Exercise 4.3 Class 10 Math Solutions – Real-Life Applications of Functions, Punjab Board

Solved Exercise 4.3 for Class 10 Mathematics, Punjab Board. Complete step-by-step notes covering real-world mathematical modeling using linear functions, composite function applications, and absolute value models in engineering, cost analysis, and physical tolerances.

This page provides complete solved solutions for Exercise 4.3 from Unit 4: Functions and Graphs, Class 10 Mathematics, Punjab Board (PCTB). It covers practical real-world applications of functions and absolute value models – including linear cost-revenue functions, temperature conversion models (F(C)), distance-time motion, manufacturing tolerances, and acceptable error margins (|x - x₀| ≤ δ). All questions are worked out step by step for Matric Part 2 students.
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Exercise Overview

Exercise 4.3 represents the culminating application chapter of Unit 4: Functions and Graphs in the Class 10 Punjab Board Mathematics curriculum. Connecting abstract algebraic functions to tangible real-world phenomena, this exercise trains students to formulate mathematical models that describe everyday physical, industrial, and financial relationships.

The exercise guides students through two principal modeling domains: standard functional relationships and absolute value inequality models. In standard modeling, students construct linear cost equations, revenue formulas, speed-distance-time trajectories, and temperature scales (such as converting between Celsius and Fahrenheit). In absolute value applications, students model quality-control tolerances, measurement accuracy margins, and target variance limits using inequalities of the form |x - target| ≤ tolerance. A heavy emphasis is placed on establishing realistic practical domains, interpreting critical boundary values, and rejecting physically inadmissible solutions.

In Punjab Board examinations (including Lahore, Faisalabad, Rawalpindi, Gujranwala, Multan, and other BISE boards), Exercise 4.3 real-world word problems frequently serve as prominent questions in Section B and Section C. These step-by-step solutions provide clearly defined variables, explicit formula derivations, and units of measurement to ensure matric students achieve top exam performance.

FAQs

Are these Exercise 4.3 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 4 Exercise 4.3 applied function problems for the 2026-2027 session.
What types of real-life problems are modeled using functions in Exercise 4.3?
Problems involve linear cost functions, revenue/profit calculations, speed-time relations, currency and temperature conversions (Celsius to Fahrenheit), and multi-step manufacturing processes.
How are absolute value functions used in real-world scenarios?
Absolute value functions model allowable tolerances, measurement error margins, distance deviations, and temperature fluctuations where deviation magnitude matters regardless of sign (e.g., |x - 50| ≤ 2).
What is the general method to solve a word problem using functions?
1) Identify given variables and constants, 2) write an algebraic function relating input and output, 3) apply specified domain constraints, and 4) solve algebraically to evaluate required values.
How do you model tolerance in manufacturing using absolute value inequalities?
If an ideal dimension is L and the allowable error is E, the actual dimension x must satisfy the absolute value inequality |x - L| ≤ E, giving L - E ≤ x ≤ L + E.
Why are physical constraints important when finding domains in real-life problems?
In physical applications, variables like time, distance, count, and absolute temperature cannot be negative, restricting practical function domains to non-negative real numbers.
Are all word problems in Exercise 4.3 solved step-by-step?
Yes, every word problem is broken down into structured variable definitions, function formulation, algebraic working, and full final statements with appropriate units.
Can students read these Exercise 4.3 solutions online?
Yes, the complete solved PDF notes for Exercise 4.3 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 4.3 solutions free for students?
Yes, all Exercise 4.3 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.