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Short Intro

Exercise 2.3 introduces students to the concept of linear patterns and how mathematical expressions can represent real-life situations involving growth and reduction. These detailed step-by-step solutions help students understand sequences, linear expressions, and pattern formation easily.

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Quick Information Box

Topic	Details
Chapter	Introduction to Linear Polynomials
Exercise	Exercise 2.3
Subject	Mathematics
Class	Grade 9
Main Concepts	Linear Patterns & Linear Expressions
Difficulty Level	Moderate
Useful For	School Exams & Olympiad Preparation

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Concepts Used (Topics Covered)

• Linear Patterns
• Sequences
• Linear Expressions
• Arithmetic Growth
• Linear Decay
• Area of Rectangle
• Volume of Cuboid
• Daily Reduction Problems
• Algebraic Representation

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Important Formulas

Linear Pattern Formula

$an+b$

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Area of Rectangle

$A=l\times b$

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Volume of Cuboid

$V=l\times b\times h$

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Savings Formula

$$\text{Total Amount} = \text{Initial Amount} + (\text{Monthly Increase})$$

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Questions & Step-by-Step Solutions

Question 1

A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression for the nth month.

Solution

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Question 2

A rally starts with 120 members. Each hour, 9 members drop out of the group. How many members will remain after 1, 2, 3, … hours? Find a linear expression to represent the number of members at the end of the n^th hour.

Solution

Question 3

Suppose the length of a rectangle is 13 cm. Find the area if breadth is 12 cm, 10 cm and 8 cm. Find the linear pattern representing the area.

Solution

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Question 4

Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if height is 5 cm, 9 cm and 13 cm. Find the linear pattern representing the volume.

Solution

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Question 5

Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages will be left after 15 days? Express this as a linear pattern.

Solution

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Common Mistakes

❌ Forgetting increase/decrease signs
❌ Using wrong formula for area or volume
❌ Multiplication errors in large numbers
❌ Confusing pattern variable with actual values

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Exam Tips

✔ Write formulas before solving
✔ Identify whether quantity increases or decreases
✔ Use variables carefully
✔ Check calculations step-by-step

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Practice MCQs

1. Which expression shows linear growth?

A) $5 – 2n$
B) $3n + 7$
C) $n^2 + 1$
D) $2^n$

Answer

✅ B) $3n + 7$

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2. What is the area of rectangle with length 13 cm and breadth 9 cm?

A) 117
B) 127
C) 107
D) 137

Answer

✅ A) 117

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3. Volume of cuboid formula is:

A) $l+b+h$
B) $l\times b$
C) $l\times b\times h$
D) $2(l+b)$

Answer

✅ C) $l\times b\times h$

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4. If 5 decreases every day from 100, expression becomes:

A) $100+5n$
B) $100-5n$
C) $5n-100$
D) $100n$

Answer

✅ B) $100-5n$

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FAQ Section

Q1. What is a linear pattern?

A linear pattern is a sequence where the difference between consecutive terms remains constant.

Q2. What is linear growth?

When a quantity increases by a fixed amount regularly, it is called linear growth.

Q3. What is linear decay?

When a quantity decreases by a fixed amount regularly, it is called linear decay.

Q4. Why are patterns important in Maths?

Patterns help us predict values and create mathematical formulas.

Q5. Can linear patterns be represented algebraically?

Yes, linear patterns can be represented using algebraic expressions.

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