Exercise 2.7 Class 10 Math Solutions – Unit 2 Quadratic Equations and Inequalities, Punjab Board

Step-by-step solutions to Exercise 2.7 of Unit 2: Quadratic Equations and Inequalities for Class 10 Punjab Board students. Covers real-world applications and word problems modeled into quadratic equations involving numbers, geometry, speed, and time.

This page provides complete solved solutions for Exercise 2.7 from Unit 2: Quadratic Equations and Inequalities, Class 10 Mathematics, Punjab Board (PCTB). It covers real-world word problems and practical applications modeled through quadratic equations, including number relations, geometry, speed, and time. All questions are worked out step by step for Matric Part 2 students.
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Exercise Overview

Exercise 2.7 represents the capstone application section of Unit 2: Quadratic Equations and Inequalities for Class 10 Punjab Board students. Moving from pure algebraic manipulation to practical problem-solving, this exercise teaches students how to model real-world scenarios into quadratic equations and extract meaningful physical answers.

The exercise guides students through a structured four-stage problem-solving methodology: defining algebraic variables for unknown physical quantities, setting up relationships based on stated problem constraints, transforming the verbal model into the standard quadratic form ax² + bx + c = 0, and solving using factoring or the quadratic formula. Problems cover integer relationships, rectangular area and perimeter dimensions, right-triangle Pythagorean calculations, and uniform motion speed-distance-time systems. An essential emphasis is placed on testing solutions against physical reality – rejecting extraneous negative values when solving for lengths, speeds, or counts.

In Punjab Board examinations (such as Lahore, Rawalpindi, Gujranwala, Faisalabad, and Multan Boards), real-world word problems from Exercise 2.7 frequently form the basis of Section C long questions. Practicing these step-by-step solutions ensures students develop the mathematical modeling and problem interpretation skills needed for full marks in board examinations.

FAQs

Are these Exercise 2.7 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, matching all prescribed topics for Unit 2 Exercise 2.7 in the 2026-2027 session.
Do these solutions cover every question in Exercise 2.7?
Yes, every real-world application and word problem in Exercise 2.7 is solved in sequence with clear variable definitions, equation formulation, and algebraic solutions.
What types of real-world applications are covered in Exercise 2.7?
Exercise 2.7 covers word problems involving consecutive numbers, geometric dimensions (area and perimeter of rectangles/triangles), speed-distance-time relations, and cost-rate calculations.
How do you translate a word problem into a quadratic equation in Exercise 2.7?
Assign a variable (e.g., x) to the unknown quantity, write expressions for related quantities from given conditions, formulate the equation, rearrange into ax² + bx + c = 0, and solve.
How do you check for extraneous or inadmissible solutions in Exercise 2.7?
Since physical quantities like lengths, dimensions, speeds, and time cannot be negative, discard negative or non-sensical algebraic roots and state the valid physical answer.
Can students read these Exercise 2.7 solutions online?
Yes, the full Exercise 2.7 solution set is available to read online on this page with no separate download required.
Are these solutions useful for Punjab Board exams?
Yes. Real-world application word problems from Exercise 2.7 are very frequently asked as high-mark subjective long questions in Punjab Board Matric exams.
Are these solutions based on the latest PCTB / PECTAA syllabus?
Yes, they are aligned with the updated PCTB and PECTAA Mathematics syllabus for Class 10 for the 2026-2027 academic session.
Are these Exercise 2.7 solutions free for students?
Yes, all Exercise 2.7 solutions on MaryamNotes.pk are completely free to read online for all Class 10 students across all Punjab boards.