A Math

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E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

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<p>The diagram shows a triangle $ABC$ with vertices $A(-5,\ 2)$ and $B(7,\ 8)$. The point $C$ lies on the perpendicular bisector of $AB$ and the equation of the line $BC$ is $y=3x-13$.</p>
<ol class="abc-list"><li data-list-item-id="cg-q13-a" data-list-item-path="cg-q13-a"><div class="list-item-paragraph">Find the equation of the perpendicular bisector of $AB$.<span class="inline-marks">[4]</span></div></li><li data-list-item-id="cg-q13-b" data-list-item-path="cg-q13-b"><div class="list-item-paragraph">Find the coordinates of $C$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q13-c" data-list-item-path="cg-q13-c"><div class="list-item-paragraph">Find the area of the triangle $ABC$.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows a triangle $ABC$ with vertices $A(-5,\ 2)$ and $B(7,\ 8)$. The point $C$ lies on the perpendicular bisector of $AB$ and the equation of the line $BC$ is $y=3x-13$.

Find the equation of the perpendicular bisector of $AB$.

Area of Rectilinear Figures

Parallel and Perpendicular Lines

Intersection of Two Lines

Equation of a Straight Line

Midpoint of a Line Segment

Perpendicular Bisectors

Perpendicular bisector and the third vertex of a triangle

Coordinate Geometry

<p>The diagram shows a triangle $ABC$ in which $A$ is $(0,\ 6)$, $B$ is $(a,\ 7)$ and $C$ is $(12,\ 0)$. The point $M$ is the midpoint of $AC$ and $BM$ is perpendicular to $AC$.</p>
<div class="graph-block" data-graph-config="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" data-width="440" data-height="280" style="width:440px;height:280px;max-width:100%;display:block;margin:0 auto;"></div>
<p>Find</p>
<ol class="i-list"><li data-list-item-id="cg-q05-i" data-list-item-path="cg-q05-i"><div class="list-item-paragraph">the coordinates of $M$,<span class="inline-marks">[1]</span></div></li><li data-list-item-id="cg-q05-ii" data-list-item-path="cg-q05-ii"><div class="list-item-paragraph">the equation of the perpendicular bisector of $AC$,<span class="inline-marks">[3]</span></div></li><li data-list-item-id="cg-q05-iii" data-list-item-path="cg-q05-iii"><div class="list-item-paragraph">the value of $a$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q05-iv" data-list-item-path="cg-q05-iv"><div class="list-item-paragraph">the area of the triangle $ABC$.<span class="inline-marks">[3]</span></div></li></ol>

The diagram shows a triangle $ABC$ in which $A$ is $(0,\ 6)$, $B$ is $(a,\ 7)$ and $C$ is $(12,\ 0)$. The point $M$ is the midpoint of $AC$ and $BM$ is perpendicular to $AC$.

the equation of the perpendicular bisector of $AC$,

Perpendicular bisector of a side of a triangle

<p>Two points $ A(-3,-6) $ and $ B (7,-6) $ lie on a circle centre $ G$. The equation of the tangent to the circle at the point $ Q(1,-12) $ is $x+5y+59=0$.</p>
<ol class="abc-list"><li data-list-item-id="item-1773467964823-vim5kux87"><div class="list-item-paragraph">Show that the coordinates of $G$ is $ (2,-7) $<span class="inline-marks">[5]</span></div></li><li data-list-item-id="item-1773467967295-xi8wvogbp"><div class="list-item-paragraph">Find the equation of the circle in the form of $x^2+y^2+2gx+2fy+c=0$, stating the value of $f$, $g$ and  $c$.<span class="inline-marks">[3]</span></div></li></ol>

Two points $A(-3,-6)$ and $B(7,-6)$ lie on a circle with centre $G$. The equation of the tangent to the circle at the point $Q(1,-12)$ is $x+5y+59=0$.

Show that the coordinates of $G$ is $(2,-7)$.

Find the equation of the circle in the form of $x^2+y^2+2gx+2fy+c=0$, stating the value of $f$, $g$ and $c$.

Finding the Equation of a Circle

Tangents and Normals to Circles

2025 MSHS PRELIMS P2 Q7

<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/1782643154194-60z17dgtnt8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODI2NDMxNTQxOTQtNjB6MTdkZ3RudDgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNiwiZXhwIjoxNzkyNjk2MTE2fQ.sJGI0iZHd0xHgRPstU82l_O4n-Wcal2lYzzNxoUgscs" style="max-width: min(250px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>The diagram shows a triangle $PQR$ with vertices $P(9,10)$ and $Q(1,-2)$. The point $R$ lies on the perpendicular bisector of $PQ$ and the equation of the line $QR$ is $y = 8x - 10$.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-content"><span class="list-item-text">Find the equation of the perpendicular bisector of $PQ$.</span><span class="inline-marks">[4]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-content"><span class="list-item-text">Find the coordinates of $R$.</span><span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-content"><span class="list-item-text">Find the area of triangle $PQR$.</span><span class="inline-marks">[2]</span></div></li></ol>

The diagram shows a triangle $PQR$ with vertices $P(9,10)$ and $Q(1,-2)$. The point $R$ lies on the perpendicular bisector of $PQ$ and the equation of the line $QR$ is $y=8x-10$.

Find the equation of the perpendicular bisector of $PQ$.

2025 DSS PRELIMS P1 Q12

<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/1770805603072-58nwvw5dd8k.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA4MDU2MDMwNzItNThud3Z3NWRkOGsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNiwiZXhwIjoxNzkyNjk2MTE2fQ.tzDycKW6HnobgOWrUQuctVa-aoM9-xKp0vMWwzy86jI" style="max-width: min(250px, 100%); height: auto; display: block;" alt="The diagram shows an isosceles triangle $PQR$ on a coordinate plane." class="aligncenter custom-width" /></figure></div>
<p>The diagram shows an isosceles triangle $PQR$ with vertices at $P(0, k)$, $Q(3, 9)$ and $R(h, 6)$, where&nbsp;$h$ and $k$ are positive constants and $h &gt; k$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that&nbsp;$h + k = 12$.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">It is now given that&nbsp;$h = 7$.<br>The point $S$ is such that&nbsp;$PQRS$ is a kite. Given that&nbsp;$S$ lies on the line $21y = 7x - 8$, find the coordinates of $S$.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Find the area of the kite.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows an isosceles triangle $PQR$ with vertices at $P(0, k)$, $Q(3, 9)$ and $R(h, 6)$, where $h$ and $k$ are positive constants and $h > k$.

It is now given that $h = 7$.\nThe point $S$ is such that $PQRS$ is a kite. Given that $S$ lies on the line $21y = 7x - 8$, find the coordinates of $S$.

Length of a Line Segment

IP3 Class Test (May 2025) Q11 (2023 ACSBR AM Prelim P2 Q5)

<p>The point $P$ has the coordinates of $(-3, 8)$ and the line joining the points $P$ and $Q$ has a gradient of $-\frac{3}{4}$.</p>
<p>The perpendicular bisector of $PQ$ passes through the point $(8, 6)$.</p>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the equation of $PQ$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the coordinates of $Q$.</span></div></li></ol>

The point $P$ has the coordinates of $(-3, 8)$ and the line joining the points $P$ and $Q$ has a gradient of $-\frac{3}{4}$.

The perpendicular bisector of $PQ$ passes through the point $(8, 6)$.

<p>The line passing through the points $P(-2, 5)$ and $Q(q, 8)$ is parallel to the line $3x + 4y + 4 = 0$.</p>
<p>Find the</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">value of $q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">distance $PQ$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">equation of the perpendicular bisector of $PQ$.</span></div></li></ol>

The line passing through the points $P(-2, 5)$ and $Q(q, 8)$ is parallel to the line $3x + 4y + 4 = 0$.

equation of the perpendicular bisector of $PQ$.

<p>The line $y + x = 1$ intersects the curve $x^2 + y^2 - 2y = 7$ at $P$ and $Q$. Find the equation of the perpendicular bisector $PQ$.</p>

The line $y + x = 1$ intersects the curve $x^2 + y^2 - 2y = 7$ at $P$ and $Q$. Find the equation of the perpendicular bisector $PQ$.

Line–Circle Intersections

<p>The line $y + x + 7 = 0$ meets the curve $y^2 + x = 5$ at the points $P$ and $Q$.</p>
<p>Find the equation of the perpendicular bisector of $PQ$.</p>

The line $y + x + 7 = 0$ meets the curve $y^2 + x = 5$ at the points $P$ and $Q$.

Intersection of a Line and a Curve

Quadratic Functions, Equations and Inequalities

<p>Three points have coordinates $P(-3, 4)$, $Q(7, -2)$ and $R(5, m)$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the value of $m$ if&nbsp;$PQ$ is perpendicular to $PR$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the midpoint of $PQ$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the equation of the perpendicular bisector of $PQ$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the lengths of $PQ$ and $PR$,</span></div></li><li><div class="list-item-paragraph">the area of triangle $PQR$, using the results in <strong>(d)</strong>.</div></li></ol>

Three points have coordinates $P(-3, 4)$, $Q(7, -2)$ and $R(5, m)$. Find

the value of $m$ if $PQ$ is perpendicular to $PR$,

the equation of the perpendicular bisector of $PQ$,

<p>Three points have coordinates $A(1, 8)$, $B(0, 3)$ and $C(k, 5)$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the value of $k$ if&nbsp;$AC$ is perpendicular to $BC$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the midpoint of $AB$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the equation of the perpendicular bisector of $AB$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the lengths of $AB$ and $BC$,</span></div></li><li><div class="list-item-paragraph">the area of triangle $ABC$, using the results in <strong>(d)</strong>.</div></li></ol>

Three points have coordinates $A(1, 8)$, $B(0, 3)$ and $C(k, 5)$. Find

the value of $k$ if $AC$ is perpendicular to $BC$,

the equation of the perpendicular bisector of $AB$,

<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the coordinates of the centre and the radius of the circle $x^{2} + y^{2} - 4x - 8y - 5 = 0$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If the circle cuts the $x$-axis at $P$ and $Q$, find the equation of the perpendicular bisector of the line $PQ$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given that the line $2y - 6x + 4 = 0$ intersects the circle at $R$ and $S$, find the coordinates of $R$ and $S$. Hence show that the line segment $RS$ is a diameter of the circle.</span></div></li></ol>

Find the coordinates of the centre and the radius of the circle $x^{2} + y^{2} - 4x - 8y - 5 = 0$.

If the circle cuts the $x$-axis at $P$ and $Q$, find the equation of the perpendicular bisector of the line $PQ$.

Given that the line $2y - 6x + 4 = 0$ intersects the circle at $R$ and $S$, find the coordinates of $R$ and $S$. Hence show that the line segment $RS$ is a diameter of the circle.

Finding the Centre and Radius of a Circle

<p>A circle with centre $C$ passes through points $A(-8, 3)$ and $B(-1, -4)$.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Explain why the perpendicular bisector of $AB$ will pass through $C$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given that&nbsp;$C$ lies on the line $y = 2x + 5$, find $C$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence find the equation of the circle.</span></div></li></ol>

A circle with centre $C$ passes through points $A(-8, 3)$ and $B(-1, -4)$.

Explain why the perpendicular bisector of $AB$ will pass through $C$.

Given that $C$ lies on the line $y = 2x + 5$, find $C$.

<p>The points $A(7, 7)$ and $B(-2, -5)$ are at the opposite ends of a diameter of a circle $C_1$. Find the</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">centre of the circle and the radius of the circle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">equation of the circle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">equation of the perpendicular bisector $AB$.</span></div></li></ol>
<p>The circle, $C_1$, is reflected in the $x$-axis.</p>
<ol class="abc-list" start="4"><li><div class="list-item-content"><span class="list-item-text">Find the equation of the reflected circle, $C_2$.</span></div></li></ol>

The points $A(7, 7)$ and $B(-2, -5)$ are at the opposite ends of a diameter of a circle $C_1$. Find the

centre of the circle and the radius of the circle.

equation of the perpendicular bisector $AB$.

The circle, $C_1$, is reflected in the $x$-axis.

Find the equation of the reflected circle, $C_2$.

Reflections and Translations of Circles

<p><strong>Solutions to this question by accurate drawing will not be accepted.</strong></p>
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<p>The diagram shows a rhombus $ABCD$ with vertices $A$ and $C$ at the points $(0, 2)$ and $(-6, 4)$ respectively. $B$ lies on the $x$-axis and the line $DC$ produced intersects with the $x$-axis at $E$.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Find the coordinates of $B$.</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Explain if&nbsp;$ABCD$ is a square.</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Find the coordinates of $E$.</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">Find the area of $ABED$.</div></li></ol>

**Solutions to this question by accurate drawing will not be accepted.**

The diagram shows a rhombus $ABCD$ with vertices $A$ and $C$ at the points $(0, 2)$ and $(-6, 4)$ respectively. $B$ lies on the $x$-axis and the line $DC$ produced intersects with the $x$-axis at $E$.

<p>$A$ is the point $(3, 7)$ and the line joining the points $A$ and $B$ has a gradient of $\frac{1}{5}$.</p>
<p>The perpendicular bisector of $AB$ passes through the point $(6, 3)$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the equation of $AB$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the coordinates of $B$.</span></div></li></ol>

$A$ is the point $(3, 7)$ and the line joining the points $A$ and $B$ has a gradient of $\frac{1}{5}$.

The perpendicular bisector of $AB$ passes through the point $(6, 3)$. Find

<p>The line $y + 2x = 1$ intersects the curve $x^2 - 2xy + y^2 = 8$ at $P$ and $Q$. Find</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-content"><span class="list-item-text">the coordinates of $P$ and $Q$ in exact form,</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-content"><span class="list-item-text">the equation of the perpendicular bisector $PQ$.</span></div></li></ol>

The line $y + 2x = 1$ intersects the curve $x^2 - 2xy + y^2 = 8$ at $P$ and $Q$. Find

the coordinates of $P$ and $Q$ in exact form,

the equation of the perpendicular bisector $PQ$.

<p>The points $A$ and $B$ have coordinates $\left( 6,3 \right)$ and $\left( 13,5 \right)$ respectively. Find the equation of the perpendicular bisector of the line $AB$.</p>

The points $A$ and $B$ have coordinates $\left( 6,3 \right)$ and $\left( 13,5 \right)$ respectively. Find the equation of the perpendicular bisector of the line $AB$.

<p>The line $y = x + 6$ meets the curve $y^2 = x + 12$ at the points $A$ and $B$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the coordinates of $A$ and $B$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the equation of the perpendicular bisector of $AB$.</span></div></li></ol>

The line $y = x + 6$ meets the curve $y^2 = x + 12$ at the points $A$ and $B$. Find

the equation of the perpendicular bisector of $AB$.

<p>The diagram shows a rhombus with vertices $A(0, 5)$, $B(m, 11)$, $C(14, 19)$ and $D$.</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/1768310970952-4zd6lx7zvsc.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjgzMTA5NzA5NTItNHpkNmx4N3p2c2MucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNiwiZXhwIjoxNzkyNjk2MTE2fQ.WGktA87nTEXKfrnWG_OeyX9-9Ql_aYPNKjva98l27aA" style="max-width: min(250px, 100%); height: auto; display: block;" alt="A rhombus ABCD on a Cartesian plane with vertex A on the y-axis." class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the equation of the perpendicular bisector of $AC$.</span><span class="inline-marks">[4]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Show that $m = 8$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the coordinates of $D$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the area of the rhombus.</span><span class="inline-marks">[2]</span></div></li></ol>

The diagram shows a rhombus with vertices $A(0, 5)$, $B(m, 11)$, $C(14, 19)$ and $D$.

Find the equation of the perpendicular bisector of $AC$.

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