
2. Graph x ≤ 3. (1 point)
3. Explain why one graph uses an open circle and the other a closed circle. (1 point)

Question 5 Real-world statements (2 points)

Write an inequality for each situation.

1. A bus holds at most 48 passengers (p). (1 point)
2. A museum ticket costs more than $12.50 (c). (1 point)

Question 6 Trampoline weight limit (3 points)

A trampoline park lets jumpers weigh no more than 250 pounds.

1. Write an inequality for the weight w. (1 point)
2. Which of 180, 250 and 251.5 pounds may jump? (1 point)
3. Are there infinitely many possible weights? Explain. (1 point)

Question 7 Closed versus open (3 points)

Compare x ≥ 4 and x > 4.

1. Is 4 a solution of each? (1 point)
2. How do their graphs differ? (1 point)
3. Give a number that is a solution of both. (1 point)

Question 8 Fundraiser goal (3 points)

A scout troop needs to raise at least $600 and has raised $425 so far.

1. Write an inequality for the total r raised. (1 point)
2. Does a total of $610 meet the goal? (1 point)
3. What is the least additional amount needed? (1 point)