Negative Reciprocal: Problem Solving & Reasoning
Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and applying the concept of negative reciprocal in the context of perpendicular lines, including problem solving and real-world applications.
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Negative Reciprocal: 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.
Find the negative reciprocal of the slope 3/4.
[2 marks]2.
Calculate the slope of a line that is perpendicular to a line with slope -2.
[2 marks]3.
What is the negative reciprocal of -5?
[2 marks]4.
Construct a line with a slope of 2 on the grid. Draw a perpendicular line passing through the same point.
[3 marks]B
Problem Solving & Reasoning
Answer the following multi-step problems with explanations.
1.
A line has a slope of 7/3. Find the slope of a line perpendicular to it. Then, determine the negative reciprocal of that slope and explain why it is used to find perpendicular lines.
[4 marks]2.
Given a line with equation y= -2x + 5, find the equation of a line perpendicular to it passing through the point (4, 2).
[4 marks]C
Real-world Applications
Solve these contextual problems involving negative reciprocals.
1.
A road runs with a slope of 3/4. A perpendicular path crosses this road at a point where the slope of the path is negative reciprocal. What is the slope of this path, and in what type of situation might this be relevant?
[3 marks]D
Challenge & Extension
Attempt these more difficult questions to extend your understanding.
1.
Prove that if two lines are perpendicular, then their slopes are negative reciprocals. Use algebra to justify your reasoning.
[4 marks]2.
A line has slope 1/3. Find the negative reciprocal and verify that the product of the slopes is -1.
[3 marks]E
Mixed Review
Answer these questions to consolidate your understanding.
1.
Identify the error: A student claims that the negative reciprocal of 2 is -2. Is this correct? Explain why or why not.
[3 marks]2.
Match each slope with its negative reciprocal: 5, -1/4, 0, undefined. (Answer in list form)
[4 marks]F
Error Analysis
Review the common mistake provided and correct it.
1.
A student states that the negative reciprocal of 0 is undefined. Is this correct? Justify your answer.
[3 marks]Quick Actions
What is Remix?
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet