{"id":3327,"date":"2025-08-18T14:43:39","date_gmt":"2025-08-18T06:43:39","guid":{"rendered":"https:\/\/cikguhayat.com\/v1.0\/?p=3327"},"modified":"2025-08-18T15:20:57","modified_gmt":"2025-08-18T07:20:57","slug":"ulang-kaji-ogif-matematik-tingkatan-5-nota-slaid-lembaran-kerja","status":"publish","type":"post","link":"https:\/\/cikguhayat.com\/v1.0\/ulang-kaji-ogif-matematik-tingkatan-5-nota-slaid-lembaran-kerja\/","title":{"rendered":"Ulang Kaji Ogif Matematik Tingkatan 5 | Nota, Slaid &amp; Lembaran Kerja"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"3327\" class=\"elementor elementor-3327\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2691b2d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2691b2d\" data-element_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-100 elementor-top-column elementor-element elementor-element-00e9994\" data-id=\"00e9994\" data-element_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-d0d8023 elementor-widget elementor-widget-text-editor\" data-id=\"d0d8023\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Berikut di kongsikan sedikit Nota dan Latihan untuk ulangkaji Matematik SPM\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\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-8d22bad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8d22bad\" data-element_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-100 elementor-top-column elementor-element elementor-element-5eea1f4\" data-id=\"5eea1f4\" data-element_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-d6ca059 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"d6ca059\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\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-d3d0428 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"d3d0428\" data-element_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-100 elementor-top-column elementor-element elementor-element-73d23ce\" data-id=\"73d23ce\" data-element_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-980e259 elementor-widget elementor-widget-html\" data-id=\"980e259\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<!doctype html>\r\n<html lang=\"ms\">\r\n<head>\r\n  <meta charset=\"utf-8\" \/>\r\n  <meta name=\"viewport\" content=\"width=device-width,initial-scale=1\" \/>\r\n  <title>Slaid Interaktif Cerah: Ogif (Graf Kekerapan Longgokan)<\/title>\r\n  <style>\r\n    :root{\r\n      --bg: #f7fafc;       \/* very light *\/\r\n      --card: #ffffff;     \/* white cards *\/\r\n      --text: #0f172a;     \/* dark text *\/\r\n      --muted: #475569;    \/* slate-600 *\/\r\n      --accent: #2563eb;   \/* blue-600 *\/\r\n      --accent-2: #10b981; \/* emerald-500 *\/\r\n      --glass: rgba(15,23,42,0.04);\r\n      --border: rgba(15,23,42,0.08);\r\n    }\r\n    *{box-sizing:border-box}\r\n    html,body{height:100%}\r\n    body{\r\n      margin:0; font:15px\/1.5 Inter, system-ui, -apple-system, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial;\r\n      background: linear-gradient(180deg, #e6f0ff 0%, var(--bg) 60%);\r\n      color:var(--text);\r\n      -webkit-font-smoothing:antialiased;\r\n      -moz-osx-font-smoothing:grayscale;\r\n    }\r\n    .deck{position:relative; height:100vh; overflow:hidden; display:flex; flex-direction:column}\r\n    .slides{flex:1; display:flex; transition:transform .45s cubic-bezier(.22,.9,.3,1); will-change:transform}\r\n    .slide{min-width:100%; padding:48px; 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border:1px solid rgba(15,23,42,0.06); color:var(--text)}\r\n    .badge{display:inline-block; padding:6px 10px; border-radius:999px; background:#eef2ff; color:var(--accent); font-weight:700; font-size:13px}\r\n    .tip{font-size:13px; color:var(--muted)}\r\n    .canvas-wrap{background:linear-gradient(180deg,#ffffff,#f8fafc); border-radius:10px; padding:10px; border:1px solid rgba(15,23,42,0.04)}\r\n    canvas{width:100%; height:360px; display:block}\r\n    label{font-size:14px; color:var(--muted)}\r\n    select,input[type=number]{padding:8px 10px; border-radius:8px; border:1px solid rgba(15,23,42,0.06); background:transparent; color:var(--text)}\r\n    .stack{display:flex; flex-direction:column; gap:10px}\r\n    .progress{height:6px; background:rgba(15,23,42,0.06); border-radius:999px; overflow:hidden}\r\n    .progress > i{display:block; height:100%; width:0; background: linear-gradient(90deg,var(--accent),var(--accent-2)); transition:width .35s}\r\n    .quiz-grid{display:grid; grid-template-columns:1fr 1fr; gap:12px}\r\n    .muted{color:var(--muted)}\r\n    @media (max-width:920px){ .row{grid-template-columns:1fr} .grid-3{grid-template-columns:1fr} h1{font-size:28px} }\r\n  <\/style>\r\n<\/head>\r\n<body>\r\n  <div class=\"deck\" id=\"deck\">\r\n    <div class=\"slides\" id=\"slides\">\r\n      <!-- Slide 1: Title -->\r\n      <section class=\"slide\">\r\n        <div style=\"display:flex;gap:12px;align-items:center;width:100%;justify-content:space-between\">\r\n          <div>\r\n            <span class=\"badge\">Statistik \u2022 Tingkatan 5<\/span>\r\n            <h1>Ogif (Graf Kekerapan Longgokan)<\/h1>\r\n            <p class=\"muted\">Slaid interaktif \u2014 guna kekunci \u2190 \/ \u2192 atau butang navigasi. Tema cerah untuk muat naik ke laman cikguhayat.com<\/p>\r\n          <\/div>\r\n          <div style=\"text-align:right\">\r\n            <div class=\"tip\">Kelas: Ulang Kaji (1 jam 20 minit)<\/div>\r\n            <div class=\"tip\" style=\"margin-top:6px\">BBM: Slaid interaktif, Lembaran Kerja, Kuiz Ringkas<\/div>\r\n          <\/div>\r\n        <\/div>\r\n\r\n        <div class=\"row\" style=\"margin-top:14px\">\r\n          <div class=\"card\">\r\n            <h2>Apa yang akan dipelajari<\/h2>\r\n            <ul style=\"margin-top:8px;color:var(--muted)\">\r\n              <li>Membina ogif <b>kurang daripada<\/b> & <b>lebih daripada<\/b><\/li>\r\n              <li>Menentukan median, Q1, Q3 & IQR<\/li>\r\n              <li>Gunakan ogif untuk menyelesaikan masalah sebenar<\/li>\r\n            <\/ul>\r\n          <\/div>\r\n          <div class=\"card\">\r\n            <h2>Nota Ringkas<\/h2>\r\n            <p class=\"muted\" style=\"margin-top:8px\">Plot titik CF pada sempadan kelas (atas untuk 'kurang daripada', bawah untuk 'lebih daripada') dan sambung dengan garis licin. Median pada CF = n\/2.<\/p>\r\n          <\/div>\r\n        <\/div>\r\n      <\/section>\r\n\r\n      <!-- Slide 2: Intro -->\r\n      <section class=\"slide\">\r\n        <h2>Pengenalan Ogif<\/h2>\r\n        <div class=\"row\" style=\"margin-top:10px\">\r\n          <div class=\"card\">\r\n            <p><strong>Ogif<\/strong> ialah graf <em>cumulative frequency<\/em> (kekerapan longgokan).<\/p>\r\n            <ul style=\"margin-top:8px;color:var(--muted)\">\r\n              <li><b>Kurang daripada<\/b> \u2014 guna sempadan atas kelas pada paksi-x.<\/li>\r\n              <li><b>Lebih daripada<\/b> \u2014 guna sempadan bawah kelas pada paksi-x.<\/li>\r\n            <\/ul>\r\n          <\/div>\r\n          <div class=\"card\">\r\n            <p class=\"muted\">Tip guru: semasa demonstrasi, tunjuk kedua-dua jenis ogif untuk satu set data supaya murid nampak perbezaan praktikal.<\/p>\r\n          <\/div>\r\n        <\/div>\r\n      <\/section>\r\n\r\n      <!-- Slide 3: Steps -->\r\n      <section class=\"slide\">\r\n        <h2>Langkah Mudah Membina Ogif<\/h2>\r\n        <div class=\"grid-3\" style=\"margin-top:10px\">\r\n          <div class=\"card\"><strong>1) Jadualkan<\/strong><p class=\"muted\">Bina jadual kekerapan dan kira cumulative frequency (CF).<\/p><\/div>\r\n          <div class=\"card\"><strong>2) Titik Plot<\/strong><p class=\"muted\">Gunakan sempadan kelas (atas\/bawah) sebagai x, CF sebagai y.<\/p><\/div>\r\n          <div class=\"card\"><strong>3) Lukis<\/strong><p class=\"muted\">Sambungkan titik dengan garis licin. Tandakan median\/Q1\/Q3.<\/p><\/div>\r\n        <\/div>\r\n        <p class=\"tip\" style=\"margin-top:10px\">Formula cepat: Q1 = CF @ n\/4, Median = CF @ n\/2, Q3 = CF @ 3n\/4, IQR = Q3 \u2212 Q1<\/p>\r\n      <\/section>\r\n\r\n      <!-- Slide 4: Example data -->\r\n      <section class=\"slide\">\r\n        <h2>Contoh Data: Markah Matematik (40 murid)<\/h2>\r\n        <div class=\"card\" style=\"margin-top:10px\">\r\n          <table>\r\n            <thead><tr><th>Julat Markah<\/th><th>Kekerapan<\/th><\/tr><\/thead>\r\n            <tbody>\r\n              <tr><td>0\u20139<\/td><td>2<\/td><\/tr>\r\n              <tr><td>10\u201319<\/td><td>6<\/td><\/tr>\r\n              <tr><td>20\u201329<\/td><td>10<\/td><\/tr>\r\n              <tr><td>30\u201339<\/td><td>8<\/td><\/tr>\r\n              <tr><td>40\u201349<\/td><td>9<\/td><\/tr>\r\n              <tr><td>50\u201359<\/td><td>5<\/td><\/tr>\r\n            <\/tbody>\r\n          <\/table>\r\n        <\/div>\r\n        <p class=\"tip\" style=\"margin-top:8px\">Gunakan data ini pada demo interaktif di slaid seterusnya.<\/p>\r\n      <\/section>\r\n\r\n      <!-- Slide 5: Interactive demo -->\r\n      <section class=\"slide\">\r\n        <h2>Demo Interaktif: Bina Ogif<\/h2>\r\n        <div class=\"row\" style=\"margin-top:8px\">\r\n          <div class=\"card stack\">\r\n            <label for=\"datasetSel\">Pilih dataset<\/label>\r\n            <select id=\"datasetSel\" aria-label=\"Pilih dataset\">\r\n              <option value=\"marks\">Markah Matematik (40)<\/option>\r\n              <option value=\"masa\">Masa Tugasan (50)<\/option>\r\n              <option value=\"berat\">Berat (40)<\/option>\r\n            <\/select>\r\n\r\n            <div style=\"display:flex;gap:8px;align-items:center\">\r\n              <label>Jenis ogif<\/label>\r\n              <button class=\"btn primary\" id=\"btnKurang\" aria-pressed=\"true\">Kurang daripada<\/button>\r\n              <button class=\"btn alt\" id=\"btnLebih\">Lebih daripada<\/button>\r\n            <\/div>\r\n\r\n            <div style=\"display:flex;gap:8px;align-items:center\">\r\n              <label>Ketepatan grid<\/label>\r\n              <input id=\"nMarkers\" type=\"range\" min=\"4\" max=\"12\" value=\"8\" aria-label=\"Ketepatan grid\"\/>\r\n            <\/div>\r\n\r\n            <div>\r\n              <label for=\"probeVal\">Anggaran bilangan \u2264 x (masukkan x)<\/label>\r\n              <input id=\"probeVal\" type=\"number\" value=\"35\" \/>\r\n              <div style=\"margin-top:8px\">\r\n                <button class=\"btn ghost\" id=\"probeBtn\">Anggar<\/button>\r\n                <span id=\"probeOut\" class=\"muted\" style=\"margin-left:10px\">\u2014<\/span>\r\n              <\/div>\r\n            <\/div>\r\n\r\n          <\/div>\r\n\r\n          <div class=\"card canvas-wrap\">\r\n            <canvas id=\"chart\" width=\"900\" height=\"500\" role=\"img\" aria-label=\"Graf ogif interaktif\"><\/canvas>\r\n          <\/div>\r\n        <\/div>\r\n      <\/section>\r\n\r\n      <!-- Slide 6: Interpret -->\r\n      <section class=\"slide\">\r\n        <h2>Mentafsir<\/h2>\r\n        <div class=\"row\" style=\"margin-top:8px\">\r\n          <div class=\"card\">\r\n            <ul style=\"color:var(--muted)\">\r\n              <li><strong>Median<\/strong>: nilai pada CF = n\/2<\/li>\r\n              <li><strong>Q1<\/strong>: nilai pada CF = n\/4<\/li>\r\n              <li><strong>Q3<\/strong>: nilai pada CF = 3n\/4<\/li>\r\n              <li><strong>IQR<\/strong> = Q3 \u2212 Q1<\/li>\r\n            <\/ul>\r\n          <\/div>\r\n          <div class=\"card\">\r\n            <p class=\"muted\">Contoh praktikal: Untuk cari bilangan skor \u2265 35 pada ogif kurang daripada, kira n \u2212 CF(\u226434.9).<\/p>\r\n          <\/div>\r\n        <\/div>\r\n      <\/section>\r\n\r\n      <!-- Slide 7: Application & Comparison -->\r\n      <section class=\"slide\">\r\n        <h2>Aplikasi & Perbandingan<\/h2>\r\n        <div class=\"row\" style=\"margin-top:8px\">\r\n          <div class=\"card\">\r\n            <p class=\"muted\">Banding dua set data (contoh Kelas A & B) menggunakan median & IQR \u2014 lebih kecil IQR bermaksud data lebih tumpu.<\/p>\r\n          <\/div>\r\n          <div class=\"card\">\r\n            <p class=\"muted\">Gunakan ogif untuk membuat anggaran, bukan nilai tepat \u2014 sebaiknya gabungkan dengan jadual untuk ketepatan.<\/p>\r\n          <\/div>\r\n        <\/div>\r\n      <\/section>\r\n\r\n      <!-- Slide 8: Quick quiz -->\r\n      <section class=\"slide\">\r\n        <h2>Kuiz Pantas<\/h2>\r\n        <div class=\"card quiz-grid\" style=\"margin-top:10px\">\r\n          <div>\r\n            <p><strong>S1.<\/strong> Jika n = 40, CF = 20 merujuk kepada:<\/p>\r\n            <label><input type=\"radio\" name=\"q1\" value=\"median\"> Median<\/label><br\/>\r\n            <label><input type=\"radio\" name=\"q1\" value=\"q1\"> Kuartil Pertama (Q1)<\/label><br\/>\r\n            <label><input type=\"radio\" name=\"q1\" value=\"q3\"> Kuartil Ketiga (Q3)<\/label><br\/>\r\n            <div style=\"margin-top:8px\">\r\n              <button class=\"btn primary\" id=\"check1\">Semak<\/button>\r\n              <span id=\"ans1\" class=\"muted\" style=\"margin-left:8px\">\u2014<\/span>\r\n            <\/div>\r\n          <\/div>\r\n\r\n          <div>\r\n            <p><strong>S2.<\/strong> IQR ditakrif sebagai:<\/p>\r\n            <label><input type=\"radio\" name=\"q2\" value=\"q3q1\"> Q3 \u2212 Q1<\/label><br\/>\r\n            <label><input type=\"radio\" name=\"q2\" value=\"mean\"> Min \u2212 Median<\/label><br\/>\r\n            <label><input type=\"radio\" name=\"q2\" value=\"range\"> Maks \u2212 Min<\/label><br\/>\r\n            <div style=\"margin-top:8px\">\r\n              <button class=\"btn alt\" id=\"check2\">Semak<\/button>\r\n              <span id=\"ans2\" class=\"muted\" style=\"margin-left:8px\">\u2014<\/span>\r\n            <\/div>\r\n          <\/div>\r\n        <\/div>\r\n      <\/section>\r\n\r\n    <\/div>\r\n\r\n    <!-- navigation -->\r\n    <div style=\"padding:12px 48px; display:flex; align-items:center; gap:12px; justify-content:space-between\">\r\n      <div style=\"display:flex;gap:8px;align-items:center\">\r\n        <button class=\"btn ghost\" id=\"prev\">\u2190 Sebelum<\/button>\r\n        <button class=\"btn primary\" id=\"next\">Seterusnya \u2192<\/button>\r\n      <\/div>\r\n      <div style=\"flex:1; margin-left:18px; margin-right:18px\">\r\n        <div class=\"progress\"><i id=\"bar\" style=\"width:12.5%\"><\/i><\/div>\r\n      <\/div>\r\n      <div class=\"tip muted\">Gunakan kekunci \u2190 \/ \u2192<\/div>\r\n    <\/div>\r\n  <\/div>\r\n\r\n  <script>\r\n    \/\/ -------- Deck controller --------\r\n    const slidesEl = document.getElementById('slides');\r\n    const totalSlides = slidesEl.children.length;\r\n    let idx = 0;\r\n    const bar = document.getElementById('bar');\r\n\r\n    function 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canvas.getContext('2d');\r\n\r\n    \/\/ Make canvas pixel-ratio aware\r\n    function resizeCanvas(){\r\n      const ratio = window.devicePixelRatio || 1;\r\n      const styleW = canvas.clientWidth;\r\n      const styleH = canvas.clientHeight;\r\n      canvas.width = Math.floor(styleW * ratio);\r\n      canvas.height = Math.floor(styleH * ratio);\r\n      ctx.setTransform(ratio,0,0,ratio,0,0);\r\n    }\r\n    window.addEventListener('resize', ()=>drawOgive(currentMode));\r\n    resizeCanvas();\r\n\r\n    function cumulativeLessThan(classes){\r\n      let cf=0; const pts=[];\r\n      for(const [a,b,f] of classes){ cf += f; pts.push([b + 0.0, cf]); }\r\n      return pts;\r\n    }\r\n    function cumulativeMoreThan(classes){\r\n      let total = classes.reduce((s,c)=>s+c[2],0);\r\n      const pts = [];\r\n      for(const [a,b,f] of classes){\r\n        pts.push([a + 0.0, total]);\r\n        total -= f;\r\n      }\r\n      \/\/ append final lower bound\r\n      const lastB = classes[classes.length-1][1];\r\n      pts.push([lastB + 1.0, 0]);\r\n      return pts;\r\n    }\r\n    function extentX(classes){\r\n      const xmin = classes[0][0] - 1;\r\n      const xmax = classes[classes.length-1][1] + 1;\r\n      return [xmin, xmax];\r\n    }\r\n\r\n    function drawAxes(xmin,xmax,ymax,grid){\r\n      \/\/ clear\r\n      ctx.clearRect(0,0,canvas.width,canvas.height);\r\n      \/\/ geometry (using CSS pixels)\r\n      const padL = 64, padR = 24, padT = 24, padB = 56;\r\n      const W = canvas.clientWidth - padL - padR;\r\n      const H = canvas.clientHeight - padT - padB;\r\n      \/\/ axes\r\n      ctx.strokeStyle = 'rgba(15,23,42,0.12)'; ctx.lineWidth = 1.2;\r\n      ctx.beginPath(); ctx.moveTo(padL, padT); ctx.lineTo(padL, padT+H); ctx.lineTo(padL+W, padT+H); ctx.stroke();\r\n      ctx.fillStyle = 'rgba(15,23,42,0.65)'; ctx.font = '12px Inter, system-ui';\r\n      \/\/ y ticks\r\n      for(let i=0;i<=grid;i++){\r\n        const y = padT + H - (i\/grid)*H;\r\n        const val = Math.round((i\/grid)*ymax);\r\n        ctx.beginPath(); ctx.strokeStyle = 'rgba(15,23,42,0.06)'; ctx.moveTo(padL, y); ctx.lineTo(padL+W, y); ctx.stroke();\r\n        ctx.fillText(val.toString(), 12, y+4);\r\n      }\r\n      \/\/ x ticks\r\n      for(let i=0;i<=grid;i++){\r\n        const x = padL + (i\/grid)*W;\r\n        const val = Math.round(xmin + (i\/grid)*(xmax-xmin));\r\n        ctx.beginPath(); ctx.strokeStyle = 'rgba(15,23,42,0.04)'; ctx.moveTo(x, padT); ctx.lineTo(x, padT+H); ctx.stroke();\r\n        ctx.fillText(val.toString(), x-10, padT+H+20);\r\n      }\r\n      return {padL,padT,W,H};\r\n    }\r\n\r\n    function scalePoint(x,y,xmin,xmax,ymax,geom){\r\n      const {padL,padT,W,H} = geom;\r\n      const X = padL + ( (x - xmin) \/ (xmax - xmin) ) * W;\r\n      const Y = padT + H - ( y \/ ymax ) * H;\r\n      return [X,Y];\r\n    }\r\n\r\n    function drawLine(points,xmin,xmax,ymax,geom){\r\n      ctx.strokeStyle = '#2563eb'; ctx.lineWidth = 2.8; ctx.beginPath();\r\n      points.forEach((p,i)=>{\r\n        const [X,Y] = scalePoint(p[0], p[1], xmin,xmax,ymax,geom);\r\n        if(i===0) ctx.moveTo(X,Y); else ctx.lineTo(X,Y);\r\n      });\r\n      ctx.stroke();\r\n      \/\/ draw points\r\n      ctx.fillStyle = '#10b981';\r\n      for(const p of points){\r\n        const [X,Y] = scalePoint(p[0], p[1], xmin,xmax,ymax,geom);\r\n        ctx.beginPath(); ctx.arc(X,Y,4,0,Math.PI*2); ctx.fill();\r\n      }\r\n    }\r\n\r\n    function lerpXAtCF(points, target){\r\n      for(let i=1;i<points.length;i++){\r\n        const [x1,y1] = points[i-1]; const [x2,y2] = points[i];\r\n        if((target >= Math.min(y1,y2) && target <= Math.max(y1,y2))){\r\n          const t = (target - y1) \/ (y2 - y1);\r\n          return x1 + t * (x2 - x1);\r\n        }\r\n      }\r\n      return points[points.length-1][0];\r\n    }\r\n\r\n    function drawOgive(kind='kurang'){\r\n      resizeCanvas();\r\n      const key = document.getElementById('datasetSel').value;\r\n      const data = datasets[key];\r\n      const classes = data.classes;\r\n      const n = classes.reduce((s,c)=>s+c[2],0);\r\n      const [xmin,xmax] = extentX(classes);\r\n      const points = (kind === 'kurang') ? cumulativeLessThan(classes) : cumulativeMoreThan(classes);\r\n      const grid = Number(document.getElementById('nMarkers').value || 8);\r\n      const geom = drawAxes(xmin,xmax,n,grid);\r\n      drawLine(points,xmin,xmax,n,geom);\r\n\r\n      \/\/ draw Q1\/Median\/Q3 guides\r\n      const q1 = n\/4, med = n\/2, q3 = 3*n\/4;\r\n      [[q1,'Q1'],[med,'Median'],[q3,'Q3']].forEach(([cf,label])=>{\r\n        const xEstimate = lerpXAtCF(points, cf);\r\n        const [X,Y] = scalePoint(xEstimate, cf, xmin, xmax, n, geom);\r\n        ctx.save();\r\n        ctx.strokeStyle = 'rgba(15,23,42,0.2)'; ctx.setLineDash([6,6]); ctx.lineWidth = 1;\r\n        ctx.beginPath(); ctx.moveTo(geom.padL, Y); ctx.lineTo(X, Y); ctx.stroke();\r\n        ctx.beginPath(); ctx.moveTo(X, geom.padT+geom.H); ctx.lineTo(X, Y); ctx.stroke();\r\n        ctx.restore();\r\n        ctx.fillStyle = '#0f172a'; ctx.font = '12px Inter, system-ui'; ctx.fillText(label, X+8, Y-8);\r\n      });\r\n    }\r\n\r\n    \/\/ Probe: estimate CF \u2264 x for current 'kurang' ogif\r\n    function probeCF(x){\r\n      const key = document.getElementById('datasetSel').value;\r\n      const classes = datasets[key].classes;\r\n      const pts = cumulativeLessThan(classes);\r\n      \/\/ if x below first point\r\n      if(x <= pts[0][0]) return 0;\r\n      if(x >= pts[pts.length-1][0]) return pts[pts.length-1][1];\r\n      for(let i=1;i<pts.length;i++){\r\n        const [x1,y1] = pts[i-1], [x2,y2] = pts[i];\r\n        if(x <= x2){\r\n          const t = (x - x1) \/ (x2 - x1);\r\n          return Math.round(y1 + t*(y2 - y1));\r\n        }\r\n      }\r\n      return 0;\r\n    }\r\n\r\n    \/\/ UI wiring\r\n    let currentMode = 'kurang';\r\n    document.getElementById('btnKurang').addEventListener('click', ()=>{\r\n      currentMode = 'kurang';\r\n      document.getElementById('btnKurang').setAttribute('aria-pressed','true');\r\n      document.getElementById('btnLebih').setAttribute('aria-pressed','false');\r\n      drawOgive(currentMode);\r\n    });\r\n    document.getElementById('btnLebih').addEventListener('click', ()=>{\r\n      currentMode = 'lebih';\r\n      document.getElementById('btnKurang').setAttribute('aria-pressed','false');\r\n      document.getElementById('btnLebih').setAttribute('aria-pressed','true');\r\n      drawOgive(currentMode);\r\n    });\r\n    document.getElementById('datasetSel').addEventListener('change', ()=>drawOgive(currentMode));\r\n    document.getElementById('nMarkers').addEventListener('input', ()=>drawOgive(currentMode));\r\n    document.getElementById('probeBtn').addEventListener('click', ()=>{\r\n      const x = Number(document.getElementById('probeVal').value);\r\n      if(Number.isNaN(x)){ document.getElementById('probeOut').textContent = 'Sila masukkan nombor yang sah'; return; }\r\n      const cf = probeCF(x);\r\n      document.getElementById('probeOut').textContent = `Anggaran bilangan \u2264 ${x} ialah \u2248 ${cf}`;\r\n    });\r\n\r\n    \/\/ Quiz handlers \u2014 use checked input (NO FormData)\r\n    document.getElementById('check1').addEventListener('click', ()=>{\r\n      const sel = document.querySelector('input[name=\"q1\"]:checked');\r\n      const out = document.getElementById('ans1');\r\n      if(!sel){ out.textContent = 'Sila pilih jawapan'; out.style.color = ''; return; }\r\n      if(sel.value === 'median'){ out.innerHTML = '\u2705 Betul \u2014 Median ialah CF = n\/2'; out.style.color = 'var(--accent)'; }\r\n      else { out.innerHTML = '\u274c Jawapan kurang tepat. Median berada pada CF = n\/2'; out.style.color = '#ef4444'; }\r\n    });\r\n    document.getElementById('check2').addEventListener('click', ()=>{\r\n      const sel = document.querySelector('input[name=\"q2\"]:checked');\r\n      const out = document.getElementById('ans2');\r\n      if(!sel){ out.textContent = 'Sila pilih jawapan'; out.style.color = ''; return; }\r\n      if(sel.value === 'q3q1'){ out.innerHTML = '\u2705 Betul \u2014 IQR = Q3 \u2212 Q1'; out.style.color = 'var(--accent)'; }\r\n      else { out.innerHTML = '\u274c Tidak tepat. IQR = Q3 \u2212 Q1'; out.style.color = '#ef4444'; }\r\n    });\r\n\r\n    \/\/ init\r\n    go(0);\r\n    drawOgive(currentMode);\r\n\r\n    \/\/ ensure canvas redraw on slide change (in case size changes)\r\n    new ResizeObserver(()=>drawOgive(currentMode)).observe(document.getElementById('chart'));\r\n\r\n  <\/script>\r\n<\/body>\r\n<\/html>\r\n\t\t\t\t<\/div>\n\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-8d17fa2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8d17fa2\" data-element_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-100 elementor-top-column elementor-element elementor-element-26e70cc\" data-id=\"26e70cc\" data-element_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-5906e81 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5906e81\" data-element_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-100 elementor-top-column elementor-element elementor-element-5c36391\" data-id=\"5c36391\" data-element_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-09d817c elementor-widget elementor-widget-text-editor\" data-id=\"09d817c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Berikut di sediakan sekali set soalan Ogif interaktif untuk di gunakan di dalam kelas.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\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-737ed3e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"737ed3e\" data-element_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-100 elementor-top-column elementor-element elementor-element-72fe713\" data-id=\"72fe713\" data-element_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-c90324c elementor-widget elementor-widget-html\" data-id=\"c90324c\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<!DOCTYPE html>\r\n<html lang=\"ms\">\r\n<head>\r\n  <meta charset=\"UTF-8\">\r\n  <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\r\n  <title>Lembaran Kerja Interaktif: Ogif<\/title>\r\n  <style>\r\n    body {font-family: Arial, sans-serif; background:#f9f9f9; padding:20px; line-height:1.6;}\r\n    h1 {text-align:center; margin-bottom:30px;}\r\n    .question {background:#fff; padding:15px; margin-bottom:20px; border-radius:8px; box-shadow:0 2px 4px rgba(0,0,0,0.1);}\r\n    button {padding:6px 12px; margin-top:10px; cursor:pointer;}\r\n    .answer {display:none; margin-top:10px; font-weight:bold; color:green;}\r\n  <\/style>\r\n<\/head>\r\n<body>\r\n\r\n<h1>Lembaran Kerja Interaktif: Ogif<\/h1>\r\n\r\n<div class=\"question\">\r\n  <p><b>1.<\/b> Berdasarkan data berikut, tentukan kekerapan terkumpul bagi kelas 20\u201329.<\/p>\r\n  <pre>\r\n0\u20139 : 2\r\n10\u201319 : 5\r\n20\u201329 : 8\r\n30\u201339 : 10\r\n40\u201349 : 5\r\n  <\/pre>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Kekerapan terkumpul = 2 + 5 + 8 = <b>15<\/b><\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>2.<\/b> Nyatakan paksi mendatar (x) dalam ogif.<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Paksi-x = <b>Sempadan atas kelas<\/b><\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>3.<\/b> Nyatakan paksi menegak (y) dalam ogif.<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Paksi-y = <b>Kekerapan terkumpul<\/b><\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>4.<\/b> Tentukan titik ogif pertama jika kelas pertama ialah 0\u20139 dengan kekerapan 2.<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Titik pertama = (0,0) atau (9,2) bergantung pada definisi sempadan kelas.<\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>5.<\/b> Data: 5, 10, 12, 18, 20, 25, 30, 32, 35, 40.  \r\nBina kekerapan terkumpul sebelum melukis ogif.<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Sediakan kelas (0\u20139, 10\u201319, \u2026), kira kekerapan \u2192 buat kekerapan terkumpul mengikut kelas.  \r\nContoh: 0\u20139:1, 10\u201319:3, 20\u201329:2, 30\u201339:3, 40\u201349:1 \u2192 Kekerapan terkumpul = 1, 4, 6, 9, 10.<\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>6.<\/b> Apakah bentuk ogif yang diperoleh apabila data semakin meningkat?<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Bentuk ogif = <b>lengkung menaik<\/b><\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>7.<\/b> Berdasarkan ogif, bagaimana kita mencari median?<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Cari kedudukan <i>(n\/2)<\/i> pada paksi-y, tarik garisan mendatar \u2192 turunkan ke paksi-x.<\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>8.<\/b> Apakah kegunaan ogif selain menentukan median?<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Untuk menentukan <b>kuartil, persentil, dan taburan data<\/b>.<\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>9.<\/b> Satu set data mempunyai kekerapan terkumpul akhir = 50. Apakah maksud nilai ini?<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Jumlah keseluruhan data = <b>50 pemerhatian<\/b><\/div>\r\n<\/div>\r\n\r\n<div class=\"question\">\r\n  <p><b>10.<\/b> Bezakan antara ogif \"kurang daripada\" dan \"lebih daripada\".<\/p>\r\n  <button onclick=\"toggleAnswer(this)\">Lihat Jawapan<\/button>\r\n  <div class=\"answer\">Ogif \"kurang daripada\": gunakan kekerapan terkumpul kurang daripada sempadan atas.  \r\nOgif \"lebih daripada\": gunakan kekerapan terkumpul lebih daripada sempadan bawah.<\/div>\r\n<\/div>\r\n\r\n<script>\r\n  function toggleAnswer(btn) {\r\n    const ans = btn.nextElementSibling;\r\n    ans.style.display = (ans.style.display === \"block\") ? \"none\" : \"block\";\r\n  }\r\n<\/script>\r\n\r\n<\/body>\r\n<\/html>\r\n\t\t\t\t<\/div>\n\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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Berikut di kongsikan sedikit Nota dan Latihan untuk ulangkaji Matematik SPM\u00a0 Slaid Interaktif Cerah: Ogif (Graf Kekerapan Longgokan) Statistik \u2022 Tingkatan 5 Ogif (Graf Kekerapan Longgokan) Slaid interaktif \u2014 guna kekunci \u2190 \/ \u2192 atau butang navigasi. Tema cerah untuk muat naik ke laman cikguhayat.com Kelas: Ulang Kaji (1 jam 20 minit) BBM: Slaid interaktif, [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":2419,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[112,216,4,215,115],"tags":[221,119,208,485],"class_list":{"0":"post-3327","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-akademik","8":"category-aktiviti-matematik","9":"category-guru","10":"category-matematik","11":"category-perkongsian","12":"tag-kssm-2","13":"tag-kssm","14":"tag-matematik","15":"tag-tingkatan-5"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ulang Kaji Ogif Matematik Tingkatan 5 | Nota, Slaid &amp; Lembaran Kerja - Cikgu Hayat<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cikguhayat.com\/v1.0\/ulang-kaji-ogif-matematik-tingkatan-5-nota-slaid-lembaran-kerja\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ulang Kaji Ogif Matematik Tingkatan 5 | Nota, Slaid &amp; Lembaran Kerja - Cikgu Hayat\" \/>\n<meta property=\"og:description\" content=\"Berikut di kongsikan sedikit Nota dan Latihan untuk ulangkaji Matematik SPM\u00a0 Slaid Interaktif Cerah: Ogif (Graf Kekerapan Longgokan) Statistik \u2022 Tingkatan 5 Ogif (Graf Kekerapan Longgokan) Slaid interaktif \u2014 guna kekunci \u2190 \/ \u2192 atau butang navigasi. 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