{"id":50973,"date":"2025-08-05T10:12:38","date_gmt":"2025-08-05T02:12:38","guid":{"rendered":"https:\/\/www.wukongsch.com\/blog\/?p=50973"},"modified":"2026-08-19T10:31:54","modified_gmt":"2026-08-19T02:31:54","slug":"2025-amc-8-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/www.wukongsch.com\/blog\/2025-amc-8-problems-and-solutions-post-50973\/","title":{"rendered":"2025 AMC 8 Problems and Answers"},"content":{"rendered":"<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>\n<p>The <strong>2025 AMC\u202f8<\/strong>, held between <strong>January\u202f22 and 28, 2025<\/strong>, once again encouraged thousands of students to test their mettle in creative mathematics under time constraints. Prepared by expert instructors from the <strong><a href=\"https:\/\/www.wukongsch.com\/learn-math\/amc-8\/\" target=\"_blank\" rel=\"noreferrer noopener\">WuKong AMC 8 Course<\/a><\/strong>, this complete answer key and solution analysis provides clear breakdowns for all 25 questions.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/image-161-1024x683.png\" alt=\"AMC 8 2025\" class=\"wp-image-50974\" style=\"width:554px;height:auto\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/image-161-1024x683.png 1024w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/image-161-300x200.png 300w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/image-161-768x512.png 768w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/image-161-920x613.png 920w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/image-161.png 1200w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"1-2025-amc-8-problems-and-answers\"><\/span>1. 2025 AMC 8 Problems and Answers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Here we have provided the real exam questions and their answers. If you want to learn the solution methods, please visit <a href=\"https:\/\/www.wukongsch.com\/math\/\">WuKong Math<\/a>.<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/AMC2025\u771f\u9898.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of &lt;strong&gt;2025 AMC 8 Problems and Answers&lt;\/strong&gt;.\"><\/object><a id=\"wp-block-file--media-8c3a4fd8-fc1f-4682-9ca0-bf0868393235\" href=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/AMC2025\u771f\u9898.pdf\"><strong>2025 AMC 8 Problems and Answers<\/strong><\/a><a href=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/08\/AMC2025\u771f\u9898.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-8c3a4fd8-fc1f-4682-9ca0-bf0868393235\">Download<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"2-2025-amc-8-topic-distribution\"><\/span>2. 2025 AMC 8 Topic Distribution<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Below is a visual text-based representation of the topic breakdown across the 25 problems contained in the exam paper:<\/p>\n\n\n<div class=\"retention-card-new\" data-lang=\"en\" data-subject=\"MATH\" data-btnName=\"Get started free!\" data-subTitle=\"Suitable for students worldwide, from grades K-12.\">\r\n    <div class=\"retention-card-l\">\r\n        <div class=\"trustpilot-image\">\r\n            <!-- TrustBox widget - Micro Star -->\r\n            <div class=\"trustpilot-widget\" data-locale=\"en-US\" data-template-id=\"5419b732fbfb950b10de65e5\" data-businessunit-id=\"60c847b7f033d300019ff3a1\" data-style-height=\"24px\" data-style-width=\"272px\" data-token=\"7dc9fdab-8926-4826-ad90-81ab38cc0953\">\r\n              <a href=\"https:\/\/www.trustpilot.com\/review\/wukongsch.com\" target=\"_blank\" rel=\"noopener\">Trustpilot<\/a>\r\n            <\/div>\r\n            <!-- End TrustBox widget -->\r\n        <\/div>\r\n        <h3><p>Discovering the maths whiz in every child,<br \/>\n<span>that&#8217;s what we do.<\/span><\/p>\n<\/h3>\r\n        <p>Suitable for students worldwide, from grades K-12.<\/p>\r\n        <a class=\"retention-card-button is-point\" href=\"https:\/\/www.wukongsch.com\/independent-appointment\/?subject=math&amp;l=eafd8b18-486b-4e0a-b93d-4105d41d2067&amp;booking_triggerevent=BLOG_DETAIL_MODEL_CTA_BUTTON\" data-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u70b9\u51fb\" data-event=\"C_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" data-expose-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u66dd\u5149\" data-expose-event=\"D_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" target=\"_blank\" title=\"Get started free!\">\r\n            Get started free!\r\n        <\/a>\r\n    <\/div>\r\n    <div class=\"retention-card-r\"><\/div>\r\n<\/div>\n\n\n<div id=\"wk-amc-2025-container\">\n    <div class=\"wk-amc-card\">\n        <!-- \u4f7f\u7528\u81ea\u5b9a\u4e49\u7c7b\u540d\u4ee3\u66ff H \u6807\u7b7e\uff0c\u5f7b\u5e95\u907f\u514d\u4e3b\u9898\u6837\u5f0f\u5e72\u6270 -->\n        <div class=\"wk-amc-section-title\">2025 AMC 8 Topic Distribution<\/div>\n\n        <div class=\"wk-amc-dashboard\">\n            <!-- \u997c\u56fe\u533a\u57df -->\n            <div class=\"wk-amc-pie-area\">\n                <canvas id=\"wkAmc25Canvas\"><\/canvas>\n            <\/div>\n\n            <!-- \u56fe\u4f8b\u533a\u57df -->\n            <div class=\"wk-amc-legend-area\">\n                <ul class=\"wk-amc-legend-list\" id=\"wkAmc25Legend\">\n                    <!-- JS \u52a8\u6001\u6e32\u67d3 -->\n                <\/ul>\n            <\/div>\n        <\/div>\n    <\/div>\n\n    <style>\n        \/* \u6839\u5bb9\u5668\u9694\u79bb *\/\n        #wk-amc-2025-container {\n            margin: 20px auto;\n            padding: 10px;\n            max-width: 880px;\n            font-family: 'Inter', system-ui, -apple-system, BlinkMacSystemFont, \"Segoe UI\", Roboto, sans-serif;\n            color: #1a3c5e;\n            line-height: 1.5;\n            clear: both; \/* \u907f\u514d\u6d6e\u52a8\u51b2\u7a81 *\/\n        }\n\n        \/* \u5185\u90e8\u5143\u7d20\u91cd\u7f6e\uff0c\u4e0d\u5f71\u54cd\u5916\u90e8 *\/\n        #wk-amc-2025-container * {\n            box-sizing: border-box;\n            margin: 0;\n            padding: 0;\n        }\n\n        #wk-amc-2025-container .wk-amc-card {\n            background: #ffffff;\n            border-radius: 24px;\n            box-shadow: 0 10px 30px rgba(0, 0, 0, 0.05);\n            border: 1px solid #f0f4f8;\n            padding: 30px;\n        }\n\n        #wk-amc-2025-container .wk-amc-section-title {\n            font-size: 1.5rem;\n            font-weight: 700;\n            color: #1e293b;\n            margin-bottom: 25px;\n            padding-left: 15px;\n            border-left: 5px solid #6fb3e0;\n            line-height: 1.2;\n        }\n\n        #wk-amc-2025-container .wk-amc-dashboard {\n            display: flex;\n            flex-wrap: wrap;\n            gap: 30px;\n            align-items: center;\n            justify-content: center;\n        }\n\n        #wk-amc-2025-container .wk-amc-pie-area {\n            flex: 0 0 auto;\n            display: flex;\n            justify-content: center;\n        }\n\n        #wk-amc-2025-container canvas {\n            display: block;\n            width: 280px; \/* CSS \u63a7\u5236\u663e\u793a\u5c3a\u5bf8 *\/\n            height: 280px;\n        }\n\n        #wk-amc-2025-container .wk-amc-legend-area {\n            flex: 1;\n            min-width: 280px;\n        }\n\n        #wk-amc-2025-container .wk-amc-legend-list {\n            list-style: none !important;\n            display: flex;\n            flex-direction: column;\n            gap: 12px;\n        }\n\n        #wk-amc-2025-container .wk-amc-legend-item {\n            display: flex;\n            align-items: center;\n            gap: 12px;\n            padding: 12px 16px;\n            background: #f8fbff;\n            border-radius: 12px;\n            transition: transform 0.2s ease;\n        }\n\n        #wk-amc-2025-container .wk-amc-legend-item:hover {\n            transform: translateX(5px);\n            background: #f1f7ff;\n        }\n\n        #wk-amc-2025-container .wk-amc-color-badge {\n            width: 14px;\n            height: 14px;\n            border-radius: 4px;\n            flex-shrink: 0;\n            box-shadow: 0 1px 2px rgba(0,0,0,0.1);\n        }\n\n        #wk-amc-2025-container .wk-amc-topic-content {\n            flex: 1;\n            font-size: 0.95rem;\n            font-weight: 500;\n            color: #334155;\n        }\n\n        #wk-amc-2025-container .wk-amc-stat {\n            font-size: 0.85rem;\n            color: #64748b;\n            background: #fff;\n            padding: 2px 10px;\n            border-radius: 20px;\n            border: 1px solid #e2e8f0;\n            white-space: nowrap;\n        }\n\n        \/* \u79fb\u52a8\u7aef\u9002\u914d *\/\n        @media (max-width: 600px) {\n            #wk-amc-2025-container .wk-amc-card { padding: 20px; }\n            #wk-amc-2025-container .wk-amc-dashboard { flex-direction: column; }\n            #wk-amc-2025-container canvas { width: 240px; height: 240px; }\n            #wk-amc-2025-container .wk-amc-legend-area { width: 100%; }\n        }\n    <\/style>\n\n    <script>\n    (function() {\n        const data = [\n            { label: \"Algebra & Pre-Algebra\", count: 9, percent: 36, color: \"#5A9BC7\" },\n            { label: \"Combinatorics & Probability\", count: 8, percent: 32, color: \"#7EB5D9\" },\n            { label: \"Geometry\", count: 5, percent: 20, color: \"#9DC8E8\" },\n            { label: \"Number Theory\", count: 3, percent: 12, color: \"#C0DDF5\" }\n        ];\n\n        const canvas = document.getElementById('wkAmc25Canvas');\n        if (!canvas) return;\n\n        const ctx = canvas.getContext('2d');\n        const dpr = window.devicePixelRatio || 1;\n        const size = 300; \/\/ \u5185\u90e8\u903b\u8f91\u5206\u8fa8\u7387\n        \n        \/\/ \u5904\u7406\u9ad8\u6e05\u5c4f\u6a21\u7cca\u95ee\u9898\n        canvas.width = size * dpr;\n        canvas.height = size * dpr;\n        ctx.scale(dpr, dpr);\n\n        function drawPie() {\n            let startAngle = -Math.PI \/ 2;\n            const centerX = size \/ 2;\n            const centerY = size \/ 2;\n            const radius = 135;\n\n            data.forEach(item => {\n                const sliceAngle = (item.count \/ 25) * Math.PI * 2;\n                \n                ctx.beginPath();\n                ctx.moveTo(centerX, centerY);\n                ctx.arc(centerX, centerY, radius, startAngle, startAngle + sliceAngle);\n                ctx.closePath();\n                \n                ctx.fillStyle = item.color;\n                ctx.fill();\n\n                \/\/ \u767d\u8272\u8fb9\u6846\u7ebf\n                ctx.strokeStyle = \"#ffffff\";\n                ctx.lineWidth = 2;\n                ctx.stroke();\n\n                startAngle += sliceAngle;\n            });\n\n            \/\/ \u7ed8\u5236\u5185\u5706\u88c5\u9970\uff08\u73af\u5f62\u6548\u679c\uff0c\u66f4\u73b0\u4ee3\uff09\n            ctx.beginPath();\n            ctx.arc(centerX, centerY, 60, 0, Math.PI * 2);\n            ctx.fillStyle = \"#ffffff\";\n            ctx.fill();\n        }\n\n        function renderLegend() {\n            const legendEl = document.getElementById('wkAmc25Legend');\n            if (!legendEl) return;\n            legendEl.innerHTML = data.map(item => `\n                <li class=\"wk-amc-legend-item\">\n                    <div class=\"wk-amc-color-badge\" style=\"background: ${item.color}\"><\/div>\n                    <span class=\"wk-amc-topic-content\">${item.label}<\/span>\n                    <span class=\"wk-amc-stat\">${item.percent}% (${item.count}\/25)<\/span>\n                <\/li>\n            `).join('');\n        }\n\n        \/\/ \u521d\u59cb\u5316\n        drawPie();\n        renderLegend();\n\n        \/\/ \u7a97\u53e3\u7f29\u653e\u91cd\u7ed8\u76d1\u542c\n        let resizeTimer;\n        window.addEventListener('resize', () => {\n            clearTimeout(resizeTimer);\n            resizeTimer = setTimeout(drawPie, 250);\n        });\n    })();\n    <\/script>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"3-2025-amc-8-detailed-answer-analysis\"><\/span>3. 2025 AMC 8 Detailed Answer Analysis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The table below breaks down the 2025 AMC 8 problems by core mathematical category, specific problem numbers, total count, and their difficulty scale on the test.<\/p>\n\n\n\n<p><em>(Note: On the AMC 8, difficulty traditionally increases along with the problem numbers: Problems 1\u20135 are Foundational, 6\u201310 are Easy-Medium, 11\u201315 are Medium, 16\u201320 are Medium-Hard, and 21\u201325 are Advanced.)<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Module Analysis Table<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>Core Category<\/strong><\/td><td><strong>Specific Problem Numbers<\/strong><\/td><td><strong>Total Count<\/strong><\/td><td><strong>Difficulty Tier<\/strong><\/td><td><strong>Key Concepts Tested<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>Algebra &amp; Pre-Algebra<\/strong><\/td><td>2, 3, 4, 7, 9, 14, 19, 20, 22<\/td><td>9<\/td><td>Foundational to Advanced<\/td><td>Ancient numeration systems, ratio adjustments, arithmetic progressions, threshold logic, mean\/median statistics, piecewise motion, and product-based sequences.<\/td><\/tr><tr><td><strong>Combinatorics, Counting &amp; Prob.<\/strong><\/td><td>5, 11, 15, 16, 17, 21, 23, 25<\/td><td>8<\/td><td>Foundational to Advanced<\/td><td>Shortest-path grid networks, logic deductions, matrix shading, pigeonhole minimization\/maximization, grid graph labeling constraints, and compound probability.<\/td><\/tr><tr><td><strong>Geometry<\/strong><\/td><td>1, 8, 10, 12, 24<\/td><td>5<\/td><td>Foundational to Advanced<\/td><td>Grid area decomposition, 3D cube surface and volume, 90-degree coordinate rotations, maximum circle packing, and unshaded similar triangle ratios.<\/td><\/tr><tr><td><strong>Number Theory<\/strong><\/td><td>6, 13, 18<\/td><td>3<\/td><td>Easy-Medium to Medium-Hard<\/td><td>Modular sum adjustments, remainder frequency histograms, and prime factor divisibility.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Questions 1\u20139<\/strong>: These questions were relatively straightforward, focusing on basic school-level knowledge such as calculating the area and perimeter of rectangles and squares, computing averages, and understanding place value principles.<\/li>\n\n\n\n<li><strong>Questions<\/strong><strong> 10\u201318<\/strong>: This segment concentrated on geometry and word problems. The geometry questions, in particular, increased significantly (4 out of 9 questions), requiring students to extract and transform information before applying core concepts.<\/li>\n\n\n\n<li><strong>Questions 19\u201325<\/strong>: The difficulty level of these questions decreased compared to previous years, with no extremely challenging problems. Notably, the traditionally difficult topics of counting, probability, and statistics were less emphasized in this section.<\/li>\n<\/ul>\n\n\n\n<p>Overall, while the 2025 exam presented a more balanced difficulty level, it demanded a broader understanding of middle school mathematical concepts and a stronger grasp of core principles. <\/p>\n\n\n\n<p>Analyzing the 2025 paper underscores the importance of mastering number theory and geometry fundamentals early. Joining a comprehensive <strong><a href=\"https:\/\/www.wukongsch.com\/learn-math\/amc-8\/\" target=\"_blank\" rel=\"noreferrer noopener\">AMC 8 Prep Course<\/a><\/strong> helps students address knowledge gaps and prepare for higher-level contests like the AMC 10.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"4-important-example-problems-analysis\"><\/span>4. Important Example Problems Analysis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Below is an in-depth mathematical analysis of four classic problems featured in this paper, representing a wide variety of difficulty levels and topics.<\/p>\n\n<h3>Example A: Problem 1 (Geometry \/ Area Percentage) \u2014 Foundational<\/h3>\n<ul>\n  <li><strong>Context:<\/strong> An eight-pointed star is woven into a popular quilting pattern on a 4 \u00d7 4 grid. Determine what percent of the entire grid is covered by the star.<\/li>\n  <li><strong>Strategy:<\/strong> Complementary Area Counting.<\/li>\n  <li><strong>Analysis &#038; Solution:<\/strong> The total area of the 4 \u00d7 4 grid is 4 \u00d7 4 = 16 square units. Instead of calculating the star directly, find the area left unshaded around the corners of the grid. Each of the 4 corners contains exactly 1 full unit square and 2 half-unit triangles, totaling 1 + 0.5 + 0.5 = 2 square units of unshaded area per corner.<\/li>\n<\/ul>\n<p style=\"text-align: center;\">Total Unshaded Area = 4 \u00d7 2 = 8 square units<\/p>\n<p style=\"text-align: center;\">Star Area = 16 \u2212 8 = 8 square units<\/p>\n<p style=\"text-align: center;\">Percentage = 8 \/ 16 \u00d7 100% = 50%<\/p>\n\n<h3>Example B: Problem 14 (Algebra \/ Statistical Variation) \u2014 Medium<\/h3>\n<ul>\n  <li><strong>Context:<\/strong> A new number N is inserted into the existing list of five numbers: 2, 6, 7, 7, 28. After the insertion, the mean of the list is exactly twice as great as its median. Find the value of N.<\/li>\n  <li><strong>Strategy:<\/strong> Median Casework and Algebraic Balancing.<\/li>\n  <li><strong>Analysis &#038; Solution:<\/strong> The original ordered list contains 5 terms. Inserting N creates a list of 6 terms. Let&#8217;s assume N is a relatively large integer (N \u2265 7). The middle two elements of the sorted 6-number list will be 7 and 7, meaning the median remains constant at (7+7)\/2 = 7. The sum of the original 5 numbers is 2 + 6 + 7 + 7 + 28 = 50. With N included, the new mean is:<\/li>\n<\/ul>\n<p style=\"text-align: center;\">Mean = (50 + N) \/ 6<\/p>\n<p>Set the mean to be twice the median (2 \u00d7 7 = 14):<\/p>\n<p style=\"text-align: center;\">(50 + N) \/ 6 = 14  \u21d2  50 + N = 84  \u21d2  N = 34<\/p>\n<p>Since 34 \u2265 7, our structural median assumption is verified, making 34 the final answer.<\/p>\n\n<h3>Example C: Problem 20 (Algebra \/ Infinite Geometric Series) \u2014 Medium-Hard<\/h3>\n<ul>\n  <li><strong>Context:<\/strong> Three friends share a block of cheese sequentially: Sarika eats half of it, then Dev eats half of what remains, followed by Rajiv eating half of the rest. The turn then loops back to Sarika, and they repeat this cycle indefinitely until nothing remains. Approximately what fraction of the total cheese does Sarika consume?<\/li>\n  <li><strong>Strategy:<\/strong> Infinite Geometric Series Formulation.<\/li>\n  <li><strong>Analysis &#038; Solution:<\/strong> In the initial round of consumption:<\/li>\n<\/ul>\n<ul>\n  <li>Sarika eats 1\/2 of the total cheese.<\/li>\n  <li>Dev eats 1\/2 \u00d7 1\/2 = 1\/4 of the total cheese.<\/li>\n  <li>Rajiv eats 1\/2 \u00d7 1\/4 = 1\/8 of the total cheese.<\/li>\n<\/ul>\n<p>Together, they consume 1\/2 + 1\/4 + 1\/8 = 7\/8 of the available block, leaving exactly 1\/8 of it behind for the next round. In each subsequent round, Sarika will always consume exactly 1\/2 of whatever remained from the prior round. This forms an infinite geometric series representing Sarika&#8217;s total share:<\/p>\n<p style=\"text-align: center;\">Total = 1\/2 + 1\/2 \u00d7 (1\/8) + 1\/2 \u00d7 (1\/8)\u00b2 + &#8230;<\/p>\n<p>Using the sum formula S = a \/ (1 \u2212 r) where the initial term a = 1\/2 and common ratio r = 1\/8:<\/p>\n<p style=\"text-align: center;\">S = (1\/2) \/ (1 \u2212 1\/8) = (1\/2) \/ (7\/8) = 1\/2 \u00d7 8\/7 = 4\/7<\/p>\n\n<h3>Example D: Problem 22 (Algebra &#038; Number Theory \/ Non-Linear Recurrences) \u2014 Advanced<\/h3>\n<ul>\n  <li><strong>Context:<\/strong> In a sequence of positive integers, each term after the second is found by multiplying the previous two terms together. Given that the sixth term (x\u2086) equals 4000, determine the value of the sequence&#8217;s very first term (x\u2081).<\/li>\n  <li><strong>Strategy:<\/strong> Exponential Recurrence Tracking and Prime Factorization.<\/li>\n  <li><strong>Analysis &#038; Solution:<\/strong> Let the first term be x\u2081 = a and the second term be x\u2082 = b. We write subsequent terms tracking their exponential powers:<\/li>\n<\/ul>\n<ul>\n  <li>x\u2083 = a \u00b7 b<\/li>\n  <li>x\u2084 = b \u00b7 (a \u00b7 b) = a\u00b9 \u00b7 b\u00b2<\/li>\n  <li>x\u2085 = (a \u00b7 b) \u00b7 (a \u00b7 b\u00b2) = a\u00b2 \u00b7 b\u00b3<\/li>\n  <li>x\u2086 = (a \u00b7 b\u00b2) \u00b7 (a\u00b2 \u00b7 b\u00b3) = a\u00b3 \u00b7 b\u2075<\/li>\n<\/ul>\n<p>We are given that x\u2086 = 4000. Break 4000 down into its unique prime factorization:<\/p>\n<p style=\"text-align: center;\">4000 = 40 \u00d7 100 = 2\u2075 \u00d7 5\u00b3<\/p>\n<p>Equating this to our exponential expression gives:<\/p>\n<p style=\"text-align: center;\">a\u00b3 \u00b7 b\u2075 = 5\u00b3 \u00d7 2\u2075<\/p>\n<p>By direct structural inspection, we match the bases to their matching exponents (a\u00b3 = 5\u00b3 and b\u2075 = 2\u2075), which yields a = 5 and b = 2. Because a and b must be integers, this is the unique integer solution. The first term (x\u2081 = a) is 5.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"5-strategic-tips-for-amc%e2%80%af8-2025-prep\"><\/span>5. Strategic Tips for AMC\u202f8 2025 Prep<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Use time wisely<\/strong>: Skip hard problems initially\u2014no penalty for wrong answers, but don\u2019t waste time.<\/li>\n\n\n\n<li><strong>Master core topics<\/strong>: Focus on geometry, combinatorics, ratios &amp; proportions, probability, and basic number theory.<\/li>\n\n\n\n<li><strong>Elimination is powerful<\/strong>: Casting out two obviously wrong choices raises odds significantly.<\/li>\n\n\n\n<li><strong>Simulate test conditions<\/strong>: Practice full 25-question sets under 40-minute timers.<\/li>\n\n\n\n<li><strong>Review past tests<\/strong>: Especially finals from previous years\u2014recurring themes are real.<\/li>\n\n\n\n<li><strong>Visual tools help<\/strong>: Draw diagrams for geometry\/counting setups to avoid mistakes.<\/li>\n\n\n\n<li><strong>Build mental stamina<\/strong>: Regular practice mitigates fatigue; don\u2019t cram last minute.<\/li>\n<\/ol>\n\n\n\n<p>Find more practical tips and information in our <a href=\"https:\/\/www.wukongsch.com\/blog\/how-to-prepare-amc-8-guide-post-51202\/\">comprehensive guide for AMC 8<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"6-master-the-amc-8-with-wukong-education\"><\/span>6. Master the AMC 8 with WuKong Education<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Is your child ready to conquer the <strong>AMC 8<\/strong>? To win at this level, students need more than just math skills\u2014they need a winning strategy.<\/p>\n\n\n\n<p><strong><a href=\"https:\/\/www.wukongsch.com\/math\/\">WuKong Math Course<\/a><\/strong> is the ultimate preparation track. Led by an elite faculty (<strong>87% hold Master\u2019s\/Ph.D. degrees<\/strong>), our 24-lesson program transforms students into competitors.<\/p>\n\n\n\n<p><strong>Why WuKong?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>The 3-Stage Advantage:<\/strong> Our proven model moves from <strong>Specialized Breakthrough<\/strong> (building the foundation), to <strong>Comprehensive Strengthening<\/strong> (mastering hard problems), and finally <strong>Sprint &amp; Polish<\/strong> (mock exams and high-frequency traps).<\/li>\n\n\n\n<li><strong>Complete Coverage:<\/strong> We tackle all 5 core modules: Algebra, Number Theory, Geometry, Statistics, and Applications.<\/li>\n<\/ul>\n\n\n\n<p>Don\u2019t just study hard\u2014study smart. Give your child the expert guidance they need to stand out.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"amc-8-past-papers-solutions\"><\/span>AMC 8 Past Papers &amp; Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Use this directory to download official previous test papers, access accurate answer keys, and study step-by-step mathematical problem breakdowns arranged by exam year.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>Exam Year<\/strong><\/td><td><strong>Article Link<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>2026 Exam<\/strong><\/td><td><a href=\"https:\/\/www.wukongsch.com\/blog\/2026-amc-8-answer-key-post-61141\/\" target=\"_blank\" rel=\"noreferrer noopener\">2026 AMC 8 Problems, Answer Key &amp; Full Analysis<\/a><\/td><\/tr><tr><td><strong>2025 Exam<\/strong><\/td><td>2025 AMC 8 Problems, Solutions and Step-by-Step Analysis (this article)<\/td><\/tr><tr><td><strong>2024 Exam<\/strong><\/td><td><a href=\"https:\/\/www.wukongsch.com\/blog\/free-2024-amc-8-problems-and-answers-analysis-post-23945\/\">Free 2024 AMC 8 Past Problems and Detailed Answers Analysis<\/a> <\/td><\/tr><tr><td><strong>2023 Exam<\/strong><\/td><td><a href=\"https:\/\/www.wukongsch.com\/blog\/2023-amc-8-problems-and-answers-insights-and-tips-post-19682\/\" target=\"_blank\" rel=\"noreferrer noopener\">2023 AMC 8 Problems and Answers: Core Insights &amp; Test Tips<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"faqs-about-amc-8-2025\"><\/span><strong>FAQs about AMC 8 2025<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"schema-faq\"><div class=\"schema-faq-section\" id=\"faq-question-1761644133462\"><strong class=\"schema-faq-question\"><strong>Q: How to Prepare for AMC?<\/strong><\/strong> <p class=\"schema-faq-answer\">You can prepare for the AMC test by improving your mathematical problem-solving skills. There\u2019s no exact duration or source material to prepare. You can try different books, problems, etc.\u00a0<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1761644195013\"><strong class=\"schema-faq-question\"><strong>Q: How to Apply for the AMC 8 Exam?<\/strong><\/strong> <p class=\"schema-faq-answer\">You can apply for the AMC 8 2026 exam by visiting the Mathematical Association of America official website. There, you will find registration dates, a teacher\u2019s manual, and other instructions to note before applying.\u00a0<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1761644203584\"><strong class=\"schema-faq-question\"><strong>Q: What Do I need to Apply for the AMC Test?<\/strong><\/strong> <p class=\"schema-faq-answer\">You can download the form from the Mathematical Association of America website. Fill out the form and send it back to MAA via mail, fax, or email.\u00a0<\/p> <\/div> <\/div>\n\n\n<div class=\"retention-card-new\" data-lang=\"en\" data-subject=\"MATH\" data-btnName=\"Get started free!\" data-subTitle=\"Suitable for students worldwide, from grades K-12.\">\r\n    <div class=\"retention-card-l\">\r\n        <div class=\"trustpilot-image\">\r\n            <!-- TrustBox widget - Micro Star -->\r\n            <div class=\"trustpilot-widget\" data-locale=\"en-US\" data-template-id=\"5419b732fbfb950b10de65e5\" data-businessunit-id=\"60c847b7f033d300019ff3a1\" data-style-height=\"24px\" data-style-width=\"272px\" data-token=\"7dc9fdab-8926-4826-ad90-81ab38cc0953\">\r\n              <a href=\"https:\/\/www.trustpilot.com\/review\/wukongsch.com\" target=\"_blank\" rel=\"noopener\">Trustpilot<\/a>\r\n            <\/div>\r\n            <!-- End TrustBox widget -->\r\n        <\/div>\r\n        <h3><p>Discovering the maths whiz in every child,<br \/>\n<span>that&#8217;s what we do.<\/span><\/p>\n<\/h3>\r\n        <p>Suitable for students worldwide, from grades K-12.<\/p>\r\n        <a class=\"retention-card-button is-point\" href=\"https:\/\/www.wukongsch.com\/independent-appointment\/?subject=math&amp;l=eafd8b18-486b-4e0a-b93d-4105d41d2067&amp;booking_triggerevent=BLOG_DETAIL_MODEL_CTA_BUTTON\" data-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u70b9\u51fb\" data-event=\"C_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" data-expose-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u66dd\u5149\" data-expose-event=\"D_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" target=\"_blank\" title=\"Get started free!\">\r\n            Get started free!\r\n        <\/a>\r\n    <\/div>\r\n    <div class=\"retention-card-r\"><\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The 2025 AMC\u202f8, held between January\u202f22 and 28, 2025, once again encouraged thousands of students to test their mettle in creative mathematics under time constraints. Prepared by expert instructors from the WuKong AMC 8 Course, this complete answer key and solution analysis provides clear breakdowns for all 25 questions. 1. 2025 AMC 8 Problems and Answers Here we have provided the real exam questions and their answers. If you want to learn the solution methods, please visit WuKong Math. 2. 2025 AMC 8 Topic Distribution Below is a visual text-based representation of the topic breakdown across the 25 problems contained in the exam paper: 2025 AMC 8 Topic Distribution 3. 2025 AMC 8 Detailed Answer Analysis The table below breaks&#46;&#46;&#46;<\/p>\n","protected":false},"author":211806805,"featured_media":50974,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[137530],"tags":[137518,137542,137127],"class_list":["post-50973","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-wukong-amc-8","tag-amc-8","tag-amc-8-problems","tag-amc-math-competition"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - 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