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PSLE Foundation Mathematics

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>In the diagram, \(O\) is the centre of the circle with a radius of \(5\) cm and chord \(AB\) has a length of \(8\) cm.<br>Find</p><ol class="abc-list"><li><div class="list-item-paragraph">\(x\),</div></li><li><div class="list-item-paragraph">\(y\).</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1780570879316-s7rd72klp.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODA1NzA4NzkzMTYtczdyZDcya2xwLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI3MjU1MzgsImV4cCI6MTc5MjcyNTgzOH0.GD2ySj7t8YfR4B1ygwO1fHcK4dS-RegKZ4UOZzgU3_4" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Applications of Pythagoras’ Theorem

Equal Chords and Distances from the Centre

Perpendicular Bisectors of Chords

Theoretical Principles of Circular Symmetry

Properties of Circle

Proofs in Plane Geometry

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>The figure below shows a circle with centre \(O\) and chords \(AB\) and \(CD\).<br>\(AB=5\) cm and \(OM=ON=3\) cm.<br>Calculate</p><ol class="abc-list"><li><div class="list-item-paragraph">the length of \(CN\).</div></li><li><div class="list-item-paragraph">the radius of the circle.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767596878608-znphqhb6v.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTY4Nzg2MDgtem5waHFoYjZ2LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI3MjU1MzgsImV4cCI6MTc5MjcyNTgzOH0.Ipdx8PGpIkp4VF7UR8DVu3yOhUg8yfp6E7-Dohmyx6M" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Symmetry and Right-Angled Triangles in Circles

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>In the diagram below, \(A\), \(C\), \(D\) and \(F\) lie on a circle with centre \(O\).<br>Line \(OB\) is perpendicular to chord \(AC\) and \(E\) is the mid-point of chord \(DF\).<br>Given that&nbsp;\(AC=6\) cm, \(DF=10\) cm, \(OE=5\) cm and \(OB=y\) cm, find the value of \(y\) correct to \(3\) significant figures.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767596697176-dbdb5y3ynui.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTY2OTcxNzYtZGJkYjV5M3ludWkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTUzOCwiZXhwIjoxNzkyNzI1ODM4fQ.-oVAH5qUejcpl5yrMRUkI3FbSmSiYUPD7UT0gcTRghg" style="max-width: min(220px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Circle Geometry: Chord-Radius Intersections

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>The perpendicular bisector of a chord, \(RS\), cuts it at \(T\) and the circumference of the circle at \(P\).<br>If&nbsp;\(RS=20\) cm and \(TP=8\) cm, find the radius of the circle.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767596534914-1u8ekgtep55.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTY1MzQ5MTQtMXU4ZWtndGVwNTUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTUzOCwiZXhwIjoxNzkyNzI1ODM4fQ.Yd7bNK0NgxtrXL0ILoI10ymIGzXukv9jG117Gk6EOp8" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Properties of Equidistant Chords in Circles

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The figure shows a circle with centre \(O\).<br>\(AB=8\) cm and \(OM=ON=3\) cm.</p><ol class="abc-list"><li><div class="list-item-paragraph">Find the length of \(CN\).</div></li><li><div class="list-item-paragraph">Find the radius of the circle.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767596200973-buj3wb30wzg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTYyMDA5NzMtYnVqM3diMzB3emcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTUzOCwiZXhwIjoxNzkyNzI1ODM4fQ.ObzqzgHi0UViX9M81xMTH3NxoOS2JPsbt3D0ZreTSN8" style="max-width: min(180px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Symmetrical Properties of Chords in a Circle

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>\(PQ\) is a chord of a circle, centre \(O\) and with radius \(17\) cm.<br>Given that&nbsp;\(PQ=30\) cm, find the perpendicular distance from centre \(O\) to the chord \(PQ\).</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767595923833-3mysobo93vj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTU5MjM4MzMtM215c29ibzkzdmoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTUzOCwiZXhwIjoxNzkyNzI1ODM4fQ.tuxf1AZiQOq-L5pUHIxr4QUGe_2eiNu-SdfjO-wxwfk" style="max-width: min(130px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Symmetry Properties of Circle Chords

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>The diagram above is a circle with a centre \(O\), \(OX=5\) cm and \(AB=PQ=14\) cm.<br>\(OX\) is perpendicular to \(AB\) and \(OY\) is perpendicular to \(PQ\).<br>Find the length of</p><ol class="abc-list"><li><div class="list-item-paragraph">\(OY\),</div></li><li><div class="list-item-paragraph">\(YQ\).</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767595339915-fa2u4mvm3dm.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTUzMzk5MTUtZmEydTRtdm0zZG0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTUzOCwiZXhwIjoxNzkyNzI1ODM4fQ.91V8c2J0lksEnMEd4gisnYu1ccc_1hhOMjrc7hMKpHE" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Applications of Circle Symmetric Property 2

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p style="text-align: left">The following shows a circle with centre \(O\).<br>\(CD\) is a chord of length \(24\) cm.<br>The perpendicular from \(O\) to chord \(CD\) meets it at \(M\), with \(OM=5\) cm.<br>Find the radius of the circle.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767595160465-7l77ji0bqgy.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTUxNjA0NjUtN2w3N2ppMGJxZ3kucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTUzOCwiZXhwIjoxNzkyNzI1ODM4fQ.purc1JYy-jelnhTQ_Oe3JaxLXZ76GQrlk61m6l9E4l4" style="max-width: min(300px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

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