<, >, =: Problem Solving & Reasoning
Mathematics
GCSE Higher
16 questions
~32 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and applying <, >, = symbols through problem solving, reasoning, and real-world contexts for GCSE Higher students.
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<, >, =: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the value of x if 3x + 5 < 20.
[2 marks]2.
Determine whether the statement 7 > 4 + 2 is true or false.
[1 mark]3.
Solve for y: y/2 ≥ 3.
[2 marks]4.
Express the inequality: x + 4 > 10 in symbols.
[1 mark]B
Problem Solving & Reasoning
Answer all questions carefully, showing reasoning and working where appropriate.
1.
A student scores at least 80 marks to pass an exam. The maximum marks are 100. Write an inequality to represent the passing scores and determine the minimum score needed.
[3 marks]2.
A car travels faster than 60 km/h but less than 80 km/h. Write the inequality to represent this speed range.
[2 marks]3.
A box contains more than 15 but fewer than 25 chocolates. Write the inequality and state the possible number of chocolates.
[2 marks]4.
A rectangle's length is at least 10 cm and less than 15 cm, while its width is greater than 5 cm. Write inequalities to describe these dimensions.
[3 marks]5.
A shop offers discounts greater than 20% but less than 50%. Write this as an inequality.
[2 marks]C
Real-world Applications
Solve these contextual problems involving inequalities.
1.
A temperature is considered safe if it is less than 50°C but more than 0°C. Write the inequality representing this condition and give an example of a safe temperature.
[3 marks]2.
A bank account balance must be at least £100 but less than £1000. Write the inequality and specify a possible balance.
[3 marks]D
Challenge & Extension
Attempt these more difficult questions requiring deeper reasoning.
1.
Solve for x: 2x - 7 > 3x + 5 and interpret the solution.
[3 marks]2.
A company's profit P is more than £50,000 but less than £200,000. Write the inequality and discuss what this range indicates about the company's performance.
[3 marks]E
Mixed Review
Answer these questions which involve various inequality concepts.
1.
Order the following inequalities from smallest to largest: 3 < 5, 2 + 2 > 3, 7 = 7, 10 > 8.
[2 marks]F
Error Analysis
Identify the mistake in each of the following inequalities and correct it.
1.
Incorrect: 5 < 3 + 4. Correct the inequality and explain the mistake.
[2 marks]2.
Incorrect: x > 2 and x < 5. Write the correct combined inequality for x in this range.
[2 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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet