Algebraic: Problem Solving & Reasoning on Simultaneous Equations
Mathematics
Grade 7
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on solving simultaneous equations involving one linear and one quadratic equation. Designed for Grade 7 students to develop procedural skills, reasoning, and application in algebra.
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Algebraic: Problem Solving & Reasoning on Simultaneous Equations
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Solve the following problems by applying algebraic methods. Show all working in the grid spaces provided.
1.
Solve for x and y:
x + y = 7
y = x^2 - 2
[3 marks]2.
Find the values of x and y:
2x + y = 10
y = 4 - x^2
[3 marks]3.
Solve for x:
x^2 + 3x = 10
y = 2x + 1
[3 marks]B
Problem Solving & Reasoning
Tackle these multi-step problems involving simultaneous equations. Show detailed working.
1.
A ball is tossed into the air with height modeled by y = -x^2 + 4x, where y is the height in meters and x is the time in seconds. Find the time when the ball reaches the maximum height and the maximum height itself.
[4 marks]2.
A rectangular garden's length and width are related by the equations:
length = x + 2
width = x^2 - 1 ", and the area is 40 m². Find possible values of x and the dimensions of the garden.
[4 marks]C
Real-world Applications
Apply your algebraic skills to these contextual problems.
1.
A company's revenue R in thousands of dollars depends on the advertising spend x (in thousands) as follows: R = -x^2 + 12x. Find the advertising spend that maximizes revenue and the maximum revenue.
[4 marks]2.
A car rental company charges a flat fee plus a per-day cost. The total cost y in dollars for x days is given by y = 50 + 20x. The company also offers a discount when total cost reaches a quadratic relation y = -x^2 + 70x. Find the number of days x where the total cost under both schemes is the same.
[4 marks]D
Challenge & Extension
Attempt these more complex problems. Detailed solutions are encouraged.
1.
Solve for x and y:
x^2 - y = 5
y = 3x - 1 ext{ and } y = x^2 + 7
[4 marks]2.
Given the equations:
y = x^2 + 2x + 1
2x + y = 10,
find all solutions where both equations hold simultaneously.
[4 marks]E
Mixed Review
Solve a variety of algebraic questions to reinforce your understanding.
1.
Simplify: (x^2 + 3x + 2) - (x^2 - x - 4).
[2 marks]2.
If y = 2x + 3 and y = x^2 + 5, find the value(s) of x where both equations are true.
[3 marks]F
Error Analysis
Review the following typical mistake and correct it.
1.
A student tries to solve the equations:
x + y = 5
y = x^2 + 2. They set x + y = 5 and y = x^2 + 2, then substitute y into the first equation to get:
x + x^2 + 2 = 5
discuss what mistake the student made and how to correctly solve the system.
[4 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