{"id":22738,"date":"2026-09-29T06:53:16","date_gmt":"2026-09-29T06:53:16","guid":{"rendered":"https:\/\/oratrics.com\/blogs\/?p=22738"},"modified":"2026-09-29T09:01:17","modified_gmt":"2026-09-29T09:01:17","slug":"maths-olympiad-questions-for-class-10","status":"publish","type":"post","link":"https:\/\/oratrics.com\/blogs\/math-explorer-program\/maths-olympiad-questions-for-class-10\/","title":{"rendered":"Maths Olympiad Questions for Class 10 with Solutions"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"22738\" class=\"elementor elementor-22738\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-181a6ea elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"181a6ea\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-090fb46\" data-id=\"090fb46\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9ef6959\" data-id=\"9ef6959\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e784c54 elementor-widget elementor-widget-heading\" data-id=\"e784c54\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Maths Olympiad Questions for Class 10 with Solutions\n<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8f37457 elementor-widget elementor-widget-text-editor\" data-id=\"8f37457\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Here&#8217;s something many students notice on their first olympiad paper: every chapter looks familiar, but the questions don&#8217;t. You know the formula, yet you can&#8217;t see where to use it. That gap is exactly what <\/span><b>maths olympiad questions for class 10<\/b><span style=\"font-weight: 400;\"> are designed to test, and it closes only with practice.<\/span><\/p><p><span style=\"font-weight: 400;\">This article gives you 20 solved questions from the class 10 syllabus, each with a short note on what makes it tricky, and five more for you to solve alone. Try each question first. Even five honest minutes of trying teaches you more than reading the answer straight away.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-06e0c4f elementor-align-center elementor-widget elementor-widget-button\" data-id=\"06e0c4f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/demo.oratrics.com\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Book a Free Demo Today<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ab6b303 elementor-widget elementor-widget-image\" data-id=\"ab6b303\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"647\" src=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/09\/ChatGPT-Image-Sep-29-2026-01_52_58-PM-1024x647.webp\" class=\"attachment-large size-large wp-image-22842\" alt=\"Maths Olympiad questions for Class 10 featuring a student solving challenging mathematics problems with geometry and equations in the background.\" srcset=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/09\/ChatGPT-Image-Sep-29-2026-01_52_58-PM-1024x647.webp 1024w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/09\/ChatGPT-Image-Sep-29-2026-01_52_58-PM-300x190.webp 300w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/09\/ChatGPT-Image-Sep-29-2026-01_52_58-PM-768x486.webp 768w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/09\/ChatGPT-Image-Sep-29-2026-01_52_58-PM-1536x971.webp 1536w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/09\/ChatGPT-Image-Sep-29-2026-01_52_58-PM.webp 1577w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-316e145\" data-id=\"316e145\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-69afd53 elementor-widget elementor-widget-html\" data-id=\"69afd53\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Poppins:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\r\n\r\n<div class=\"toc-wrapper\">\r\n    \r\n    \r\n    <div class=\"custom-toc\" id=\"custom-toc\">\r\n        <div class=\"toc-title\">\r\n            \u2630 Table of Contents\r\n        <\/div>\r\n        <ul class=\"toc-list\" id=\"toc-list\"><\/ul>\r\n    <\/div>\r\n    \r\n<\/div>\r\n\r\n<style>\r\n\/* Parent Fixed Wrapper holding both components together *\/\r\n.toc-wrapper {\r\n    position: fixed;\r\n    top: 150px; 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\r\n        overflow-y: visible;\r\n    }\r\n\r\n    .custom-toc .toc-title {\r\n        font-size: 25px;\r\n    }\r\n\r\n    .custom-toc .toc-list a {\r\n        font-size: 14px;\r\n    }\r\n}\r\n<\/style>\r\n\r\n<script>\r\ndocument.addEventListener(\"DOMContentLoaded\", function () {\r\n    const tocList = document.getElementById(\"toc-list\");\r\n    const h1 = document.querySelector(\"h1\");\r\n    const h2s = document.querySelectorAll(\"h2\");\r\n\r\n    function createId(text) {\r\n        return text.toLowerCase().replace(\/[^a-z0-9]+\/g, '-');\r\n    }\r\n\r\n    if (h1) {\r\n        if (!h1.id) {\r\n            h1.id = createId(h1.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.innerHTML = `<a href=\"#${h1.id}\">${h1.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    }\r\n\r\n    h2s.forEach(h2 => {\r\n        if (!h2.id) {\r\n            h2.id = createId(h2.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.classList.add(\"toc-h2\");\r\n        li.innerHTML = `<a href=\"#${h2.id}\">${h2.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    });\r\n});\r\n<\/script>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-54478db elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"54478db\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ddf9ba7\" data-id=\"ddf9ba7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6551354\" data-id=\"6551354\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-518a04b elementor-widget elementor-widget-heading\" data-id=\"518a04b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">What Is a Maths Olympiad?\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a92806c elementor-widget elementor-widget-text-editor\" data-id=\"a92806c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">A maths olympiad tests how well you can reason, not how many formulas you can recall. Class 10 students in India usually hear about two exams. The International Mathematics Olympiad (IMO), conducted by the Science Olympiad Foundation (SOF), is open to school students. The Indian Olympiad Qualifier in Mathematics (IOQM) is the first step towards the national and international olympiads.<\/span><\/p><p><span style=\"font-weight: 400;\">Why is it worth attempting?<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It strengthens your basics, which helps in your board exam.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It builds speed and the habit of staying calm under time pressure.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It gives you a head start for NTSE, JEE and scholarship tests.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It looks good on your academic record.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-babd253\" data-id=\"babd253\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ce31b6e elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"ce31b6e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-a3914dd\" data-id=\"a3914dd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-45ea2df\" data-id=\"45ea2df\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-488d39c elementor-widget elementor-widget-heading\" data-id=\"488d39c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">What to Study\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fda4ae9 elementor-widget elementor-widget-text-editor\" data-id=\"fda4ae9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">You don&#8217;t need to learn anything new. Most questions come from these chapters:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Real Numbers<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Polynomials and Quadratic Equations<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Pair of Linear Equations<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Arithmetic Progressions<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Triangles and Circles<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Coordinate Geometry<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Trigonometry and its Applications<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Surface Areas and Volumes<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Statistics and Probability<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Papers also include logical reasoning, mathematical reasoning, everyday mathematics and a harder achievers section. Formats change from time to time, so confirm the latest pattern on the official website.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ca9d14e\" data-id=\"ca9d14e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a885052 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"a885052\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-eee478c\" data-id=\"eee478c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6cc5c52\" data-id=\"6cc5c52\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f56fcd6 elementor-widget elementor-widget-heading\" data-id=\"f56fcd6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Maths Olympiad Questions for Class 10 with Answers\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b7deb6 elementor-widget elementor-widget-text-editor\" data-id=\"9b7deb6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<h4><b>Real Numbers<\/b><\/h4><p><b>Q1. Find the HCF and LCM of 96 and 404 using prime factorisation. Then check that HCF \u00d7 LCM equals 96 \u00d7 404.<\/b><\/p><p><span style=\"font-weight: 400;\">96 = 2\u2075 \u00d7 3 and 404 = 2\u00b2 \u00d7 101.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> HCF = 2\u00b2 = <\/span><b>4<\/b><b><br \/><\/b><span style=\"font-weight: 400;\"> LCM = 2\u2075 \u00d7 3 \u00d7 101 = <\/span><b>9696<\/b><b><br \/><\/b><span style=\"font-weight: 400;\"> Check: 4 \u00d7 9696 = 38,784 = 96 \u00d7 404.<\/span><\/p><p><i><span style=\"font-weight: 400;\">Watch out:<\/span><\/i><span style=\"font-weight: 400;\"> HCF takes the smallest power of each common prime, LCM takes the biggest power of every prime.<\/span><\/p><p><b>Q2. Find the smallest number that leaves remainder 5 when divided by 12, 15 and 20.<\/b><\/p><p><span style=\"font-weight: 400;\">The LCM of 12, 15 and 20 is 60. Any multiple of 60 leaves remainder 0, so add 5.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Answer: <\/span><b>65<\/b><\/p><p><b>Q3. How many zeros are there at the end of 100!?<\/b><\/p><p><span style=\"font-weight: 400;\">Each zero needs a 2 and a 5. Twos are plentiful, so count the fives:<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> \u230a100\/5\u230b + \u230a100\/25\u230b = 20 + 4 = 24<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Answer: <\/span><b>24 zeros<\/b><\/p><p><i><span style=\"font-weight: 400;\">Watch out:<\/span><\/i><span style=\"font-weight: 400;\"> Many students stop at 20 and forget that 25, 50, 75 and 100 each carry an extra 5.<\/span><\/p><h4><b>Polynomials and Quadratic Equations<\/b><\/h4><p><b>Q4. If \u03b1 and \u03b2 are the zeros of 2x\u00b2 \u2212 7x + 3, find \u03b1\u00b2 + \u03b2\u00b2.<\/b><\/p><p><span style=\"font-weight: 400;\">\u03b1 + \u03b2 = 7\/2 and \u03b1\u03b2 = 3\/2.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> \u03b1\u00b2 + \u03b2\u00b2 = (\u03b1 + \u03b2)\u00b2 \u2212 2\u03b1\u03b2 = 49\/4 \u2212 3 = <\/span><b>37\/4<\/b><\/p><p><b>Q5. If x + 1\/x = 3, find x\u00b3 + 1\/x\u00b3.<\/b><\/p><p><span style=\"font-weight: 400;\">Use a\u00b3 + b\u00b3 = (a + b)\u00b3 \u2212 3ab(a + b) with a = x, b = 1\/x. Here ab = 1.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> x\u00b3 + 1\/x\u00b3 = 27 \u2212 9 = <\/span><b>18<\/b><\/p><p><b>Q6. For what value of k does 2x\u00b2 + kx + 3 = 0 have equal roots?<\/b><\/p><p><span style=\"font-weight: 400;\">Set the discriminant to zero: k\u00b2 \u2212 24 = 0, so k = <\/span><b>\u00b12\u221a6<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Q7. The product of two consecutive positive integers is 306. Find them.<\/b><\/p><p><span style=\"font-weight: 400;\">Let them be n and n + 1. Then n\u00b2 + n \u2212 306 = 0, which gives (n + 18)(n \u2212 17) = 0.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Since n is positive, the integers are <\/span><b>17 and 18<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h4><b>Pair of Linear Equations<\/b><\/h4><p><b>Q8. Solve 2x + 3y = 11 and 2x \u2212 4y = \u221224. Then find m if y = mx + 3.<\/b><\/p><p><span style=\"font-weight: 400;\">Subtract the equations: 7y = 35, so y = 5. Then 2x + 15 = 11, so x = \u22122.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Put both in y = mx + 3: 5 = \u22122m + 3, so <\/span><b>m = \u22121<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h4><b>Arithmetic Progressions<\/b><\/h4><p><b>Q9. Find the sum of the first 20 terms of 3, 7, 11, 15, \u2026<\/b><\/p><p><span style=\"font-weight: 400;\">a = 3, d = 4, n = 20.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> S\u2082\u2080 = 10 \u00d7 [6 + 76] = <\/span><b>820<\/b><\/p><p><b>Q10. Which term of the AP 5, 11, 17, 23, \u2026 is 131?<\/b><\/p><p><span style=\"font-weight: 400;\">5 + (n \u2212 1)6 = 131, so n \u2212 1 = 21 and n = 22.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> It is the <\/span><b>22nd term<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Q11. Find the sum of all two-digit numbers divisible by 7.<\/b><\/p><p><span style=\"font-weight: 400;\">The list is 14, 21, \u2026, 98. From 98 = 14 + (n \u2212 1)7, n = 13.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Sum = 13\/2 \u00d7 (14 + 98) = <\/span><b>728<\/b><\/p><h4><b>Triangles<\/b><\/h4><p><b>Q12. In triangle ABC, DE \u2225 BC, with D on AB and E on AC. If AD = 4 cm, DB = 6 cm and AE = 6 cm, find EC.<\/b><\/p><p><span style=\"font-weight: 400;\">By the Basic Proportionality Theorem, AD\/DB = AE\/EC.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> 4\/6 = 6\/EC, so EC = <\/span><b>9 cm<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Q13. The areas of two similar triangles are in the ratio 16 : 25. If the larger triangle&#8217;s perimeter is 50 cm, find the smaller one&#8217;s perimeter.<\/b><\/p><p><span style=\"font-weight: 400;\">Areas are in the ratio of squared sides, so the sides are in the ratio 4 : 5. Perimeters share that ratio.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> (4\/5) \u00d7 50 = <\/span><b>40 cm<\/b><\/p><p><b>Q14. A right triangle has legs 5 cm and 12 cm. Find the altitude to the hypotenuse.<\/b><\/p><p><span style=\"font-weight: 400;\">Hypotenuse = 13 cm and area = 30 cm\u00b2. Using the hypotenuse as base, \u00bd \u00d7 13 \u00d7 h = 30.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> h = <\/span><b>60\/13 cm<\/b><span style=\"font-weight: 400;\">, about 4.62 cm.<\/span><\/p><h4><b>Coordinate Geometry<\/b><\/h4><p><b>Q15. Find the point on the x-axis equidistant from (2, \u22125) and (\u22122, 9).<\/b><\/p><p><span style=\"font-weight: 400;\">Let the point be (x, 0) and equate squared distances:<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> (x \u2212 2)\u00b2 + 25 = (x + 2)\u00b2 + 81<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> \u22124x + 29 = 4x + 85, so x = \u22127.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> The point is <\/span><b>(\u22127, 0)<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Q16. Find the area of the triangle with vertices (1, 2), (4, 6) and (7, 2).<\/b><\/p><p><span style=\"font-weight: 400;\">Area = \u00bd |1(6 \u2212 2) + 4(2 \u2212 2) + 7(2 \u2212 6)| = \u00bd \u00d7 24 = <\/span><b>12 square units<\/b><span style=\"font-weight: 400;\">.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Check: base 6, height 4, so \u00bd \u00d7 6 \u00d7 4 = 12.<\/span><\/p><h4><b>Trigonometry<\/b><\/h4><p><b>Q17. Find sin\u00b21\u00b0 + sin\u00b22\u00b0 + sin\u00b23\u00b0 + \u2026 + sin\u00b289\u00b0.<\/b><\/p><p><span style=\"font-weight: 400;\">Pair the first term with the last: sin\u00b21\u00b0 + sin\u00b289\u00b0 = sin\u00b21\u00b0 + cos\u00b21\u00b0 = 1. This works for 44 pairs (1\u00b0 to 44\u00b0), and sin\u00b245\u00b0 = 1\/2 is left in the middle.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Total = <\/span><b>44.5<\/b><\/p><p><i><span style=\"font-weight: 400;\">Watch out:<\/span><\/i><span style=\"font-weight: 400;\"> Students often count 45 pairs. Remember that 45\u00b0 pairs with itself.<\/span><\/p><p><b>Q18. Prove that (sin \u03b8 + cosec \u03b8)\u00b2 + (cos \u03b8 + sec \u03b8)\u00b2 = 7 + tan\u00b2\u03b8 + cot\u00b2\u03b8.<\/b><\/p><p><span style=\"font-weight: 400;\">Expand the left side:<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> sin\u00b2\u03b8 + 2 + cosec\u00b2\u03b8 + cos\u00b2\u03b8 + 2 + sec\u00b2\u03b8<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> = 1 + 4 + (1 + cot\u00b2\u03b8) + (1 + tan\u00b2\u03b8)<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> = 7 + tan\u00b2\u03b8 + cot\u00b2\u03b8. Proved.<\/span><\/p><p><b>Q19. From a point 30 m from the foot of a tower, the angle of elevation of the top is 60\u00b0. Find the height.<\/b><\/p><p><span style=\"font-weight: 400;\">tan 60\u00b0 = h\/30, so h = 30\u221a3 \u2248 <\/span><b>51.96 m<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h4><b>Circles<\/b><\/h4><p><b>Q20. PA and PB are tangents from an external point P to a circle with centre O. If \u2220APB = 80\u00b0, find \u2220OAB.<\/b><\/p><p><span style=\"font-weight: 400;\">The radius meets the tangent at 90\u00b0, so \u2220OAP = \u2220OBP = 90\u00b0. In quadrilateral OAPB, \u2220AOB = 360\u00b0 \u2212 90\u00b0 \u2212 90\u00b0 \u2212 80\u00b0 = 100\u00b0.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> OA = OB, so \u2220OAB = (180\u00b0 \u2212 100\u00b0)\/2 = <\/span><b>40\u00b0<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6a1ce3d\" data-id=\"6a1ce3d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-001ad73 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"001ad73\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9bbfd05\" data-id=\"9bbfd05\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-3eb5e7b\" data-id=\"3eb5e7b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-712c645 elementor-widget elementor-widget-heading\" data-id=\"712c645\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Try These Yourself\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-58df494 elementor-widget elementor-widget-text-editor\" data-id=\"58df494\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Two concentric circles have radii 5 cm and 3 cm. Find the length of the chord of the larger circle that touches the smaller one. <\/span><i><span style=\"font-weight: 400;\">(Answer: 8 cm)<\/span><\/i><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A cone has radius 7 cm and height 24 cm. Find its curved surface area. <\/span><i><span style=\"font-weight: 400;\">(Answer: 550 cm\u00b2)<\/span><\/i><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A metal sphere of radius 3 cm is melted and recast into a cylinder of radius 1 cm. Find the cylinder&#8217;s height. <\/span><i><span style=\"font-weight: 400;\">(Answer: 36 cm)<\/span><\/i><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Two dice are thrown together. What is the probability that the sum is a prime number? <\/span><i><span style=\"font-weight: 400;\">(Answer: 5\/12)<\/span><\/i><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The mean of five numbers is 27. After one number is removed, the mean of the other four is 25. Find the removed number. <\/span><i><span style=\"font-weight: 400;\">(Answer: 35)<\/span><\/i><\/li><\/ol><p><span style=\"font-weight: 400;\">A set like this makes good practice maths olympiad questions for 10th graders, especially right after you finish a chapter.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-996b0c3\" data-id=\"996b0c3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0e27bfe elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"0e27bfe\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-fc2825f\" data-id=\"fc2825f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-00a9623\" data-id=\"00a9623\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-08fe59a elementor-widget elementor-widget-heading\" data-id=\"08fe59a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Where to Find Maths Olympiad Past Papers for Class 10\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ea72889 elementor-widget elementor-widget-text-editor\" data-id=\"ea72889\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">An actual paper shows you the true difficulty better than any guide. If you&#8217;re wondering where to find maths olympiad past papers for class 10, try these:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Official olympiad websites.<\/b><span style=\"font-weight: 400;\"> The SOF site usually lists sample and earlier papers, but availability changes, so check the current page.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>HBCSE (Homi Bhabha Centre for Science Education).<\/b><span style=\"font-weight: 400;\"> Its site shares previous question papers for IOQM and later stages.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Your school or coaching centre.<\/b><span style=\"font-weight: 400;\"> Teachers often keep old papers and mock tests.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Olympiad workbooks.<\/b><span style=\"font-weight: 400;\"> These give chapter-wise questions with full solutions.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Much of this material is shared as a class 10 maths olympiad problems PDF, which is easy to print and solve offline. Use trusted sources only, since a wrong answer key can teach you a wrong method.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-59d5e0a\" data-id=\"59d5e0a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0b22ad1 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"0b22ad1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6e5e025\" data-id=\"6e5e025\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f43fa0c\" data-id=\"f43fa0c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-36c6876 elementor-widget elementor-widget-heading\" data-id=\"36c6876\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">How to Practise Well\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-add608a elementor-widget elementor-widget-text-editor\" data-id=\"add608a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Reading solutions feels like progress, but solving is what builds skill.<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Finish NCERT first.<\/b><span style=\"font-weight: 400;\"> Olympiad problems are built on the same ideas.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Struggle for a while.<\/b><span style=\"font-weight: 400;\"> Give each question 5 to 10 minutes before checking.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Keep a mistake notebook.<\/b><span style=\"font-weight: 400;\"> Write down formulas, tricks and repeated errors.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Go chapter by chapter, then attempt timed papers.<\/b><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Redo wrong questions after a few days.<\/b><span style=\"font-weight: 400;\"> If you can solve them cold, you&#8217;ve learned them.<\/span><\/li><\/ol><p><span style=\"font-weight: 400;\">Using 10th class mathematics olympiad sample questions this way improves your speed and your confidence together.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-44e5048\" data-id=\"44e5048\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1e5b4e1 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"1e5b4e1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9a975e4\" data-id=\"9a975e4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-854a512\" data-id=\"854a512\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cef3dcf elementor-widget elementor-widget-heading\" data-id=\"cef3dcf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Common Mistakes\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d8efa1e elementor-widget elementor-widget-text-editor\" data-id=\"d8efa1e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Attempting hard problems before the basics are firm.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Reading word problems too fast and missing a condition.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Making small calculation slips.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Skipping the reasoning and everyday maths sections.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Guessing without first removing options that are clearly wrong.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-62197d8\" data-id=\"62197d8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-78e8c57 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"78e8c57\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-3a3e645\" data-id=\"3a3e645\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-80accc4\" data-id=\"80accc4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f17cb34 elementor-widget elementor-widget-heading\" data-id=\"f17cb34\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Exam Day Tips\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3540da4 elementor-widget elementor-widget-text-editor\" data-id=\"3540da4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Begin with the questions you find easy.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">In MCQs, cross out options you know are wrong.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Recheck signs and units.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">If one question eats five minutes, move on and return later.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Stay calm. Panic costs more marks than difficulty.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-04bc8ca\" data-id=\"04bc8ca\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2d8fc1f elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"2d8fc1f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-bf372e8\" data-id=\"bf372e8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9544eee\" data-id=\"9544eee\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8acef63 elementor-widget elementor-widget-heading\" data-id=\"8acef63\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73143c4 elementor-widget elementor-widget-text-editor\" data-id=\"73143c4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">There are no shortcuts here. Solve a few problems every day, learn from what you get wrong, and slowly move to full timed papers. Be patient with yourself. In a few weeks, maths olympiad questions for class 10 will feel far less intimidating, and your school exams will likely feel easier too.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ce91203\" data-id=\"ce91203\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6920acf elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"6920acf\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ab3ff72\" data-id=\"ab3ff72\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c2286c8\" data-id=\"c2286c8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eeb1bca elementor-widget elementor-widget-heading\" data-id=\"eeb1bca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Frequently Asked Questions\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e89b37e elementor-widget elementor-widget-accordion\" data-id=\"e89b37e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2431\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2431\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Are olympiad questions harder than board exam questions?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2431\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2431\"><p><span style=\"font-weight: 400;\">Usually yes. The syllabus overlaps, but you have to apply ideas in unfamiliar ways.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2432\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2432\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How much should I practise daily?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2432\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2432\"><p><span style=\"font-weight: 400;\">One to two hours of focused work, along with regular school study, is enough for most students.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2433\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-2433\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Is NCERT enough?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2433\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-2433\"><p><span style=\"font-weight: 400;\">It&#8217;s the foundation. Add a workbook and previous papers for extra practice.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2434\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-2434\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Can I find maths olympiad questions for class 10 with answers online?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2434\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-2434\"><p><span style=\"font-weight: 400;\">Yes. Official sample papers, workbooks and teacher-made worksheets often include answers. Study the method, not only the final answer.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Are olympiad questions harder than board exam questions?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Usually yes. The syllabus overlaps, but you have to apply ideas in unfamiliar ways.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"How much should I practise daily?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">One to two hours of focused work, along with regular school study, is enough for most students.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Is NCERT enough?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">It&#8217;s the foundation. Add a workbook and previous papers for extra practice.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Can I find maths olympiad questions for class 10 with answers online?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Yes. Official sample papers, workbooks and teacher-made worksheets often include answers. Study the method, not only the final answer.<\\\/span><\\\/p>\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-8671fbe\" data-id=\"8671fbe\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Maths Olympiad Questions for Class 10 with Solutions Here&#8217;s something many students notice on their first olympiad paper: every chapter [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":22842,"comment_status":"open","ping_status":"open","sticky":false,"template":"rttpg_full_width","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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