Multiple Variables: Error Analysis & Misconceptions
Mathematics
Grade 7
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring common errors and misconceptions in solving problems with multiple variables using substitution, aimed at Grade 7 students.
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Multiple Variables: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 7
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Date:
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Solve the following problems by correctly substituting the given values. Show all working in the grid spaces.
1.
Calculate the value of y if x=3 and z=4, given y = 2x + z.
[2 marks]2.
Find the value of a if x=5, y=2, and a = x + 2y.
[2 marks]3.
Evaluate the expression when x=2, y=3, z=1, where p = x + y + z.
[2 marks]B
Problem Solving & Reasoning
Solve these multi-step problems involving multiple variables. Explain your reasoning clearly.
1.
If x = y + 2 and y = 3, find the value of x and z if z = 2x + y. Show your working.
[4 marks]2.
Given p = 3x - y and q = 2y + z, find the values of p and q when x=4, y=2, z=5. Explain each step.
[4 marks]C
Real-world Applications
Apply your understanding to solve these contextual problems involving multiple variables.
1.
A rectangle's length is 3 times its width. If the perimeter is 48 units, find the length and width. (Use variables and substitution.)
[4 marks]D
Challenge & Extension
Attempt these advanced problems to extend your understanding. Show detailed solutions.
1.
Solve for x, y, z if the following system is true: y = 2x + 3, z = x + y, and 4x + 2z = 20. Find all variables.
[4 marks]E
Mixed Review
Answer these questions of various types to reinforce your understanding.
1.
Construct an algebraic expression for the sum of two variables, x and y, given x=4 and y=5. Write the expression and evaluate it.
[2 marks]2.
A student mistakenly substitutes y=3 into y=2x + y when x=4. Identify and correct the error.
[2 marks]F
Error Analysis & Misconceptions
Review the following common mistakes. Identify the mistake and suggest a correction.
1.
A student calculates y = 2x + z, with x=3, z=5, and mistakenly finds y=16. Explain the error and provide the correct calculation.
[3 marks]2.
A student forgets to substitute the value of y and directly substitutes into z = 2x + y, with y=4, x=3, z=11. What mistake did they make?
[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