A Math

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E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

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IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>A company charges $\$ y$ for&nbsp;$x$ units of electricity used.<br>The charge $\$ y$ can be represented by the function $y = ux + 20$, where&nbsp;$u$ is a constant. Some corresponding values of $x$ and $y$ are given in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 600px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$x$</th><th style="text-align: center; --cell-justify: center">$0$</th><th style="text-align: center; --cell-justify: center">$100$</th><th style="text-align: center; --cell-justify: center">$200$</th><th style="text-align: center; --cell-justify: center">$300$</th><th style="text-align: center; --cell-justify: center">$400$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$y$</td><td style="text-align: center; --cell-justify: center">$20$</td><td style="text-align: center; --cell-justify: center">$50$</td><td style="text-align: center; --cell-justify: center">$80$</td><td style="text-align: center; --cell-justify: center">$110$</td><td style="text-align: center; --cell-justify: center">$140$</td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="item-a"><div class="list-item-paragraph">On the grid, draw the graph of $y = ux + 20$ for&nbsp;$0 \le x \le 400$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-b"><div class="list-item-paragraph">Find the total cost if a household uses $140$ units of electricity.<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-c"><div class="list-item-paragraph">What does the constant term, $20$, represent?<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-d"><div class="list-item-paragraph">Find the value of $u$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-e"><div class="list-item-paragraph">What does the gradient of the graph represent in this context?<span class="inline-marks">[1]</span></div></li></ol>

A company charges $\$ y$ for $x$ units of electricity used.
The charge $\$ y$ can be represented by the function $y = ux + 20$, where $u$ is a constant. Some corresponding values of $x$ and $y$ are given in the table below.

Gradient of a Straight Line

Plotting of Straight Line on Graph Paper

Linear Graphs in Real Life Problems

2023 ACSBR EM S1 EOY Q14

Linear Graphs and Its Applications

<p>A hiker (Hiker I) starts climbing the mountain at minute-zero. Meanwhile the other hiker (Hiker II) is at the mountain top, starting to go down. There is a supply station in the middle of the mountain, where both hikers stop by to take a rest. The height-time graph below shows the height the two hikers are at with respect to time.</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/1768506074681-m8fpukhcmx.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njg1MDYwNzQ2ODEtbThmcHVraGNteC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk2MDA0LCJleHAiOjE3OTI2OTYzMDR9.qXla0oBCvkmqOHrQcShxsTpg1VJWl9YMRjasYvoqAvY" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">From the graph, find the height of the supply station.</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">From the graph, find the duration of time in minutes</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">for Hiker II to descend to $400$ m in height,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hiker I spends at the supply station.</span><span class="inline-marks">[1]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Find the gradient of each of the following line segments, and state clearly what each gradient represents.</span></div><ol class="abc-list"><li><div class="list-item-paragraph">$FG$,</div></li><li><div class="list-item-content"><span class="list-item-text">$DK$.</span><span class="inline-marks">[4]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">From the graph, will the two hikers meet each other on their journey? If yes, state the time when they meet each other. If no, state your reason. Assume that there is only one road on the mountain.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the duration of time when the difference of height between the two hikers is less than or equal to $200$ m.</span><span class="inline-marks">[1]</span></div></li></ol>

A hiker (Hiker I) starts climbing the mountain at minute-zero. Meanwhile the other hiker (Hiker II) is at the mountain top, starting to go down. There is a supply station in the middle of the mountain, where both hikers stop by to take a rest. The height-time graph below shows the height the two hikers are at with respect to time.

From the graph, find the height of the supply station.

From the graph, find the duration of time in minutes

Find the gradient of each of the following line segments, and state clearly what each gradient represents.

From the graph, will the two hikers meet each other on their journey? If yes, state the time when they meet each other. If no, state your reason. Assume that there is only one road on the mountain.

Find the duration of time when the difference of height between the two hikers is less than or equal to $200$ m.

IP1 Class Test (May 2025) Q16

<p>Hiker I starts climbing the mountain at $0000$h. At the same time, Hiker II starts descending from the mountain top. A supply station is located somewhere between the top and the foot of the mountain, where both hikers stop by to take a rest. The height-time graph below shows the heights of the two hikers after $0000$h.</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/1767607044485-dbs955ircuq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDcwNDQ0ODUtZGJzOTU1aXJjdXEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NjAwNCwiZXhwIjoxNzkyNjk2MzA0fQ.J_fpz0Bd1k3JZ6i1nKnBP9X5-L3SurXw3hQ7S_ZlfYI" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find, in metres, the height of the mountain, and the height of the supply station from the foot of the mountain.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the duration of time in minutes</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">for Hiker I to climb to $400$m in height,</span></div></li><li><div class="list-item-content"><span class="list-item-text">for Hiker II to descend to $400$m in height,</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hiker I and II spend at the supply station, respectively.</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Find the gradient of each of the following line segments, and state clearly what each gradient represents.</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$OA$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$AF$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$CD$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$DK$.</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Which hiker arrives at the supply station earlier? Explain your answer.</span></div></li><li><div class="list-item-content"><span class="list-item-text">From the graph, will the two hikers meet each other on their journey? If yes, approximately state the time when they meet each other. If no, state your reason. Assume that there is only one road on the mountain.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the duration of time when the difference of height between the two hikers is less than or equal to $200$m.</span></div></li></ol>

Hiker I starts climbing the mountain at $0000$h. At the same time, Hiker II starts descending from the mountain top. A supply station is located somewhere between the top and the foot of the mountain, where both hikers stop by to take a rest. The height-time graph below shows the heights of the two hikers after $0000$h.

Find, in metres, the height of the mountain, and the height of the supply station from the foot of the mountain.

Which hiker arrives at the supply station earlier? Explain your answer.

From the graph, will the two hikers meet each other on their journey? If yes, approximately state the time when they meet each other. If no, state your reason. Assume that there is only one road on the mountain.

Find the duration of time when the difference of height between the two hikers is less than or equal to $200$m.

Coordinate Geometry

<p>Two types of plants, A and B, grow at different rates in a garden. The height-time graph below shows the variations of height for plant A and B with respect to time.</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/1767606848689-caq5wfvpwpb.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDY4NDg2ODktY2FxNXdmdnB3cGIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NjAwNCwiZXhwIjoxNzkyNjk2MzA0fQ.svmx1KG5fldJ9jqI0nrDzjeGwh6WrD5FHqPB-44hZHo" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find, in cm, the heights of plant A and B, respectively, at the beginning.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the time it takes (in weeks) for</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">plant A to grow to $18$ cm,</span></div></li><li><div class="list-item-content"><span class="list-item-text">plant B to grow to $25$ cm,</span></div></li><li><div class="list-item-content"><span class="list-item-text">plant A to become taller than plant B, and their heights at this moment.</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Which plant grows faster? Explain your answer.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If the gardener wants to sell a plant that is taller on week $4$, which of the $2$ plants should he sell? Explain your answer.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Of the $2$ plants, the gardener sells the one that first reaches $35$ cm. Which plant is it? Explain your answer.</span></div></li></ol>

Two types of plants, A and B, grow at different rates in a garden. The height-time graph below shows the variations of height for plant A and B with respect to time.

Find, in cm, the heights of plant A and B, respectively, at the beginning.

Which plant grows faster? Explain your answer.

If the gardener wants to sell a plant that is taller on week $4$, which of the $2$ plants should he sell? Explain your answer.

Of the $2$ plants, the gardener sells the one that first reaches $35$ cm. Which plant is it? Explain your answer.

<p>Cash on hand of a company refers to the money a company can access to fund their business activities and operating cost. When a company earns money, the money is stored as cash on hand. Originally, the company earns a fixed amount of money per day. On the $5$th day, the company invests in a new facility that improves the product efficiency, which leads to a higher fixed amount of money earned per day afterwards. The cash on hand-time graph below shows the cash on hand of this company. Assume there are no other operating costs incurred in the $10$ days of operation.</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/1767606632085-la6pxj76mw.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDY2MzIwODUtbGE2cHhqNzZtdy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk2MDA0LCJleHAiOjE3OTI2OTYzMDR9.VNff5kngdHsvD2NJPhm61HbBf9ZJNLTOMv6dixVtr1Y" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Find the cash on hand (in dollars) of this company at the beginning of this month.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Find the amount of money (in dollars) the company</div><ol class="abc-list"><li data-list-item-id="iia" data-list-item-path="item-ii/iia"><div class="list-item-paragraph">earned before purchasing the new facility,</div></li><li data-list-item-id="iib" data-list-item-path="item-ii/iib"><div class="list-item-paragraph">spent on purchasing the new facility,</div></li><li data-list-item-id="iic" data-list-item-path="item-ii/iic"><div class="list-item-paragraph">earned after purchasing the new facility, until the $10$th day.</div></li></ol></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">Find the gradient of each of the following line segments, and state clearly what each gradient represents.</div><ol class="i-list"><li data-list-item-id="iiia" data-list-item-path="item-iii/iiia"><div class="list-item-paragraph">$AB$,</div></li><li data-list-item-id="iiib" data-list-item-path="item-iii/iiib"><div class="list-item-paragraph">$CD$.</div></li></ol></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">From the graph, which day does the company first recover the cost of the new facility? Round your answer to the nearest integer.</div></li></ol>

Cash on hand of a company refers to the money a company can access to fund their business activities and operating cost. When a company earns money, the money is stored as cash on hand. Originally, the company earns a fixed amount of money per day. On the $5$th day, the company invests in a new facility that improves the product efficiency, which leads to a higher fixed amount of money earned per day afterwards. The cash on hand-time graph below shows the cash on hand of this company. Assume there are no other operating costs incurred in the $10$ days of operation.

Find the cash on hand (in dollars) of this company at the beginning of this month.

Find the amount of money (in dollars) the company

From the graph, which day does the company first recover the cost of the new facility? Round your answer to the nearest integer.

<p>Emma receives $\$150$ from her parents as her allowance at the beginning of every month. Suppose Emma spends $\$4$ each day.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the amount of money Emma has left after</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$5$ days,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$15$ days,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$25$ days.</span></div></li></ol></li><li><div class="list-item-paragraph">Given that $\$M$ represents the amount of money Emma has after $n$ days, complete the table below.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767606203514-kltgvrivkz.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDYyMDM1MTQta2x0Z3ZyaXZrei5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk2MDA0LCJleHAiOjE3OTI2OTYzMDR9.HB3iS98tiXeLUNPB23G543t2i5DQv51m3xyFpxJzSAM" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="list-item-content"><span class="list-item-text">On a sheet of graph paper, using a scale of $2$ cm to represent $5$ days on the horizontal axis and $1$ cm to represent $\$10$ on the vertical axis, plot the pairs of values of $(n, M)$ given in the table above.</span></div></li><li><div class="list-item-content"><span class="list-item-text">By drawing a straight line graph through all the points in (iii), find how much money Emma has left at the end of a month. (Assume one month has $30$ days.)</span></div></li></ol>

Emma receives $\$150$ from her parents as her allowance at the beginning of every month. Suppose Emma spends $\$4$ each day.

Find the amount of money Emma has left after

Given that $\$M$ represents the amount of money Emma has after $n$ days, complete the table below.

On a sheet of graph paper, using a scale of $2$ cm to represent $5$ days on the horizontal axis and $1$ cm to represent $\$10$ on the vertical axis, plot the pairs of values of $(n, M)$ given in the table above.

By drawing a straight line graph through all the points in (iii), find how much money Emma has left at the end of a month. (Assume one month has $30$ days.)

<p>A taxi company charges $\$4$ as the starting price (also known as flag-down rate), and charges at a rate of $\$1$ per kilometre.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Andrew takes a taxi from this company. Find the total amount of money spent after</div><ol class="abc-list"><li data-list-item-id="ia" data-list-item-path="item-i/ia"><div class="list-item-paragraph">$0.5$ km,</div></li><li data-list-item-id="ib" data-list-item-path="item-i/ib"><div class="list-item-paragraph">$3$ km,</div></li><li data-list-item-id="ic" data-list-item-path="item-i/ic"><div class="list-item-paragraph">$7.5$ km.</div></li></ol></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Given that&nbsp;$\$T$ represents the amount of money Andrew spent after $d$ kilometres, complete the table below.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767605924991-fpfpxl8zgao.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDU5MjQ5OTEtZnBmcHhsOHpnYW8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NjAwNCwiZXhwIjoxNzkyNjk2MzA0fQ.0d8HsIFq8k3WGo1ZbDvuyyxGiPCzttvR0IKZyB_l9Cg" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">On a sheet of graph paper, using a scale of 1 cm to represent $1$ km on the horizontal axis and $1$ cm to represent $\$1$ on the vertical axis, plot the pairs of values of $(d, T)$ given in the above table.</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">By drawing a straight line graph through all the points in (iii), find the distance after which Andrew spends more than $\$10$.</div></li></ol>

A taxi company charges $\$4$ as the starting price (also known as flag-down rate), and charges at a rate of $\$1$ per kilometre.

Andrew takes a taxi from this company. Find the total amount of money spent after

<p>Mr Lim has a coffeeshop gift card with $\$250$ stored in it. Every day, he buys a cup of coffee which costs $\$7.50$ by using the gift card.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the money left in the gift card after</div><ol class="i-list"><li><div class="list-item-paragraph">$5$ days,</div></li><li><div class="list-item-paragraph">$15$ days,</div></li><li><div class="list-item-paragraph">$30$ days.</div></li></ol></li><li><div class="list-item-paragraph">Given that&nbsp;$\$T$ represents the amount of money left in the gift card after $x$ days, complete the table.</div><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$x$</th><th style="text-align: center; --cell-justify: center">$5$</th><th style="text-align: center; --cell-justify: center">$15$</th><th style="text-align: center; --cell-justify: center">$30$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$T$</td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></li><li><div class="list-item-paragraph">On a sheet of graph paper, using a scale of $2$ cm represents $5$ days on the horizontal axis and $2$ cm represents $\$25$ on the vertical axis, plot the pair of values of $\left( x,T \right)$.</div></li><li><div class="list-item-paragraph">From the graph, find the number of days during which the gift card has more than $\$100$ stored</div></li></ol>

Mr Lim has a coffeeshop gift card with $\$250$ stored in it. Every day, he buys a cup of coffee which costs $\$7.50$ by using the gift card.

Modelling Balance on a Gift Card Over Time

<p>A fitness centre charges $\$200$ upon registration and a subscription fee of $\$120$ charged monthly.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Derrick registers on the 1st January of 2021, find the total amount of money spent after</div><ol class="i-list"><li><div class="list-item-paragraph">1 month, </div></li><li><div class="list-item-paragraph">6 months,</div></li><li><div class="list-item-paragraph">12 months.</div></li></ol></li><li><div class="list-item-paragraph">Given that&nbsp;$\$C$ represents the amount of money Derrick spent after $n$ months, complete the table.</div><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$n$</th><th style="text-align: center; --cell-justify: center">$1$</th><th style="text-align: center; --cell-justify: center">$6$</th><th style="text-align: center; --cell-justify: center">$12$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$C$ </td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></li><li><div class="list-item-paragraph">On a sheet of graph paper, using a scale of $1$cm represents $1$ month on the horizontal axis and $1$ cm represents $\$100$ on the vertical axis, plot the pairs of values of $\left( n,C \right)$ .</div></li><li><div class="list-item-paragraph">From the graph, find the month when Derrick will first spend more than $\$1000$.</div></li></ol>

A fitness centre charges $\$200$ upon registration and a subscription fee of $\$120$ charged monthly.

Modelling Monthly Costs with a Linear Function

<p>The figure below shows a swimming pool that consists of two parts, the shallow cuboid part, where the depth is $1.2$ m, and the deep trapezoidal-prism part, where the depth is from $1.2$ m to $3$ m. The two parts are equal in length ($30$ m) and breadth ($9$ m), and the two parts are connected such that water is filled and drained simultaneously into and out of the pool.</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/1777978100597-38b6630yjdm.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5NzgxMDA1OTctMzhiNjYzMHlqZG0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NjAwNCwiZXhwIjoxNzkyNjk2MzA0fQ.onAkpmVa-EeKDwH8rB5OzJvvFa_iG5pkbGg0SxLrxho" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-paragraph">Find the volume of the shallow cuboid part and the deep trapezoidal-prism part, respectively. Hence, find the total volume of the whole swimming pool.</div></li><li><div class="list-item-paragraph">Given that the whole swimming pool is completely filled with water originally, for maintenance need, water is drained out at a constant rate of $9$ m$^{3}$ per minute. Find</div><ol class="abc-list"><li><div class="list-item-paragraph">the amount of time after which the shallow cuboid part is completely drained,</div></li><li><div class="list-item-paragraph">the amount of time after which the whole swimming pool is completely drained, and</div></li><li><div class="list-item-paragraph">the depth of water (measured from the bottom of the deep part) after $36$ minutes.</div></li><li><div class="list-item-paragraph">Determine the type of the shape formed by the remaining water after $90$ minutes.</div></li></ol></li><li><div class="list-item-paragraph">After maintenance, water is refilled into the empty swimming pool at a constant rate of $9$ m$^{3}$ per minute. In the grid below, draw the graph of the depth, $h$, of water with respect to time, $t$. Approximately sketch the curved part and accurately draw the straight-line part of the graph, if there is any.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1777978440480-7w0t1whzcg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5Nzg0NDA0ODAtN3cwdDF3aHpjZy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk2MDA0LCJleHAiOjE3OTI2OTYzMDR9.rhFV9qOzPxGYyM5x82Lq0PuOIkMMlbY1GAjusvWCh3s" alt="List item image" class="aligncenter custom-width" style="max-width: min(600px, 100%); height: auto;" /></div></li></ol>

The figure below shows a swimming pool that consists of two parts, the shallow cuboid part, where the depth is $1.2$ m, and the deep trapezoidal-prism part, where the depth is from $1.2$ m to $3$ m. The two parts are equal in length ($30$ m) and breadth ($9$ m), and the two parts are connected such that water is filled and drained simultaneously into and out of the pool.

Volume and Surface Area of Composite Solids

Water-Level Graphs at Constant Volume Flow

Calculating Rates and Quantities

IP1U13 HOT Q9

Volume and Surface Area of Prisms

Ratio, Rate and Speed

Functions and Graphs

<p>The graph below shows the charges by FAST TRACK, a package delivering company.</p>
<p>There is a fixed charge of $\$3$ and for the first $20$ km is charged at $50$ cents per km, next $25$ km at $\$1$ per km and any additional km at $y$ dollars per km.</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/converted/1760431766270-jutygntnbs8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzE3NjYyNzAtanV0eWdudG5iczgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NjAwNCwiZXhwIjoxNzkyNjk2MzA0fQ.VeZw2CK_xfZMS-48__IIl7WDbw2Hz-Xoe0ftGHER2lc" style="max-width: min(450px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the value of $y$.</div></li><li><ol class="i-list"><li><div class="list-item-paragraph">Find the cost of delivering the package $50$km away.</div></li><li><div class="list-item-paragraph">If the cost of delivery is $\$33$, find the distance the package was delivered.</div></li></ol></li><li><div class="list-item-paragraph">Another company GHL, delivers package and charges a flat rate of $\$1.50$ per km but does not have a fixed charge.</div><ol class="i-list"><li><div class="list-item-paragraph">Draw a line on the grid to represent the charge by GHL.</div></li><li><div class="list-item-paragraph">For a particular distance, the charges from both companies are the same. Find this distance.</div></li></ol></li></ol>

The graph below shows the charges by FAST TRACK, a package delivering company.

There is a fixed charge of $\$3$ and for the first $20$ km is charged at $50$ cents per km, next $25$ km at $\$1$ per km and any additional km at $y$ dollars per km.

Package Delivery Charges by Distance (FAST TRACK)

<p>The graphs below show the charges of two taxi companies – $\mathrm{M}2$ Taxi and $\mathrm{D5}$ Taxi.</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/converted/1760431664254-pnjxhk030p.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzE2NjQyNTQtcG5qeGhrMDMwcC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk2MDA0LCJleHAiOjE3OTI2OTYzMDR9.64CAdyrpIERfPpsq5VEAFVT72ghXW2DFIrU3yX8lwP4" style="max-width: min(450px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">What is the flagdown fare for both taxi companies?</div></li><li><div class="list-item-paragraph">Hariq travelled $6$km on an $\mathrm{M}2$ Taxi. How much does Hariq need to pay?</div></li><li><div class="list-item-paragraph">Tyson wants to travel $11$ km. Which taxi company should he hire? Why?</div></li><li><div class="list-item-paragraph">At what rate was $\mathrm{M}2$ Taxi charging after the first $2$ km?</div></li></ol>

The graphs below show the charges of two taxi companies – $\mathrm{M}2$ Taxi and $\mathrm{D5}$ Taxi.

Taxi Fare Charges Compared by Distance Travelled

<p>Water was poured into $3$ identical containers $A$, $B$ and $C$ till they were completely filled.</p>
<p>Container $A$ was empty and water was poured in at a fixed rate.</p>
<p>Container $B$ already had some water in it and water was poured in at a fixed rate.</p>
<p>Container $C$ was empty and water was poured in at a fixed rate after a certain amount of time.</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/converted/1760431233481-6ai6l6pxlas.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzEyMzM0ODEtNmFpNmw2cHhsYXMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NjAwNCwiZXhwIjoxNzkyNjk2MzA0fQ.Y0fwOF9MjUV8XJ-P6dvdAahSyGHXQB--dMIEChS51yg" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Which graph above best represents the filling of water over time for</div><ol class="i-list"><li><div class="list-item-paragraph">container $A$, and</div></li><li><div class="list-item-paragraph">container $B$?</div></li></ol></li><li><div class="list-item-paragraph">What was the capacity of each container?</div></li><li><div class="list-item-paragraph">In which container was water poured in at the slowest rate, and what was this rate?</div></li><li><div class="list-item-paragraph">Which container took the shortest time to be completely filled, and what is this time?</div></li></ol>

Water was poured into $3$ identical containers $A$, $B$ and $C$ till they were completely filled.

Container $A$ was empty and water was poured in at a fixed rate.

Container $B$ already had some water in it and water was poured in at a fixed rate.

Container $C$ was empty and water was poured in at a fixed rate after a certain amount of time.

Filling of Water in Identical Containers Over Time

<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/converted/1760431120199-a35jlv9rpg7.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzExMjAxOTktYTM1amx2OXJwZzcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NjAwNCwiZXhwIjoxNzkyNjk2MzA0fQ.gaU49Sw-qGwT0g61I56RAwgq1B9fpMyB0tGl-DkluNk" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>The graph shows the value of a car over time. In $4$ years’ time, the car will be worth $\$20\mathrm{000}$. Assume that the value of the car depreciates at a constant rate, use the graph to estimate,</p>
<ol class="abc-list"><li data-list-item-id="item-1760431111261-m66qdkmts" data-list-item-path="item-1760431111261-m66qdkmts"><div class="list-item-paragraph">the initial value of the car,</div></li><li data-list-item-id="item-1760431111936-4jsb9p00o" data-list-item-path="item-1760431111936-4jsb9p00o"><div class="list-item-paragraph">the rate of depreciation of the car,</div></li><li data-list-item-id="item-1760431113811-2lwfe7ams" data-list-item-path="item-1760431113811-2lwfe7ams"><div class="list-item-paragraph">the value of the car in $2$ years’ time.</div></li></ol>

The graph shows the value of a car over time. In $4$ years’ time, the car will be worth $\$20\mathrm{000}$. Assume that the value of the car depreciates at a constant rate, use the graph to estimate,

Depreciation of a Car’s Value Over Time

<p>The temperature of a frozen chicken was ${-8^\circ\mathrm{C}}$ when it was taken from the freezer.</p>
<p>The frozen chicken was placed in a hot oven.</p>
<p>The temperature rose at a constant rate for 10 minutes.</p>
<p>At the end of $10$ minutes, the temperature was ${22^\circ\mathrm{C}}$.</p>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-paragraph">the temperature after ${6}$ minutes,<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">the time it took to reach ${0^\circ\mathrm{C}}$. Give your answer in minutes and seconds.<span class="inline-marks">[2]</span></div></li></ol>

The temperature of a frozen chicken was ${-8^\circ\mathrm{C}}$ when it was taken from the freezer.

The frozen chicken was placed in a hot oven.

The temperature rose at a constant rate for 10 minutes.

At the end of $10$ minutes, the temperature was ${22^\circ\mathrm{C}}$.

Math Question Bank