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
Name:
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)
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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet