{"id":35844,"date":"2025-09-25T10:32:25","date_gmt":"2025-09-25T02:32:25","guid":{"rendered":"https:\/\/blog-admin.thethinkacademy.com\/?p=35844"},"modified":"2026-04-27T17:06:56","modified_gmt":"2026-04-27T09:06:56","slug":"algebra-formulas-for-amc-8","status":"publish","type":"post","link":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2025\/09\/25\/algebra-formulas-for-amc-8\/","title":{"rendered":"Algebra Formula Worksheet: 7 Must-Know Algebra Formulas for AMC 8"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Introduction<\/strong><\/h2>\n\n\n\n<p>The <a href=\"https:\/\/www.thinkacademy.ca\/blog\/blog\/2026\/04\/15\/amc-8-math-competition-guide-for-parents\/\" target=\"_blank\" rel=\"noreferrer noopener\">AMC 8 math contest<\/a> challenges middle school students with tricky problems that go beyond school textbooks. <strong>Algebra alone makes up a big portion of the test<\/strong>\u2014from simple arithmetic identities to sequences and word problems. Therefore, it is important to learn algebra formulas for AMC 8 during the preparation.<\/p>\n\n\n\n<p>In this guide, we\u2019ll walk through an algebra formula worksheet with 7 must-know AMC 8 algebra formulas, each paired with a real AMC-8 problem, a quick solution, and a \u201cwhy it matters\u201d tip. By the end, you\u2019ll have a compact AMC 8 algebra formula sheet that\u2019s both practical and contest-ready.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/www.thinkacademy.ca\/amc-free-trial\" target=\"_blank\" rel=\" noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"744\" height=\"298\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.40-PM.png\" alt=\"Think Academy AMC 8 free evaluation banner \u2014 blue background with gold button reading &quot;Take the free evaluation&quot;\" class=\"wp-image-60940\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.40-PM.png 744w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.40-PM-300x120.png 300w\" sizes=\"auto, (max-width: 744px) 100vw, 744px\" \/><\/a><figcaption class=\"wp-element-caption\">Not sure where your child stands? Take Think Academy&#8217;s free math evaluation to find out.<\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>1.<\/strong><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/strong><strong>Basic Operations (Distributive, Commutative, Associative)<\/strong><\/h2>\n\n\n\n<p>Formulas:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"865\" height=\"389\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/1-1-1.png\" alt=\"Basic algebra formulas for AMC 8 including commutative and associative laws of addition and multiplication\" class=\"wp-image-35847\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/1-1-1.png 865w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/1-1-1-300x135.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/1-1-1-768x345.png 768w\" sizes=\"auto, (max-width: 865px) 100vw, 865px\" \/><\/figure>\n\n\n\n<p><strong>Example (AMC 8 2017, Problem 8)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/1-2.png\" alt=\"AMC 8 algebra problem example: two-digit house number puzzle with prime, even, divisible by 7, and digit 9 conditions\" class=\"wp-image-35864\"\/><\/figure>\n\n\n\n<p><strong>Why it matters:<\/strong> Long expressions collapse with grouping. Students who don\u2019t see the pattern often waste time adding term by term.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>2. Fractions and Ratios<\/strong><\/h2>\n\n\n\n<p>Formulas:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"870\" height=\"885\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/2-1.png\" alt=\"Fraction and ratio formulas for AMC 8 algebra, including addition, multiplication, division of fractions, ratios, and percentage rules\" class=\"wp-image-35851\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/2-1.png 870w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/2-1-295x300.png 295w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/2-1-768x781.png 768w\" sizes=\"auto, (max-width: 870px) 100vw, 870px\" \/><\/figure>\n\n\n\n<p><strong>Example (AMC 8 2020, Problem 15):<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"508\" height=\"124\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/2-2.png\" alt=\"AMC 8 algebra word problem example: percentage relationship between x and y, solving 15 percent of x equals 20 percent of y\" class=\"wp-image-35852\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/2-2.png 508w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/2-2-300x73.png 300w\" sizes=\"auto, (max-width: 508px) 100vw, 508px\" \/><\/figure>\n\n\n\n<p><strong>Why it matters:<\/strong> Percent word problems are common. The trick is setting up the correct ratio before calculating.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>3. Exponents and Quadratics<\/strong><\/h2>\n\n\n\n<p>Formulas:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"845\" height=\"321\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/3-1.png\" alt=\"Exponents formulas for AMC 8 algebra, including product rule, power of a power, power of a product, and power of a quotient\" class=\"wp-image-35853\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/3-1.png 845w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/3-1-300x114.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/3-1-768x292.png 768w\" sizes=\"auto, (max-width: 845px) 100vw, 845px\" \/><\/figure>\n\n\n\n<p><strong>Example (AMC 8 2019, Problem 20):<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"563\" height=\"155\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/3-2-1.png\" alt=\"AMC 8 algebra problem example: quadratic equation solving number of real solutions for (x squared minus 5) squared equals 16\" class=\"wp-image-35866\" style=\"width:805px;height:auto\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/3-2-1.png 563w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/3-2-1-300x83.png 300w\" sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/figure>\n\n\n\n<p><strong>Why it matters:<\/strong> Substitution is a contest lifesaver. Missing the \u201c\u00b1\u201d is a classic mistake.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/www.thinkacademy.ca\/amc-free-trial\" target=\"_blank\" rel=\" noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"728\" height=\"293\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.45-PM.png\" alt=\"Think Academy AMC 8 course banner \u2014 green background with teal button reading &quot;Find the right course&quot;\" class=\"wp-image-60941\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.45-PM.png 728w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.45-PM-300x121.png 300w\" sizes=\"auto, (max-width: 728px) 100vw, 728px\" \/><\/a><figcaption class=\"wp-element-caption\">Think Academy students have earned 1,700+ AMC 8 medals since 2021. Find the right course level for your child.<\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>4. Radicals (Nested Roots)<\/strong><\/h2>\n\n\n\n<p>Formula:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"843\" height=\"283\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/4-1.png\" alt=\"Radical operation formulas for AMC 8 algebra, including square root properties and simplifying expressions with radicals\" class=\"wp-image-35855\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/4-1.png 843w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/4-1-300x101.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/4-1-768x258.png 768w\" sizes=\"auto, (max-width: 843px) 100vw, 843px\" \/><\/figure>\n\n\n\n<p><strong>Example (AMC 8 2017, Problem 3):<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"673\" height=\"185\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/4-2.png\" alt=\"AMC 8 algebra problem example: nested square root expression with 16, 8, and 4, testing radical simplification skills\" class=\"wp-image-35856\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/4-2.png 673w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/4-2-300x82.png 300w\" sizes=\"auto, (max-width: 673px) 100vw, 673px\" \/><\/figure>\n\n\n\n<p><strong>Why it matters:<\/strong> Always work inside out. Skipping steps here almost always leads to mistakes.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>5. Absolute Value<\/strong><\/h2>\n\n\n\n<p>Formulas:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"830\" height=\"359\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-1.png\" alt=\"Absolute value formulas for AMC 8 algebra, including properties of negative, subtraction, multiplication, and division with absolute values\" class=\"wp-image-35857\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-1.png 830w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-1-300x130.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-1-768x332.png 768w\" sizes=\"auto, (max-width: 830px) 100vw, 830px\" \/><\/figure>\n\n\n\n<p><strong>Example (AMC 8 2017, Problem 21):<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"164\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-2-1024x164.png\" alt=\"AMC 8 algebra problem example: absolute value expression with variables a, b, c where a plus b plus c equals zero\" class=\"wp-image-35858\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-2-1024x164.png 1024w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-2-300x48.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-2-768x123.png 768w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/5-2.png 1094w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong>Why it matters:<\/strong> Absolute value problems often reduce to sign-case logic.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>6. Algebraic Operations (Special Products)<\/strong><\/h2>\n\n\n\n<p>Formulas:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"835\" height=\"245\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/6-1.png\" alt=\"Algebraic operations formulas for AMC 8 algebra, including difference of squares and expansion of binomials\" class=\"wp-image-35859\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/6-1.png 835w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/6-1-300x88.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/6-1-768x225.png 768w\" sizes=\"auto, (max-width: 835px) 100vw, 835px\" \/><\/figure>\n\n\n\n<p><strong>Example (AMC 8 2017, Problem 5):<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"746\" height=\"169\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/6-2.png\" alt=\"AMC 8 algebra problem example: evaluate factorial-style product 1 to 8 divided by the sum 1 plus 2 plus ... plus 8\" class=\"wp-image-35860\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/6-2.png 746w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/6-2-300x68.png 300w\" sizes=\"auto, (max-width: 746px) 100vw, 746px\" \/><\/figure>\n\n\n\n<p><strong>Why it matters:<\/strong> These identities save time when expanding or collapsing large expressions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>7. Arithmetic Sequences<\/strong><\/h2>\n\n\n\n<p>Formulas:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"853\" height=\"308\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/7-1.png\" alt=\"Arithmetic sequence formulas for AMC 8 algebra, including nth term formula, sum of n terms, and common difference calculation\" class=\"wp-image-35861\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/7-1.png 853w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/7-1-300x108.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/7-1-768x277.png 768w\" sizes=\"auto, (max-width: 853px) 100vw, 853px\" \/><\/figure>\n\n\n\n<p><strong>Example (AMC 8 2018, Problem 5):<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"599\" height=\"90\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/7-2.png\" alt=\"AMC 8 algebra problem example: alternating sum of odd and even numbers from 1 to 2019 minus 2 to 2018\" class=\"wp-image-35862\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/7-2.png 599w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2025\/09\/7-2-300x45.png 300w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/><\/figure>\n\n\n\n<p><strong>Why it matters:<\/strong> Count terms carefully\u2014miscounting is the #1 source of errors.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Wrap-Up: Turning Formulas into Points<\/strong><\/h2>\n\n\n\n<p>These 7 sections cover nearly all the algebra you\u2019ll face on AMC 8:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identities and operations<\/li>\n\n\n\n<li>Fractions and ratios<\/li>\n\n\n\n<li>Exponents and radicals<\/li>\n\n\n\n<li>Absolute value logic<\/li>\n\n\n\n<li>Sequences and special products<\/li>\n\n\n\n<li>Word problems (embedded throughout)<\/li>\n<\/ul>\n\n\n\n<p>With formulas in hand and practice on real AMC 8 questions, students can solve quickly and confidently.<\/p>\n\n\n\n<p>Looking for more real contest problems from AMC8? Check out this article: <a href=\"https:\/\/blog-admin.thethinkacademy.com\/amc-8-real-questions\/\">AMC 8 Real Questions 2025 Paper Analysis: Key Problems and How to Prepare<\/a>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>How Canadian Students Can Prepare<\/strong><\/h2>\n\n\n\n<p>At <strong>Think Academy Canada<\/strong>, our <a href=\"https:\/\/www.thinkacademy.ca\/amc-free-trial\">AMC 8 programs <\/a>guide students step by step:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Build strong foundations (fractions, equations)<\/li>\n\n\n\n<li>Practice past AMC 8 algebra problems under timed conditions<\/li>\n\n\n\n<li>Transition smoothly to AMC 10 and Waterloo contests<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/www.thinkacademy.ca\/amc-free-trial\" target=\"_blank\" rel=\" noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"711\" height=\"283\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.53-PM.png\" alt=\"Think Academy AMC 8 enrolment banner \u2014 purple background with gold &quot;Get started&quot; button and secondary &quot;Learn more&quot; button\" class=\"wp-image-60946\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.53-PM.png 711w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/04\/Screenshot-2026-04-14-at-12.30.53-PM-300x119.png 300w\" sizes=\"auto, (max-width: 711px) 100vw, 711px\" \/><\/a><figcaption class=\"wp-element-caption\">Expert teachers. Live classes. Proven results. Think Academy is an official AMC test centre \u2014 register and prepare in one place.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Introduction The AMC 8 math contest challenges middle school students with tricky problems that go beyond &hellip; <a title=\"Algebra Formula Worksheet: 7 Must-Know Algebra Formulas for AMC 8\" class=\"hm-read-more\" href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2025\/09\/25\/algebra-formulas-for-amc-8\/\"><span class=\"screen-reader-text\">Algebra Formula Worksheet: 7 Must-Know Algebra Formulas for AMC 8<\/span>Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":61488,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17153,1752,17160],"tags":[11668,11667,11670,11676,11673,11674,401,245,11672,11669,11671,11675,254],"class_list":["post-35844","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-amc-category","category-competitions","category-math-skills","tag-algebra-word-problems","tag-amc-8-algebra-formula-sheet","tag-amc-8-algebra-formulas","tag-amc-8-canada-prep","tag-amc-8-study-guide","tag-factoring-trinomials","tag-k-12-education","tag-k12-education","tag-linear-equation-word-problem","tag-quadratic-equation-word-problem","tag-radicals","tag-sequences","tag-thinkacademy"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>7 Must-Know Algebra Formulas for AMC 8 | Think Academy CA<\/title>\n<meta name=\"description\" content=\"Discover the 7 must-know Algebra Formulas for AMC 8. 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