Prepared by Muhammad Tayyab, Subject Specialist Mathematics, Govt Christian High School Daska
📌 Based on National Curriculum 2023 / PECTAA 2026 Syllabus
📖 What's Inside: This exercise covers linear function applications (balance, fare, manufacturing cost, travel time, printing charges) and absolute value inequalities (temperature deviation, rod tolerance, machine alignment). Perfect for Punjab Boards exam preparation.
📚 Related Resources – Unit 4: Functions and Graphs
Class 10 Math Unit 4 Exercise 4.3 – Linear Models & Absolute Value Inequalities: Complete Guide
Exercise 4.3 of Unit 4 applies the concepts of linear functions and absolute value inequalities to real-world problems. This exercise demonstrates how mathematics is used in everyday life – from calculating bank balances to ensuring manufacturing quality control.
What You Will Learn
By working through Exercise 4.3, students master: evaluating linear functions in real-world contexts (balance, fare, cost, time, charges), modeling real-world situations using linear functions \( f(x) = mx + b \), solving absolute value inequalities in quality control contexts, and interpreting mathematical results in practical terms.
Topics Covered in This Exercise
- Linear Function Applications – balance after t months, fare per kilometre
- Cost Functions – manufacturing sofa sets, encoding and printing charges
- Time-Distance Models – travel time calculation
- Absolute Value Inequalities – temperature deviation, rod tolerance, machine alignment
Why Exercise 4.3 Is Important
Exercise 4.3 shows students how mathematics applies to real life. Board exam papers frequently feature word problems involving linear functions and absolute value inequalities. This exercise builds essential skills in mathematical modeling and problem-solving.
Punjab Board Preparation
Students preparing for board exams under any of the 10 BISE Punjab boards should prioritise this exercise. Linear function word problems and absolute value inequalities are frequently tested topics. Practising every question by hand is highly recommended.
Exam Tips for Linear Models & Absolute Value Inequalities
- For linear functions, identify \( m \) (rate) and \( b \) (initial value) first.
- For absolute value inequalities, write \( |x - \text{target}| \le \text{tolerance} \) for acceptable range.
- Always include units in your final answer.
- Check if your answer makes sense in the given context.
Common Mistakes Students Make
- Forgetting to add the initial/fixed value in linear functions.
- Mixing up the target and tolerance in absolute value problems.
- Not including units in final answers.
- Forgetting to flip inequality sign when multiplying by negative.
📖 Exercise 4.3 – Solved Problems
1 Balance after t months
\( B(t) = 5000 + 200t \) represents total balance (in rupees) after \( t \) months. Balance after 6 months?
\[
\begin{aligned}
B(t) &= 5000 + 200t \\
B(6) &= 5000 + 200(6) \\
B(6) &= 5000 + 1200 = 6200
\end{aligned}
\]
✅ The balance after 6 months will be Rs. 6200.
2 Fare for k kilometres
\( f(k) = 150 + 20k \) represents total fare (in rupees) for \( k \) km. Fare for 12 km ride?
\[
\begin{aligned}
f(k) &= 150 + 20k \\
f(12) &= 150 + 20(12) = 150 + 240 = 390
\end{aligned}
\]
✅ Total fare = Rs. 390.
3 Cost of sofa sets
\( f(n) = 5500n \) models cost of \( n \) sofa sets. Cost of 50 sofa sets?
\[
\begin{aligned}
f(n) &= 5500n \\
f(50) &= 5500 \times 50 = 275000
\end{aligned}
\]
✅ Cost = Rs. 275,000.
4 Travel time
\( T(d) = \frac{d}{60} \) represents time in hours for distance \( d \) km. Time for 180 km?
\[
\begin{aligned}
T(d) &= \frac{d}{60} \\
T(180) &= \frac{180}{60} = 3
\end{aligned}
\]
✅ It will take 3 hours.
5 Encoding and printing charges
\( f(x) = 100 + 5x \) where \( x \) = number of pages. Charge for 55 pages?
\[
\begin{aligned}
f(x) &= 100 + 5x \\
f(55) &= 100 + 5(55) = 100 + 275 = 375
\end{aligned}
\]
✅ Company will charge Rs. 375.
6 Chemical reaction temperature deviation
Stable at 37°C, stop if \( |T - 37| > 2.5 \). Find temperature values where process is stopped.
\[
\begin{aligned}
|T - 37| &> 2.5 \\
\Rightarrow T - 37 &> 2.5 \quad \text{or} \quad -(T - 37) > 2.5 \\
T &> 39.5 \quad \text{or} \quad -T + 37 > 2.5 \\
& \quad \Rightarrow -T > -34.5 \Rightarrow T < 34.5
\end{aligned}
\]
✅ Process must be stopped for \( T < 34.5^\circ \) or \( T > 39.5^\circ \).
7 Metal rod tolerance
Length must be \( 2.5 \pm 0.04 \) metres: \( |x - 2.5| \le 0.04 \). Range of acceptable lengths?
\[
\begin{aligned}
|x - 2.5| &\le 0.04 \\
-0.04 &\le x - 2.5 \le 0.04 \\
2.46 &\le x \le 2.54
\end{aligned}
\]
✅ Acceptable lengths: between 2.46 m and 2.54 m inclusive.
8 Machine alignment rejection
Model \( |x| > 0.1 \). Positions of centre (in mm) that cause rejection?
\[
\begin{aligned}
|x| &> 0.1 \\
x &> 0.1 \quad \text{or} \quad -x > 0.1 \\
& \Rightarrow x < -0.1
\end{aligned}
\]
✅ Rejected if \( x < -0.1 \, \text{mm} \) or \( x > 0.1 \, \text{mm} \).
📝 Multiple Choice Questions (Unit 4 Review)
1. If \( B(t) = 5000 + 200t \), the balance after 6 months is:
✅ Correct Answer: (A) Rs. 6200
\( B(6) = 5000 + 200(6) = 5000 + 1200 = 6200 \)
\( B(6) = 5000 + 200(6) = 5000 + 1200 = 6200 \)
2. The fare for a 12 km ride with \( f(k) = 150 + 20k \) is:
✅ Correct Answer: (C) Rs. 390
\( f(12) = 150 + 20(12) = 150 + 240 = 390 \)
\( f(12) = 150 + 20(12) = 150 + 240 = 390 \)
3. The solution of \( |x-37| > 2.5 \) is:
✅ Correct Answer: (B) \(x < 34.5\) or \(x > 39.5\)
\( |x-37| > 2.5 \implies x-37 > 2.5 \) or \( x-37 < -2.5 \)
\( |x-37| > 2.5 \implies x-37 > 2.5 \) or \( x-37 < -2.5 \)
4. The acceptable range for \( |x-2.5| \le 0.04 \) is:
✅ Correct Answer: (A) \(2.46 \le x \le 2.54\)
\( -0.04 \le x-2.5 \le 0.04 \implies 2.46 \le x \le 2.54 \)
\( -0.04 \le x-2.5 \le 0.04 \implies 2.46 \le x \le 2.54 \)
5. The time to travel 240 km at \( \frac{d}{60} \) hours per km is:
✅ Correct Answer: (B) 4 hours
\( T(240) = \frac{240}{60} = 4 \)
\( T(240) = \frac{240}{60} = 4 \)
📈 Key Concepts – Linear & Absolute Value Models
- Linear Function: \( f(x) = mx + b \) where \( m \) is rate, \( b \) is fixed/initial value.
- Absolute Value Inequality: \( |X| < a \Rightarrow -a < X < a \) ; \( |X| > a \Rightarrow X < -a \text{ or } X > a \) (for \( a>0 \)).
- Tolerance Interpretation: \( |x - \text{target}| \le \text{tolerance} \) gives acceptable range: \( \text{target} - \text{tolerance} \le x \le \text{target} + \text{tolerance} \).
❓ Frequently Asked Questions
What is taught in Exercise 4.3 of Class 10 Math Unit 4?
Exercise 4.3 covers real-world applications of linear functions \( f(x) = mx + b \) including balance, fare, manufacturing cost, travel time, and printing charges. It also covers absolute value inequalities including temperature deviation, rod tolerance, and machine alignment problems.
How many questions are there in Unit 4 Exercise 4.3?
Exercise 4.3 has 8 questions covering linear function applications (Q1-Q5) and absolute value inequalities (Q6-Q8).
What is a linear function model?
A linear function model is of the form \( f(x) = mx + b \), where \( m \) is the rate of change and \( b \) is the initial/fixed value. It is used to model real-world situations with constant rate of change.
How do you solve absolute value inequalities in real-world problems?
To solve absolute value inequalities in real-world problems, set up \( |x - target| \le tolerance \) for acceptable range or \( |x - target| > tolerance \) for rejection conditions. Then solve using \( -tolerance \le x-target \le tolerance \) or \( x-target < -tolerance \) or \( x-target > tolerance \).
Is this solution according to the PECTAA 2026 syllabus?
Yes, these solutions are prepared according to the PECTAA 2026 / National Curriculum 2023 syllabus for Class 10 Mathematics.
Is this Exercise 4.3 solution valid for all Punjab Boards?
Yes, the content follows the unified Punjab textbook and is applicable to students of all 10 BISE Punjab boards.
Are solved PDF notes available for Exercise 4.3?
Yes, a complete solved PDF for Exercise 4.3 is embedded on this page and available to download for free.
Can I download the Unit 4 Exercise 4.3 solution as a PDF?
Yes, use the Download PDF button on this page to save the complete solved Exercise 4.3 notes to your device.
Is Exercise 4.3 important for Class 10 board exams?
Yes, linear function applications and absolute value inequalities are frequently tested in board exams. Exercise 4.3 builds essential skills in real-world mathematical modeling and problem-solving.
Who prepared these Class 10 Math Unit 4 notes?
These notes were prepared by Muhammad Tayyab, Subject Specialist Mathematics at Govt Christian High School Daska, for Hira Science Academy.