{"id":2131,"date":"2026-05-25T11:54:51","date_gmt":"2026-05-25T06:24:51","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=2131"},"modified":"2026-05-26T09:41:49","modified_gmt":"2026-05-26T04:11:49","slug":"ncert-class-9-maths-exercise-2-3-solutions-exploring-linear-patterns","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-2-3-solutions-exploring-linear-patterns\/","title":{"rendered":"NCERT Class 9 Maths Exercise 2.3 Solutions \u2013 Exploring Linear Patterns"},"content":{"rendered":"<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2131?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2131?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 2.3 introduces students to the concept of <strong>linear patterns<\/strong> 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.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Topic<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Chapter<\/td><td>Introduction to Linear Polynomials<\/td><\/tr><tr><td>Exercise<\/td><td>Exercise 2.3<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Class<\/td><td>Grade 9<\/td><\/tr><tr><td>Main Concepts<\/td><td>Linear Patterns &amp; Linear Expressions<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><tr><td>Useful For<\/td><td>School Exams &amp; Olympiad Preparation<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Linear Patterns<\/li>\n\n\n\n<li>Sequences<\/li>\n\n\n\n<li>Linear Expressions<\/li>\n\n\n\n<li>Arithmetic Growth<\/li>\n\n\n\n<li>Linear Decay<\/li>\n\n\n\n<li>Area of Rectangle<\/li>\n\n\n\n<li>Volume of Cuboid<\/li>\n\n\n\n<li>Daily Reduction Problems<\/li>\n\n\n\n<li>Algebraic Representation<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Linear Pattern Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mi>n<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">an+b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Area of Rectangle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mi>l<\/mi><mo>\u00d7<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A=l\\times b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Volume of Cuboid<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mi>l<\/mi><mo>\u00d7<\/mo><mi>b<\/mi><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V=l\\times b\\times h<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Savings Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Total&nbsp;Amount<\/mtext><mo>=<\/mo><mtext>Initial&nbsp;Amount<\/mtext><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mtext>Monthly&nbsp;Increase<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Total Amount} = \\text{Initial Amount} + (\\text{Monthly Increase})<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-Step Solutions<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A student has \u20b9500 in her savings bank account. She gets \u20b9150 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.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Initial amount = \u20b9500<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Monthly increase = \u20b9150<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">After 2nd month<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>500<\/mn><mo>+<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mn>150<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">500 + 2(150)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>500<\/mn><mo>+<\/mo><mn>300<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 500 + 300<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mtext>\u20b9<\/mtext><mn>800<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= \u20b9800<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">After 3rd month<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>500<\/mn><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>150<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">500 + 3(150)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mtext>\u20b9<\/mtext><mn>950<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= \u20b9950<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Expression<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If n = number of months,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>500<\/mn><mo>+<\/mo><mn>150<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500 + 150n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Amount after nth month = <strong>\u20b9(500 + 150n)<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A rally starts with 120 members. Each hour, 9 members drop out. Find the number of members after 1, 2, 3 \u2026 hours and write a linear expression.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Initial members = 120<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Decrease every hour = 9<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">After 1 hour<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>120<\/mn><mo>\u2212<\/mo><mn>9<\/mn><mo>=<\/mo><mn>111<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">120 &#8211; 9 = 111<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">After 2 hours<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>120<\/mn><mo>\u2212<\/mo><mn>18<\/mn><mo>=<\/mo><mn>102<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">120 &#8211; 18 = 102<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">After 3 hours<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>120<\/mn><mo>\u2212<\/mo><mn>27<\/mn><mo>=<\/mo><mn>93<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">120 &#8211; 27 = 93<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Expression<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>120<\/mn><mo>\u2212<\/mo><mn>9<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">120 &#8211; 9n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Members after nth hour = <strong>120 \u2212 9n<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">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.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Area formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mi>l<\/mi><mo>\u00d7<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A=l\\times b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length = 13 cm<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i) Breadth = 12 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>13<\/mn><mo>\u00d7<\/mo><mn>12<\/mn><mo>=<\/mo><mn>156<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">13 \\times 12 = 156<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) Breadth = 10 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>13<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><mo>=<\/mo><mn>130<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">13 \\times 10 = 130<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) Breadth = 8 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>13<\/mn><mo>\u00d7<\/mo><mn>8<\/mn><mo>=<\/mo><mn>104<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">13 \\times 8 = 104<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Pattern<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mn>13<\/mn><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A=13b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Linear expression = <strong>13b<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">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.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Volume formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mi>l<\/mi><mo>\u00d7<\/mo><mi>b<\/mi><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V=l\\times b\\times h<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length = 7 cm<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Breadth = 11 cm<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>7<\/mn><mo>\u00d7<\/mo><mn>11<\/mn><mo>=<\/mo><mn>77<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7 \\times 11 = 77<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(i) Height = 5 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>77<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo>=<\/mo><mn>385<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">77 \\times 5 = 385<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) Height = 9 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>77<\/mn><mo>\u00d7<\/mo><mn>9<\/mn><mo>=<\/mo><mn>693<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">77 \\times 9 = 693<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) Height = 13 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>77<\/mn><mo>\u00d7<\/mo><mn>13<\/mn><mo>=<\/mo><mn>1001<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">77 \\times 13 = 1001<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Pattern<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mn>77<\/mn><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V=77h<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Linear expression = <strong>77h<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">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.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Total pages = 500<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pages read daily = 20<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pages read in 15 days:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>20<\/mn><mo>\u00d7<\/mo><mn>15<\/mn><mo>=<\/mo><mn>300<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">20 \\times 15 = 300<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pages left:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>300<\/mn><mo>=<\/mo><mn>200<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">500 &#8211; 300 = 200<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Pattern<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>20<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500 &#8211; 20n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Pages left after 15 days = <strong>200<\/strong><br>\u2705 Linear expression = <strong>500 \u2212 20n<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u274c Forgetting increase\/decrease signs<br>\u274c Using wrong formula for area or volume<br>\u274c Multiplication errors in large numbers<br>\u274c Confusing pattern variable with actual values<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u2714 Write formulas before solving<br>\u2714 Identify whether quantity increases or decreases<br>\u2714 Use variables carefully<br>\u2714 Check calculations step-by-step<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. Which expression shows linear growth?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mo>\u2212<\/mo><mn>2<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">5 &#8211; 2n<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>n<\/mi><mo>+<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3n + 7<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n^2 + 1<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mi>n<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2^n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>n<\/mi><mo>+<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3n + 7<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. What is the area of rectangle with length 13 cm and breadth 9 cm?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) 117<br>B) 127<br>C) 107<br>D) 137<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 A) 117<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. Volume of cuboid formula is:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>l<\/mi><mo>+<\/mo><mi>b<\/mi><mo>+<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">l+b+h<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>l<\/mi><mo>\u00d7<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">l\\times b<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>l<\/mi><mo>\u00d7<\/mo><mi>b<\/mi><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">l\\times b\\times h<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo>+<\/mo><mi>b<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">2(l+b)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>l<\/mi><mo>\u00d7<\/mo><mi>b<\/mi><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">l\\times b\\times h<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. If 5 decreases every day from 100, expression becomes:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>100<\/mn><mo>+<\/mo><mn>5<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100+5n<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>100<\/mn><mo>\u2212<\/mo><mn>5<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100-5n<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mi>n<\/mi><mo>\u2212<\/mo><mn>100<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5n-100<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>100<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>100<\/mn><mo>\u2212<\/mo><mn>5<\/mn><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100-5n<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. What is a linear pattern?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A linear pattern is a sequence where the difference between consecutive terms remains constant.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. What is linear growth?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When a quantity increases by a fixed amount regularly, it is called linear growth.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. What is linear decay?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When a quantity decreases by a fixed amount regularly, it is called linear decay.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Why are patterns important in Maths?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Patterns help us predict values and create mathematical formulas.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. Can linear patterns be represented algebraically?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Yes, linear patterns can be represented using algebraic expressions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Practice more chapter-wise Maths solutions, MCQs, mock tests, and concept-based questions on <strong><a target=\"_blank\" rel=\"noreferrer noopener\">MyMockMate<\/a><\/strong> and strengthen your Class 9 Mathematics preparation with smart learning tools!<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2131?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2131?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p> Short Intro Exercise 2.3 introduces students to the concept of linear patterns and how mathematical<\/p>\n","protected":false},"author":1,"featured_media":2132,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[22,4,11],"tags":[696,692,697,136,689,690,685,700,699,691,693,698,688,694,701,702,695,673],"class_list":["post-2131","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","category-class-9","category-maths-class-9","tag-algebra-chapter-solutions","tag-arithmetic-patterns","tag-class-9-algebra","tag-class-9-maths","tag-exercise-2-3-solutions","tag-exploring-linear-patterns","tag-grade-9-mathematics","tag-linear-expression-questions","tag-linear-growth-problems","tag-linear-patterns-questions","tag-linear-polynomial-solutions","tag-maths-exercise-2-3","tag-mymockmate-maths","tag-pattern-based-questions","tag-pattern-recognition-maths","tag-rectangle-area-pattern","tag-sequence-and-patterns","tag-step-by-step-maths-solutions"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2131","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=2131"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2131\/revisions"}],"predecessor-version":[{"id":2133,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2131\/revisions\/2133"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/2132"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=2131"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=2131"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=2131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}