Mastering x² + bx: Challenge & Extension
Mathematics
Grade 7
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focusing on the x² + bx form, enabling students to master completing the square and its applications.
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Full preview • 13 questions
Mastering x² + bx: Challenge & Extension
Subject: MathematicsGrade: Grade 7
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Date:
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Answer the following questions to practice working with x² + bx form. Show your calculations in the grid areas provided.
1.
Simplify the expression x² + 6x.
[2 marks]2.
Rewrite x² - 8x in the form (x + p)² - q.
[3 marks]3.
Factor the quadratic expression x² + 10x + 25.
[2 marks]4.
Express x² + 12x + 36 as a perfect square.
[2 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems, explaining your reasoning clearly.
1.
A rectangular garden has length (x + 3) meters and width (x - 2) meters. If the area is 60 square meters, find the value of x.
[4 marks]2.
Solve for x: x² + 4x - 5 = 0, using completing the square.
[3 marks]C
Real-world Applications
Apply your understanding to the real-world scenarios below.
1.
A ball is thrown upwards such that its height in meters after t seconds is given by h(t) = -4t² + 8t + 2. Find the time when the ball reaches its maximum height.
[4 marks]D
Challenge & Extension
Attempt these advanced problems to deepen your understanding.
1.
Derive the quadratic formula starting from the general quadratic in x² + bx + c form by completing the square.
[5 marks]2.
Given the quadratic x² + 4x + 1, complete the square and identify the values of p and q in the form (x + p)² + q.
[3 marks]E
Mixed Review
Answer the variety of questions below without additional guidance.
1.
Expand (x + 3)² and simplify.
[2 marks]2.
Rewrite 9x² + 24x + 16 as a perfect square.
[2 marks]3.
Identify and correct the mistake in expanding (x + 2)² as x² + 4x.
[3 marks]F
Error Analysis
Review the common mistake and identify what went wrong and how to correct it.
1.
A student rewrites x² + 6x as (x + 3)² - 9. Is this correct? If not, identify and correct the mistake.
[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