≤, ≥: Problem Solving & Reasoning
Mathematics
Year 9
17 questions
~34 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and applying the inequality symbols ≤ and ≥ through problem solving, real-world contexts, and reasoning exercises.
Worksheet Preview
Full preview • 17 questions
≤, ≥: Problem Solving & Reasoning
Subject: MathematicsGrade: Year 9
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade Year 9
A
Introduction
Read the explanation below to review the key concepts.
1.
The symbols ≤ and ≥ are used to compare quantities. The symbol '≤' means 'less than or equal to,' while '≥' means 'greater than or equal to.' These inequalities help express ranges of possible values.
[2 marks]B
Fluency & Practice
Answer the following questions to practice basic inequality skills.
1.
Solve for x: 3x + 5 ≤ 20. Show your working.
[3 marks]2.
Solve for y: 2y − 4 ≥ 10. Show your working.
[3 marks]3.
Plot the graph of y = 2x on the grid.
[2 marks]4.
Construct a triangle with sides of length at least 4 cm and no more than 8 cm. Draw on the grid.
[4 marks]C
Problem Solving & Reasoning
Tackle these multi-step problems that require reasoning and explanation.
1.
A car's speed v (km/h) is at least 50 and at most 100. Write this as an inequality and explain what it means in terms of the car's speed.
[4 marks]2.
A student scores at least 70 on a test but less than 85. Write an inequality representing this and sketch the solution on the number line.
[4 marks]3.
If a rectangle's length is at least 5 cm and no more than 10 cm, and its width is at least 3 cm, what are the possible ranges for its area? Justify your reasoning.
[5 marks]D
Real-world Applications
Apply your understanding of inequalities to practical situations.
1.
A marathon runner aims to run at least 15 km but no more than 20 km in a race. Write the inequality describing her possible distances and explain the importance of these bounds.
[4 marks]2.
A factory produces at least 200 but fewer than 300 units daily. Write this as an inequality and discuss what it tells us about the production target.
[4 marks]E
Challenge & Extension
Attempt these advanced problems for extra challenge.
1.
Solve the compound inequality: 4 ≤ 2x + 1 < 10. Find all possible values of x.
[4 marks]2.
A person’s height h (cm) is at least the average height of 150 cm but less than 180 cm. Write this as an inequality and interpret it.
[4 marks]F
Mixed Review
Answer these questions to review various types of inequality problems.
1.
True or False: The statement 5 ≥ 3 is true. Explain your answer.
[1 mark]2.
Express the statement: 'x is less than or equal to 10' as an inequality.
[2 marks]3.
If y ≥ 4 and y ≤ 8, what is the range of possible y values? Write your answer and explain.
[3 marks]G
Error Analysis
Identify and correct the common mistake in each statement.
1.
A student writes: 3x + 2 ≥ 8. The student then concludes that x ≥ 2. Is this correct? If not, correct the mistake.
[3 marks]2.
A teacher states: 'If x ≥ 5, then x > 4.' Is this always true? Explain and correct if necessary.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet