{"id":2126,"date":"2026-05-25T11:35:44","date_gmt":"2026-05-25T06:05:44","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=2126"},"modified":"2026-05-25T11:58:11","modified_gmt":"2026-05-25T06:28:11","slug":"ncert-class-9-maths-exercise-2-2-solutions-linear-polynomials","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-2-2-solutions-linear-polynomials\/","title":{"rendered":"NCERT Class 9 Maths Exercise 2.2 Solutions \u2013 Linear Polynomials"},"content":{"rendered":"<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2126?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\/2126?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 2.2 focuses on evaluating linear and quadratic polynomials and solving real-life word problems using linear equations. These detailed step-by-step solutions help students understand algebra concepts easily and improve their problem-solving skills for school exams and competitive preparation.<\/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 2.2<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Class<\/td><td>Grade 9<\/td><\/tr><tr><td>Main Topics<\/td><td>Polynomial Evaluation &amp; Linear Equations<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><tr><td>Useful For<\/td><td>School Exams &amp; Olympiad Foundation<\/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 Polynomials<\/li>\n\n\n\n<li>Quadratic Polynomials<\/li>\n\n\n\n<li>Polynomial Evaluation<\/li>\n\n\n\n<li>Substitution Method<\/li>\n\n\n\n<li>Linear Equations<\/li>\n\n\n\n<li>Ratio Problems<\/li>\n\n\n\n<li>Age Problems<\/li>\n\n\n\n<li>Coin Problems<\/li>\n\n\n\n<li>Rectangle Problems<\/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 Polynomial<\/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>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">ax+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\">Quadratic Polynomial<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">ax^2+bx+c<\/annotation><\/semantics><\/math>ax2+bx+c<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Perimeter of Rectangle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><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\">P=2(l+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\">Value of Polynomial<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute the given value of the variable into the expression.<\/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\">Find the value of the linear polynomial <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x &#8211; 3<\/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\">(i) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 0<\/annotation><\/semantics><\/math><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Given polynomial:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x-3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mo stretchy=\"false\">(<\/mo><mn>0<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>3<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5(0) &#8211; 3 = -3<\/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 Value = <strong>\u22123<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = -1<\/annotation><\/semantics><\/math><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>3<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>5<\/mn><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5(-1) &#8211; 3 = -5 &#8211; 3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>=<\/mo><mo>\u2212<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= -8<\/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 Value = <strong>\u22128<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 2<\/annotation><\/semantics><\/math><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>3<\/mn><mo>=<\/mo><mn>10<\/mn><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5(2) &#8211; 3 = 10 &#8211; 3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 7<\/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 Value = <strong>7<\/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\">Find the value of the quadratic polynomial <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>7<\/mn><msup><mi>s<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><mi>s<\/mi><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7s^2 &#8211; 4s + 6<\/annotation><\/semantics><\/math> if:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(i) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>s<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">s = 0<\/annotation><\/semantics><\/math><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>7<\/mn><mo stretchy=\"false\">(<\/mo><mn>0<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>0<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7(0)^2 &#8211; 4(0) + 6<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 6<\/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 Value = <strong>6<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>s<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">s = -3<\/annotation><\/semantics><\/math><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>7<\/mn><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7(-3)^2 &#8211; 4(-3) + 6<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>7<\/mn><mo stretchy=\"false\">(<\/mo><mn>9<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>12<\/mn><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 7(9) + 12 + 6<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>63<\/mn><mo>+<\/mo><mn>18<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 63 + 18<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>81<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 81<\/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 Value = <strong>81<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(iii) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>s<\/mi><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">s = 4<\/annotation><\/semantics><\/math><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>7<\/mn><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7(4)^2 &#8211; 4(4) + 6<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>7<\/mn><mo stretchy=\"false\">(<\/mo><mn>16<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>16<\/mn><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 7(16) &#8211; 16 + 6<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>112<\/mn><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 112 &#8211; 10<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>102<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 102<\/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 Value = <strong>102<\/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\">The present age of Salil\u2019s mother is three times Salil\u2019s present age. After 5 years, their ages will add up to 70 years. Find their present ages.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let Salil\u2019s present age = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math> years<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mother\u2019s present age = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">3x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After 5 years:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Salil\u2019s age = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x + 5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mother\u2019s age = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x + 5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">According to question:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><mo>+<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><mo>=<\/mo><mn>70<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x + 5 + 3x + 5 = 70<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mn>10<\/mn><mo>=<\/mo><mn>70<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4x + 10 = 70<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mi>x<\/mi><mo>=<\/mo><mn>60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4x = 60<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 15<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mother\u2019s age:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>15<\/mn><mo>=<\/mo><mn>45<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3 \\times 15 = 45<\/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 Salil\u2019s age = <strong>15 years<\/strong><br>\u2705 Mother\u2019s age = <strong>45 years<\/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\">The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let integers be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">2x<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">5x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Difference = 63<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>63<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x &#8211; 2x = 63<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo>=<\/mo><mn>63<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x = 63<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>21<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 21<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Numbers are:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>42<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x = 42<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>=<\/mo><mn>105<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x = 105<\/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 Integers are <strong>42 and 105<\/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\">Ruby has 3 times as many two-rupee coins as she has five-rupee coins. If she has a total \u20b988, how many coins does she have of each type?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let number of five-rupee coins = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of two-rupee coins = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">3x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total value:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>88<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x + 2(3x) = 88<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>+<\/mo><mn>6<\/mn><mi>x<\/mi><mo>=<\/mo><mn>88<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x + 6x = 88<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>11<\/mn><mi>x<\/mi><mo>=<\/mo><mn>88<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">11x = 88<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 8<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Two-rupee coins:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo>=<\/mo><mn>24<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x = 24<\/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 Five-rupee coins = <strong>8<\/strong><br>\u2705 Two-rupee coins = <strong>24<\/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 6<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let shorter piece = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math> feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Longer piece = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>4<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">4x<\/annotation><\/semantics><\/math> feet<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total length:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mi>x<\/mi><mo>=<\/mo><mn>300<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x + 4x = 300<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>=<\/mo><mn>300<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x = 300<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 60<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Longer piece:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mi>x<\/mi><mo>=<\/mo><mn>240<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4x = 240<\/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 Shorter piece = <strong>60 feet<\/strong><br>\u2705 Longer piece = <strong>240 feet<\/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 7<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let width = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math> cm<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x + 3<\/annotation><\/semantics><\/math> cm<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Perimeter formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mo>+<\/mo><mi>b<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>24<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2(l+b)=24<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute values:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo stretchy=\"false\">[<\/mo><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>x<\/mi><mo stretchy=\"false\">]<\/mo><mo>=<\/mo><mn>24<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2[(2x+3)+x]=24<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>24<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2(3x+3)=24<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mi>x<\/mi><mo>+<\/mo><mn>6<\/mn><mo>=<\/mo><mn>24<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6x+6=24<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mi>x<\/mi><mo>=<\/mo><mn>18<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6x=18<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x=3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Width = 3 cm<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2(3)+3=9<\/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 Width = <strong>3 cm<\/strong><br>\u2705 Length = <strong>9 cm<\/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 brackets during substitution<br>\u274c Wrong sign handling for negative numbers<br>\u274c Using incorrect perimeter formula<br>\u274c Confusing ratio with difference<\/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 variables clearly before solving<br>\u2714 Substitute values carefully<br>\u2714 Always verify final answers<br>\u2714 Practice word problems regularly<\/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. Find value of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x + 2<\/annotation><\/semantics><\/math> when <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 4<\/annotation><\/semantics><\/math><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) 10<br>B) 12<br>C) 14<br>D) 16<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 C) 14<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. Which is a quadratic polynomial?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x+1<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>5<\/mn><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2+5x+1<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7<\/annotation><\/semantics><\/math>7<br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><msup><mi>x<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">5x^3<\/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><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>5<\/mn><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2+5x+1<\/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\">3. Perimeter of rectangle 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><\/mrow><annotation encoding=\"application\/x-tex\">l+b<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mi>l<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">2l+b<\/annotation><\/semantics><\/math><br>C) <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><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>l<\/mi><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">lb<\/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><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<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. If ratio is 2:5, numbers can be written as:<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>+<\/mo><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">2+x<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mo>+<\/mo><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">5+x<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">2x<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">5x<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x\/2<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mi mathvariant=\"normal\">\/<\/mi><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x\/5<\/annotation><\/semantics><\/math><br>D) None<\/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>2<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">2x<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">5x<\/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 polynomial evaluation?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It means finding the value of a polynomial after substituting a variable value.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. What is a linear polynomial?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A polynomial having degree 1 is called a linear polynomial.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. What is a quadratic polynomial?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A polynomial having degree 2 is called a quadratic polynomial.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Why are word problems important?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">They improve logical thinking and real-life mathematical understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. Can negative numbers be substituted in polynomials?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Yes, negative values can also be substituted.<\/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 exam preparation materials on <strong><a target=\"_blank\" rel=\"noreferrer noopener\">MyMockMate<\/a><\/strong> and improve your Class 9 Mathematics performance 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\/2126?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\/2126?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 2.2 focuses on evaluating linear and quadratic polynomials and solving real-life word<\/p>\n","protected":false},"author":1,"featured_media":2127,"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":[681,684,668,136,92,685,679,677,686,688,687,678,680,682,683,673],"class_list":["post-2126","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","category-class-9","category-maths-class-9","tag-age-problems-maths","tag-algebra-solutions","tag-algebraic-expressions","tag-class-9-maths","tag-exercise-2-2-solutions","tag-grade-9-mathematics","tag-linear-equations","tag-linear-polynomials-solutions","tag-maths-chapter-2-exercise-2-2","tag-mymockmate-maths","tag-polynomial-evaluation","tag-polynomial-value-questions","tag-quadratic-polynomial-solutions","tag-ratio-problems-class-9","tag-rectangle-perimeter-questions","tag-step-by-step-maths-solutions"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2126","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=2126"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2126\/revisions"}],"predecessor-version":[{"id":2128,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2126\/revisions\/2128"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/2127"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=2126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=2126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=2126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}