A Math

A Math (IGCSE)

E Math

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

<p>The diagram below shows a rectangular plot of land with a circular pond. It is known that the length is $3$ metres longer than twice of the width. The width of the land is $x$ m.</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/1767600843964-s9ivokqew7i.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDA4NDM5NjQtczlpdm9rcWV3N2kucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjYxNywiZXhwIjoxNzkyNjYyOTE3fQ.UoLPnXQHRjS4I0_W8AGC4dcxUV7QvdcCwIrJOgbxf4s" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down an expression, in terms of $x$, for the length of the land (in metres).</span></div></li><li><div class="list-item-paragraph">The perimeter of the land is $48$ meters and the radius of the pond is $3$ metres. Find the value of $x$.</div></li><li><div class="list-item-paragraph">Find the area of the land which is not covered by the pond, correct to $3$ significant figures.</div></li></ol>

The diagram below shows a rectangular plot of land with a circular pond. It is known that the length is $3$ metres longer than twice of the width. The width of the land is $x$ m.

Write down an expression, in terms of $x$, for the length of the land (in metres).

Perimeter and Area of Composite Figures

Applications of Linear Equations in Real Life

Forming Algebraic Expressions and Formulae

Perimeter and Area of Rectangles and Squares

Algebraic Expressions, Identities and Formulae

Linear Equations and Inequalities

Perimeter and Area of Plane Figures

<p>The age of Alan’s father is $5$ years older than $3$ times that of Alan. Let $x$ be Alan’s age (in years).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Express the father’s age (in years) in terms of $x$.</span></div></li><li><div class="list-item-paragraph">After $35$ years, Alan will be as old as his father now. Write down an equation in $x$ and solve it to find Alan’s age.</div></li></ol>

The age of Alan’s father is $5$ years older than $3$ times that of Alan. Let $x$ be Alan’s age (in years).

Express the father’s age (in years) in terms of $x$.

<p>Alice has $3x$ marbles. Beatrice has $6$ more marbles than Alice. Candice has half as many marbles as Beatrice.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down an expression, in terms of $x$, for the number of marbles that Candice has.</span></div></li><li><div class="list-item-paragraph">The total number of marbles is $114$. Find the number of marbles that Beatrice has.</div></li></ol>

Alice has $3x$ marbles. Beatrice has $6$ more marbles than Alice. Candice has half as many marbles as Beatrice.

Write down an expression, in terms of $x$, for the number of marbles that Candice has.

<p>Concert tickets were sold at $\$ \ (5x - 8)$ for an adult ticket and $\$ \ (27 - 3y)$ for a child ticket. Mr. Lim intended to bring his family to the concert and bought $2$ adult tickets and $3$ child tickets. Due to unforeseen circumstances, Mr. Lim could not make it to the concert. He sold all his tickets at a loss to Mr. Rahman at $\$ \ (31 - 5y)$ for an adult ticket and $\$ \ (24 - x)$ for a child ticket.</p>
<p>Find and simplify, in terms of $x$ and $y$, an expression for</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the total cost of tickets purchased by Mr. Lim,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the total amount paid to Mr. Lim by Mr. Rahman,</span></div></li><li><div class="list-item-content"><span class="list-item-text">Mr. Lim’s total loss of money from the sales of tickets to Mr. Rahman.</span></div></li></ol>

Concert tickets were sold at $\$ \ (5x - 8)$ for an adult ticket and $\$ \ (27 - 3y)$ for a child ticket. Mr. Lim intended to bring his family to the concert and bought $2$ adult tickets and $3$ child tickets. Due to unforeseen circumstances, Mr. Lim could not make it to the concert. He sold all his tickets at a loss to Mr. Rahman at $\$ \ (31 - 5y)$ for an adult ticket and $\$ \ (24 - x)$ for a child ticket.

Find and simplify, in terms of $x$ and $y$, an expression for

the total cost of tickets purchased by Mr. Lim,

the total amount paid to Mr. Lim by Mr. Rahman,

Mr. Lim’s total loss of money from the sales of tickets to Mr. Rahman.

 Additions and Subtractions of Linear Algebraic Expressions

<p>Adrian purchased $13$ erasers at  $\$\ (1 - x)$ each and $26$ pens at  $\$\ (2y + 3)$ each. He then bundled it into packs of $2$ pens and an eraser and sold it for&nbsp;$\$\ (8x - 3y)$ at a school fundraiser event. He sold everything at the end of the event.</p>
<p>Find and simplify, in terms of $x$ and $y$, an expression for</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the total cost of a bundled pack,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the amount of money collected from the sales of all the bundled packs,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the total profit from the sales of all the bundles packs.</span></div></li></ol>

Adrian purchased $13$ erasers at  $\$\ (1 - x)$ each and $26$ pens at  $\$\ (2y + 3)$ each. He then bundled it into packs of $2$ pens and an eraser and sold it for $\$\ (8x - 3y)$ at a school fundraiser event. He sold everything at the end of the event.

the amount of money collected from the sales of all the bundled packs,

the total profit from the sales of all the bundles packs.

Additions and Subtractions of Linear Algebraic Expressions

<p>A dozen of eggs cost $x$ cents. Find an expression, in terms of $x$ and $y$, for the number of eggs that can be bought for&nbsp;$y$ dollars.</p>
<p>Assume $x&gt;0$, eggs can be bought singly at the same unit price, and $y$ dollars buys a whole number of eggs with no money left over.</p>

A dozen of eggs cost $x$ cents. Find an expression, in terms of $x$ and $y$, for the number of eggs that can be bought for $y$ dollars.

Assume $x>0$, eggs can be bought singly at the same unit price, and $y$ dollars buys a whole number of eggs with no money left over.

[EPQ Vol 1A] Question 20

<p>Given that $x$ is an odd number. Find and simplify an expression, in terms of $x$, for the average of $x$ and the next $2$ even numbers.</p>

Given that $x$ is an odd number. Find and simplify an expression, in terms of $x$, for the average of $x$ and the next $2$ even numbers.

[EPQ Vol 1A] Question 19

<p>A rectangle field has width of $\left( 5x-y \right)$ m. It is given that the length is twice of its width.</p>
<p>The owner of the field intends to install fence around the field. The cost of installing the fence on the sides of the width is $\$55$ per metre and on the sides of the length is $\$42$ per metre.</p>
<p>Find and simplify, in terms of $x$ and $y$, an expression for</p>
<ol class="abc-list"><li data-list-item-id="item-1765260914145-8eru3yxwu" data-list-item-path="item-1765260914145-8eru3yxwu"><div class="list-item-paragraph">the perimeter of the rectangle,</div></li><li data-list-item-id="item-1765260919072-5lrafcyjh" data-list-item-path="item-1765260919072-5lrafcyjh"><div class="list-item-paragraph">the total cost of installing the fences.</div></li></ol>

A rectangle field has width of $\left( 5x-y \right)$ m. It is given that the length is twice of its width.

The owner of the field intends to install fence around the field. The cost of installing the fence on the sides of the width is $\$55$ per metre and on the sides of the length is $\$42$ per metre.

Find and simplify, in terms of $x$ and $y$, an expression for

[EPQ Vol 1A] Question 15

<p>Angie is $x$ years old.  Her sister is $12$ years older than her while their mother is twice as old as her sister.  Lily is $3$ years younger than Angie while Lily’s mother is $4$ times as old as Lily.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Express the age of Angie’s mother in terms of $x$.</div></li><li><div class="list-item-paragraph">Express the age of Lily’s mother in terms of $x$.</div></li><li><div class="list-item-paragraph">If Angie’s mother is $6$ years older than Lily’s mother, find Angie’s age.</div></li></ol>

Angie is $x$ years old.  Her sister is $12$ years older than her while their mother is twice as old as her sister.  Lily is $3$ years younger than Angie while Lily’s mother is $4$ times as old as Lily.

Word Problem: Ages and Relationships Between Family Members

<p>Amin is $x$ years old and his father is $4$ times as old as him.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down, in its simplest form, an algebraic expression in terms of $x$,</div><ol class="i-list"><li><div class="list-item-paragraph">for Amin’s father’s age now.</div></li><li><div class="list-item-paragraph">for Amin’s age in $5$ years’ time.</div></li></ol></li><li><div class="list-item-paragraph">Given that the sum of their ages in $5$ years’ time is $55$, form an equation in $x$ and find Amin’s age now.</div></li></ol>

Amin is $x$ years old and his father is $4$ times as old as him.

Word Problem: Ages (Amin and His Father)

<p>Amy has $47$ sweets and Benny has $65$ sweets.  If Amy gives some sweets to Benny, the ratio of the sweets of Amy to that of Benny becomes $3:5$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">If the number of sweets that Amy gives to Benny is $x$, write down an expression, in terms of $x$, for the remaining sweets that Amy has.</div></li><li><div class="list-item-paragraph">Write down an expression in terms of $x$, for the number of sweets that Benny has after receiving $x$ number of sweets from Amy.</div></li><li><div class="list-item-paragraph">Hence, form an equation and solve for $x$.</div></li></ol>

Amy has $47$ sweets and Benny has $65$ sweets.  If Amy gives some sweets to Benny, the ratio of the sweets of Amy to that of Benny becomes $3:5$.

Word Problem: Ratio and Transfer of Quantities

<p>There are $3$ consecutive odd integers.  Let $n-1$ be the smallest integer.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down expressions for the next two bigger consecutive odd integers after $n-1$.</div></li><li><div class="list-item-paragraph">Find, in its simplest form, the expression for the sum of these three consecutive odd integers.</div></li><li><div class="list-item-paragraph">If the sum is $159$, find the value of $n$.</div></li></ol>

There are $3$ consecutive odd integers.  Let $n-1$ be the smallest integer.

Word Problem: Consecutive Odd Integers

<p>David is $x$ years old.  David’s father is thrice the age of David.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down an expression, in terms of $x$, for the father’s age.</div></li></ol>
<p>In $5$ years’ time the sum of their ages is equal to $70$.</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Write down an expression, in terms of $x$, for the father’s age in $5$ years’ time.</div></li><li><div class="list-item-paragraph">Form an equation in terms of $x$.</div></li><li><div class="list-item-paragraph">Solve the equation and find the father’s present age.</div></li></ol>

David is $x$ years old.  David’s father is thrice the age of David.

In $5$ years’ time the sum of their ages is equal to $70$.

Word Problem: Ages (David and His Father)

<p>Nat’s mother is $4$ times as old as Nat.  Nat’s sister is $3$ years younger than Nat.</p>
<p>Let&nbsp;$n$ years old be the age of Nat.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Express in terms of $n$ the age of Nat’s mother.</div></li><li><div class="list-item-paragraph">Express in terms of $n$, the age of Nat’s sister.</div></li><li><div class="list-item-paragraph">If&nbsp;$n=9$, in how many years’ time would the age of Nat’s mother be three times his sister? Solve by first forming an equation.</div></li></ol>

Nat’s mother is $4$ times as old as Nat.  Nat’s sister is $3$ years younger than Nat.

Word Problem: Ages and Algebraic Expressions

<p>Given that&nbsp;$n$ is a positive odd integer,</p>
<ol class="abc-list"><li><div class="list-item-paragraph">write down the expression for the</div><ol class="i-list"><li><div class="list-item-paragraph">next odd number after $n$.</div></li><li><div class="list-item-paragraph">number that is $3$ less than the product of $4$ and $n$.</div></li></ol></li><li><div class="list-item-paragraph">If the difference between the answers in <strong>(a)(i)</strong> and <strong>(a)(ii)</strong> is $16$, find the integer $n$.</div></li></ol>

Given that $n$ is a positive odd integer,

Word Problem: Algebraic Expressions and Integer Relations

<p>Beatrice’s car can travel $x$ km on each litre of petrol.  She travelled $\left( x+10 \right)$ km on Monday.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down, in terms of $x$, the number of litres of petrol she used on Monday.</div></li><li><div class="list-item-paragraph">Given that she travelled $\left( 2x+15 \right)$ km on Tuesday and used $1.25$ litres of petrol more on Tuesday than on Monday, form an equation in $x$ and solve it.</div></li><li><div class="list-item-paragraph">Calculate the total distance that she travelled on Monday and Tuesday.</div></li></ol>

Beatrice’s car can travel $x$ km on each litre of petrol.  She travelled $\left( x+10 \right)$ km on Monday.

Word Problem: Fuel Consumption and Distance

<div class="graph-block" data-graph-config="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" data-width="252" data-height="169" style="width:252px;height:169px;max-width:100%;display:block;margin:0 auto;"></div>
<p>The figure shows $6$ identical rectangles of length $\left( 2x+3y \right)$cm and breadth $y$ cm, where&nbsp;$x$ and $y$ are positive integers.</p>
<ol class="abc-list"><li data-list-item-id="item-1760421173523-jze2c3sg0" data-list-item-path="item-1760421173523-jze2c3sg0"><div class="list-item-paragraph">Express the following in terms of $x$ and/or $y$.</div><ol class="i-list"><li data-list-item-id="subitem-1760421180340-7gwc9hsi4" data-list-item-path="item-1760421173523-jze2c3sg0/subitem-1760421180340-7gwc9hsi4"><div class="list-item-paragraph">$p$,</div></li><li data-list-item-id="subitem-1760421180910-zfp8kuopn" data-list-item-path="item-1760421173523-jze2c3sg0/subitem-1760421180910-zfp8kuopn"><div class="list-item-paragraph">$m$,</div></li><li data-list-item-id="subitem-1760421181615-bbi46l48c" data-list-item-path="item-1760421173523-jze2c3sg0/subitem-1760421181615-bbi46l48c"><div class="list-item-paragraph">$n$.</div></li></ol></li><li data-list-item-id="item-1760421196983-yimontvyh" data-list-item-path="item-1760421196983-yimontvyh"><div class="list-item-paragraph">What is the condition for&nbsp;$y$ when</div><ol class="i-list"><li data-list-item-id="subitem-1760421202098-0urwpndof" data-list-item-path="item-1760421196983-yimontvyh/subitem-1760421202098-0urwpndof"><div class="list-item-paragraph">$n$ is an integer,</div></li><li data-list-item-id="subitem-1760421202930-1i8c2es2q" data-list-item-path="item-1760421196983-yimontvyh/subitem-1760421202930-1i8c2es2q"><div class="list-item-paragraph">$n$ and $x$ are both even?</div></li></ol></li><li data-list-item-id="item-1760421220930-mwivket3a" data-list-item-path="item-1760421220930-mwivket3a"><div class="list-item-paragraph">State a possible value of $y$ when&nbsp;$n$ is an even number and $x$ is an odd number.</div></li></ol>

The figure shows $6$ identical rectangles of length $\left( 2x+3y \right)$cm and breadth $y$ cm, where $x$ and $y$ are positive integers.

Algebraic Proof Using Identities

Algebraic Expressions in a Composite Rectangle Diagram

<p>Ascend Hotel has a total of $27$ rooms.</p>
<p>Each room can be used as a single room or a double room.</p>
<p>The price for a single room is $\$159$ per night.</p>
<p>The price for a double room is $\$219$ per night.</p>
<p>On a particular night, all the rooms are occupied, and ${x}$ rooms are used as single rooms.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that the total price of all the rooms on the particular night is $\$\left(5913-60x\right)$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Given that the total price of all the rooms is $\$5013$, form an equation and find the value of ${x}$.</div><p style="text-align: right;">[2]</p></li></ol>

Each room can be used as a single room or a double room.

The price for a single room is $\$159$ per night.

The price for a double room is $\$219$ per night.

On a particular night, all the rooms are occupied, and ${x}$ rooms are used as single rooms.

2023 AISS EM S1 EOY P1 Q5

<p>In a farmhouse, there are chickens and pigs.</p>
<p>Each chicken has ${2}$ legs and each pig has ${4}$ legs.</p>
<p>There are a total of ${88}$ heads and ${214}$ legs.</p>
<p>Let ${x}$ be the number of chickens in the farmhouse.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Express, in terms of ${x}$, the number of pigs in the farmhouse.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Express, in terms of ${x}$, the number of legs for the pigs in the farmhouse.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Show that the total sum of legs of chickens and pigs in the farmhouse can be written as ${352 - 2x = 214}$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Find the number of pigs in the farmhouse.</div><p style="text-align: right;">[1]</p></li></ol>

In a farmhouse, there are chickens and pigs.

Each chicken has ${2}$ legs and each pig has ${4}$ legs.

There are a total of ${88}$ heads and ${214}$ legs.

Let ${x}$ be the number of chickens in the farmhouse.

2023 ACSBR EM S1 EOY P2 Q5

<p>At a factory, goods are being packed for Chinese New Year.</p>
<p>The estimate weight of each box of goods is given below.</p>
<table><thead><tr><th>Goods</th><th>Weight/kg</th></tr></thead><tbody><tr><td>${25}$ oranges</td><td>${x}$</td></tr><tr><td>${4}$ pomelos</td><td>${y}$</td></tr></tbody></table>
<p>An empty hamper basket has a mass of $1$ kg.</p>
<p>A factory worker packs $100$ oranges and $8$ pomelos into a hamper basket.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down an expression in terms of $x$, for the mass of $100$ oranges.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Write down an expression in terms of $y$, for the mass of $8$ pomelos.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Hence, write down an expression in terms of $x$ and $y$, for the total mass of the hamper basket.<span class="inline-marks">[1]</span></div></li></ol>

At a factory, goods are being packed for Chinese New Year.

The estimate weight of each box of goods is given below.

An empty hamper basket has a mass of $1$ kg.

A factory worker packs $100$ oranges and $8$ pomelos into a hamper basket.

Math Question Bank