Single Variable: Error Analysis & Misconceptions
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on error analysis and misconceptions related to substitution in algebra involving a single variable with positive values.
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Full preview • 11 questions
Single Variable: Error Analysis & Misconceptions
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.
Evaluate the expression when x = 3: 2x + 5.
[2 marks]2.
Calculate the value of y if y = 4x - 7 when x = 5.
[2 marks]3.
Simplify the expression: 3(2a + 4), given a = 2.
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working in the grid spaces provided.
1.
If the expression 5x + 3 equals 23, find the value of x. Explain your steps.
[4 marks]2.
Solve for x: 2(3x - 1) = 10. Show your working.
[3 marks]3.
A rectangle has length 4x + 1 and width x. If the area is 60, find x.
[3 marks]C
Real-world Applications
Answer all questions. Show your reasoning clearly.
1.
A car rental costs $50 plus $0.20 per mile. If the total cost is $90, how many miles were driven? Write your solution process.
[4 marks]D
Challenge & Extension
Answer all questions. Think carefully and show detailed working.
1.
The expression (x - 2)^2 = 16. Find all positive values of x and explain your reasoning.
[4 marks]2.
Given the quadratic equation 3x^2 + 2x - 1 = 0, determine the positive root using substitution, and justify your answer.
[4 marks]E
Mixed Review & Error Analysis
Answer all questions. Identify and correct the common mistake in each given solution.
1.
A student solves 3x + 4 = 19 and writes x = 19 - 4 = 15. Is this correct? If not, correct the mistake and explain.
[2 marks]2.
Identify the error in solving for x in the equation 2(4x - 3) = 16, where a student states x=2. Correct the mistake.
[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