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PSLE

PSLE Foundation Mathematics

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Construct a quadrilateral $ABCD$ such that $AB = 6.3$ cm, $AC = 8.2$ cm, $BD = 5.6$ cm, $AB$ is perpendicular to $BC$, and angle $BAD = 60^\circ$.</span></div><ol class="abc-list"><li><div class="list-item-paragraph">Measure and write down the largest possible size of angle $ADC$.</div></li><li><div class="list-item-paragraph">Construct a straight line parallel to $AB$ that passes through $C$ to meet $AD$ produced at $E$. Measure and write down the length of $CE$ and determine the type of quadrilateral $ABCE$.</div></li></ol></li></ol>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Construct a quadrilateral $ABCD$ such that $AB = 4.5$ cm, $BC = 4$ cm, $CD = 4.2$ cm, diagonal $BD = 3.4$ cm, angle $BAD = 40^\circ$ and angle $ADB$ is acute.</span></div><ol class="abc-list"><li><div class="list-item-paragraph">Measure and write down the length of $AC$.</div></li><li><div class="list-item-paragraph">Construct a point $P$ that lies on side $AD$, such that $P$ is equidistant from $A$ and $B$. Measure and write down the length of $PD$.</div></li></ol></li></ol>

Construct a quadrilateral $ABCD$ such that $AB = 6.3$ cm, $AC = 8.2$ cm, $BD = 5.6$ cm, $AB$ is perpendicular to $BC$, and angle $BAD = 60^\circ$.

Construct a quadrilateral $ABCD$ such that $AB = 4.5$ cm, $BC = 4$ cm, $CD = 4.2$ cm, diagonal $BD = 3.4$ cm, angle $BAD = 40^\circ$ and angle $ADB$ is acute.

Constructing Perpendicular Bisectors

Constructing Quadrilaterals

Loci and Regions by Construction

 Constructions of Quadrillaterals

Geometrical Constructions

<ol class="abc-list"><li><div class="list-item-paragraph">Construct a quadrilateral $ABCD$ such that&nbsp;$AB=9$ cm, $AD=8$ cm, $BC=6$ cm,$\angle BAD=60{}^\circ $ and $\angle ABC=90{}^\circ $.  </div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the perpendicular bisector of $AD$,</div></li><li><div class="list-item-paragraph">the bisector of $\angle BAD$.</div></li></ol></li><li><div class="list-item-paragraph">A point $P$ is equidistant from $AD$ and $AB$, and is also nearer to $A$ than $D$. Mark and label clearly a possible point $P$.</div></li></ol>

Constructing Angle Bisectors

Quadrilateral Construction and Locus Conditions

<p>In triangle $ABC$, $AB=15.7$ cm, $BC=9$ cm and $AC=10$ cm.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Using ruler and compasses only, draw the triangle $ABC$,</div></li><li><div class="list-item-paragraph">Measure the largest angle of the triangle,</div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the bisector of the angle $BAC$,</div></li><li><div class="list-item-paragraph">the perpendicular bisector of the line $AC$.</div></li></ol></li><li><div class="list-item-paragraph">Mark out the point $P$ on your diagram such that&nbsp;$P$ is equidistant from the points $A$ and $C$ and equidistant from the lines $AB$ and $AC$. Measure the length $PA$.</div></li></ol>

In triangle $ABC$, $AB=15.7$ cm, $BC=9$ cm and $AC=10$ cm.

Constructing Triangles

Triangle Construction and Locus Problems

<p>In the triangle $ABC$, $AB=10$ cm, $BC=8$ cm and $\angle BAC=50{}^\circ $. </p>
<ol class="abc-list"><li><div class="list-item-paragraph">Complete two possible triangles $ABC$ that are of different sizes.</div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the perpendicular bisector of $AB$,</div></li><li><div class="list-item-paragraph">the angle bisector of $\angle BAC$.</div></li></ol></li><li><div class="list-item-paragraph">Mark, with an $X$, the point that is equidistant from the points $A$ and $B$, and equidistant from the line $AC$ and $AB$.</div></li><li><div class="list-item-paragraph">Hence, measure the length of $BX$.</div></li></ol>

In the triangle $ABC$, $AB=10$ cm, $BC=8$ cm and $\angle BAC=50{}^\circ $. 

Construction: Two Possible Triangles and a Point Defined by Loci

<ol class="abc-list"><li><div class="list-item-paragraph">Construct quadrilateral $ABCD$ where&nbsp;$AB=12$ cm, $BC=6$ cm, $\angle ABC=90{}^\circ $, $CD=10.5$ cm and $AD=11.4$ cm. </div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the perpendicular bisector of $CD$,</div></li><li><div class="list-item-paragraph">the angle bisector of $\angle ABC$.</div></li></ol></li><li><div class="list-item-paragraph">Mark clearly a possible point which is inside the quadrilateral, equidistant to the points $C$ and $D$, and is nearer to lines $AB$ than $BC$. Label this point $K$.</div></li></ol>

Quadrilateral Construction and Loci

<ol class="abc-list"><li><div class="list-item-paragraph">Construct $\Delta ABC$ in the space provided below, where&nbsp;$AB=8$ cm, $AC=7$ cm and<br>$\angle CAB=60{}^\circ $.  Label the vertices of your triangle clearly.<br></div></li><li><div class="list-item-paragraph">Measure and write down the length of $BC$, giving your answer to $1$ decimal place.</div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the angle bisector of $\angle BCA$,</div></li><li><div class="list-item-paragraph">the perpendicular bisector of $BC$.</div></li></ol></li><li><div class="list-item-paragraph">Point $P$ is a point inside the triangle such that&nbsp;$BP &lt; CP$ and $P$ is located nearer to $BC$ than to $AC$.  Shade the region where&nbsp;$P$ could possibly be located.</div></li></ol>

Triangle Construction and Loci

<p>Construct triangle $XYZ$ such that&nbsp;$XY=5$ cm, angle $XYZ=120{}^\circ $ and angle $YXZ=37{}^\circ $. </p>
<ol class="abc-list"><li><div class="list-item-paragraph">Construct the perpendicular bisector of $YZ$.</div></li><li><div class="list-item-paragraph">Construct the angle bisector of angle $YXZ$.</div></li><li><div class="list-item-paragraph">Describe the point of intersection between these two bisectors.</div></li></ol>

Construct triangle $XYZ$ such that $XY=5$ cm, angle $XYZ=120{}^\circ $ and angle $YXZ=37{}^\circ $. 

Triangle Construction and Bisector Constructions

<p>Construct triangle $ABC$ where&nbsp;$BC=6$ cm and $\angle ABC=85{}^\circ $. $AB$ has already been drawn.<br><br><br><br><br><br><br><br><br><br></p>
<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/1764327866780-g8v8ijnv1bb.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQzMjc4NjY3ODAtZzh2OGlqbnYxYmIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNTk1NiwiZXhwIjoxNzkzNTA2MjU2fQ.hqEqUUUQVNruOdXyQLcHGoo7AIeDrGIASzA6rb1kWWs" style="max-width: min(320px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p><br><br><br><br><br><br><br><br><br><br><br><br><br></p>
<ol class="abc-list"><li data-list-item-id="item-1764327875547-tzp1ssahq"><div class="list-item-paragraph">Construct</div><ol class="i-list"><li data-list-item-id="subitem-1764327898512-mdl49fk2r"><div class="list-item-paragraph">the perpendicular bisector of $AB$.</div></li><li data-list-item-id="subitem-1764327909245-o0ywc53fd"><div class="list-item-paragraph">the bisector of angle $BAC$.</div></li></ol></li><li data-list-item-id="item-1764327877152-urcs1kd37"><div class="list-item-paragraph">Mark clearly a possible point which is inside the triangle, equidistant from $A$ and $B$, and 	is nearer to $AC$ than $AB$. Label this point $P$.</div></li></ol>

Construct triangle $ABC$ where $BC=6$ cm and $\angle ABC=85{}^\circ $. $AB$ has already been drawn.











Triangle Construction and Locus of Points

<p>In the triangle $PQR$, $PQ=7.5$ cm, $QR=6$ cm and $PR=11$ cm.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Draw the triangle $PQR$.</div></li><li><div class="list-item-paragraph">Construct</div><ol class="i-list"><li><div class="list-item-paragraph">the perpendicular bisector of $PQ$,</div></li><li><div class="list-item-paragraph">the angle bisector of angle $QRP$.</div></li></ol></li><li><div class="list-item-paragraph">Describe the point of intersection between lines drawn in <strong>(b)(i)</strong> and <strong>(b)(ii)</strong>. </div></li></ol>

In the triangle $PQR$, $PQ=7.5$ cm, $QR=6$ cm and $PR=11$ cm.

Constructing a Triangle and Its Perpendicular and Angle Bisectors

<ol class="abc-list"><li><div class="list-item-paragraph">Construct triangle $ABC$ with $AB=8.3$ cm, $BC=7.5$ cm and $\angle ABC=67{}^\circ $.</div></li><li><div class="list-item-paragraph">By construction, mark the point $P$, which is equidistant from $A$, $B$ and $C$.</div></li></ol>

Construction of a Triangle with 2 given sides and an angle

<ol class="abc-list"><li data-list-item-id="item-1764324727560-0wfv32r3o" data-list-item-path="item-1764324727560-0wfv32r3o"><div class="list-item-paragraph">Draw a triangle $ABC$ to scale where&nbsp;$AB\mathrm{ }=\mathrm{ }12$ cm, $AC\mathrm{ }=\mathrm{ }8.5$ cm and $BC\mathrm{ }=\mathrm{ }7$ cm.</div></li><li data-list-item-id="item-1764324728190-oi8jr5f55" data-list-item-path="item-1764324728190-oi8jr5f55"><div class="list-item-paragraph">By drawing suitable lines, locate a point $P$ such that&nbsp;$P$ is equidistant from line $AB$, line $BC$, point $A$ and point $B$.</div></li></ol>
<p>Interpret part (b) as two separate conditions: $PA=PB$, and the perpendicular distances from $P$ to the lines $AB$ and $BC$ are equal. The point-to-point distance need not equal the point-to-line distance. Requiring all four distances to be identical would have no solution.</p>

Interpret part (b) as two separate conditions: $PA=PB$, and the perpendicular distances from $P$ to the lines $AB$ and $BC$ are equal. The point-to-point distance need not equal the point-to-line distance. Requiring all four distances to be identical would have no solution.

Math Question Bank