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E Math (IGCSE)

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N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>Alex swam <strong>1.5</strong> kilometres in a pool in <strong>30</strong> minutes. He took a break for <strong>20</strong> minutes before swimming back at an average speed <strong>20%</strong> slower than his original average speed.</p>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Alex’s original swimming speed, in km/h.</div></li><li><div class="list-item-paragraph">the time taken for Alex to swim back, in minutes.</div></li><li><div class="list-item-paragraph">Alex’s average speed for the entire swim, in m/s.</div></li></ol>

Alex swam **1.5** kilometres in a pool in **30** minutes. He took a break for **20** minutes before swimming back at an average speed **20%** slower than his original average speed.

Percentage Increase and Decrease

Average Speed over a Journey

Speed

Ratio, Rate and Speed

Percentages

<p>The line graphs below show the forest coverage and air pollutant concentration in Region A from $2008$ to $2022$.</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/1767761668052-3hzanovbyw3.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjE2NjgwNTItM2h6YW5vdmJ5dzMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2OTUzOSwiZXhwIjoxNzkzNTY5ODM5fQ.IpKORs8BuMq8o7cjP3wE6-oIT-ULfb-1HTdk6Z7GOa4" style="max-width: min(300px, 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 the year with the greatest decrease in percentage points in forest coverage in Region A. Hence find the decrease in percentage points in forest coverage this year.</span></div></li><li><div class="list-item-paragraph">Find the overall percentage increase in air pollutant concentration in Region A from $2008$ to $2022$, correcting your answer to $3$ significant figures.</div></li><li><div class="list-item-content"><span class="list-item-text">The local government of Region A launched the ‘Forest Restoration’ operation. State in which year the government most likely started this operation and briefly explain the reason.</span></div></li><li><div class="list-item-content"><span class="list-item-text">State one advantage and one disadvantage, respectively, of the drawing of the graphs above, where the vertical axes do not start from zero.</span></div></li></ol>

The line graphs below show the forest coverage and air pollutant concentration in Region A from $2008$ to $2022$.

Find the year with the greatest decrease in percentage points in forest coverage in Region A. Hence find the decrease in percentage points in forest coverage this year.

The local government of Region A launched the ‘Forest Restoration’ operation. State in which year the government most likely started this operation and briefly explain the reason.

State one advantage and one disadvantage, respectively, of the drawing of the graphs above, where the vertical axes do not start from zero.

Interpreting and Evaluating Statistical Representations

Line Graphs

Statistics

<p>The pie charts below show the energy sources of a power plant in electricity generating in $2000$  and $2020$ , respectively.</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/1767761183040-1mbpie6wglc.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjExODMwNDAtMW1icGllNndnbGMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2OTUzOSwiZXhwIjoxNzkzNTY5ODM5fQ.mnILBscgLp_5E11CsmiiFZglUYctNVsQsMCsmE7QFKc" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li data-list-item-id="item-1767761189674-moikj7n1j" data-list-item-path="item-1767761189674-moikj7n1j"><div class="list-item-paragraph">Given that in $2000$ , the energy sources used by the power plant in the order of Coal $:$  Hydropower $:$  Wind Energy $:$  Oil is $ 13:2:1:4$ , find the values of $w$ , $x$ , $y$  and $z$ , respectively.</div></li><li data-list-item-id="item-1767761190298-v180fbbr9" data-list-item-path="item-1767761190298-v180fbbr9"><div class="list-item-paragraph"> From the pie chart, find the ratio of the energy source used by the power plant in the order of Coal $:$  Hydropower $:$  Wind Energy $:$  Oil in $2020$ .</div></li><li data-list-item-id="item-1767761190914-zckz9x7qb" data-list-item-path="item-1767761190914-zckz9x7qb"><div class="list-item-paragraph">Given that the annual energy consumption in electricity generating of the power plant in $2020$  is twice that of the power plant in $2000$ , find the percentage change of energy consumption by each energy source, respectively, from $2000$  to $2020$ , correcting your answer(s) to $3$  significant figures if not exact.</div></li><li data-list-item-id="item-1767761191561-gr8mu3ey6" data-list-item-path="item-1767761191561-gr8mu3ey6"><div class="list-item-paragraph">It is known that coal and oil are highly polluting traditional fossil energy sources, while hydropower and wind energy are clean energy sources. From the perspective of environmental protection, make one comment on the energy sources used by the power plant from $2000$  to $2020$ .</div></li></ol>

The pie charts below show the energy sources of a power plant in electricity generating in $2000$  and $2020$ , respectively.

Pie Charts

Simplifying Ratios

<p>The line graph below shows the unit price of a product over several months of a year.</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/1767697661114-by6ntbz0wbo.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTc2NjExMTQtYnk2bnRiejB3Ym8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2OTUzOSwiZXhwIjoxNzkzNTY5ODM5fQ.FlGzZtCUrZW-lWEFj9r46jnF7KxDwwaV6zX88ZHG_Ao" 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-content"><span class="list-item-text">Using the data from the line graph, complete the table below.</span></div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Month</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Jan</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Feb</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Mar</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Apr</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">May</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Jun</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Jul</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Aug</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Sep</th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Unit price ($)</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">195</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">175</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"></td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"></td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"></td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"></td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">180</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">195</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">210</td></tr></tbody></table></div></div>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the percentage increase in the unit price of the product from May to September.</span></div></li><li><div class="list-item-paragraph">From September to December, given that the monthly decrement in the unit price of the product is $\$10$, complete the line graph above.</div></li></ol>

The line graph below shows the unit price of a product over several months of a year.

Using the data from the line graph, complete the table below.

Find the percentage increase in the unit price of the product from May to September.

<p>The line graph below shows the height of a plant in $6$ months.</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/1767697497359-l7wtdpqqwzo.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTc0OTczNTktbDd3dGRwcXF3em8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2OTUzOSwiZXhwIjoxNzkzNTY5ODM5fQ.xyvtt1FhlS4vm1B6Bx1pn9u8weeGMwDwzRksY6dja1c" 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-content"><span class="list-item-text">Using the data from the line graph, complete the table below.</span></div></li></ol>
<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/1767697513141-ot1s2kcxkof.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTc1MTMxNDEtb3QxczJrY3hrb2YucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2OTUzOSwiZXhwIjoxNzkzNTY5ODM5fQ.HwKgfKuQV5-y031JPYp7YWDcvvKo2hX5OGiCOJLR-Qg" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Find the percentage increase in the height of the plant from month $2$ to month $4$, correcting your answer to $3$ significant figures.</div></li></ol>

The line graph below shows the height of a plant in $6$ months.

<p>Amy expected that her monthly income could be increased by $20\%$ this year compared to her monthly income last year, but due to company’s financial situation, her salary was cut down by $15\%$. As a result, Amy’s monthly salary was reduced by $\$1,680$ compared to her expectation.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the monthly income of Amy’s in the last year.</span></div></li><li><div class="list-item-content"><span class="list-item-text">When financial situation recovers, the company decides to increase Amy’s monthly income to her expectation. Find the percentage increase in Amy’s monthly income (Correct your answer to $3$ significant figures).</span></div></li></ol>

Amy expected that her monthly income could be increased by $20\%$ this year compared to her monthly income last year, but due to company’s financial situation, her salary was cut down by $15\%$. As a result, Amy’s monthly salary was reduced by $\$1,680$ compared to her expectation.

Find the monthly income of Amy’s in the last year.

When financial situation recovers, the company decides to increase Amy’s monthly income to her expectation. Find the percentage increase in Amy’s monthly income (Correct your answer to $3$ significant figures).

Reverse Percentages

 Percentages involving Finances: Profit and Loss

<p>The breadth of a cuboid is $6$ cm. The length of the cuboid is $150\%$ that of its breadth, and the breadth of the cuboid is $150\%$ that of its height.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the length and height of the cuboid.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the volume of the cuboid.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If the length of the cuboid is increased by $50\%$ and the breadth of the cuboid is decreased by $50\%$, while the height of the cuboid does not change. Find the new length and breadth of the cuboid.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Based on your answers in (iii), determine whether the volume of the cuboid is the same as original. If yes, state your reasons by providing detailed workings. If not, find the new volume and the percentage change in the volume of the cuboid.</span></div></li></ol>

The breadth of a cuboid is $6$ cm. The length of the cuboid is $150\%$ that of its breadth, and the breadth of the cuboid is $150\%$ that of its height.

Find the length and height of the cuboid.

If the length of the cuboid is increased by $50\%$ and the breadth of the cuboid is decreased by $50\%$, while the height of the cuboid does not change. Find the new length and breadth of the cuboid.

Based on your answers in (iii), determine whether the volume of the cuboid is the same as original. If yes, state your reasons by providing detailed workings. If not, find the new volume and the percentage change in the volume of the cuboid.

Percentage of a Quantity

 Percentage Change and Reverse Percentage

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">The length of a rectangle is increased by $30\%$ and the breadth of the rectangle is increased by $40\%$. Find the percentage change in its area.</span></div></li><li><div class="list-item-content"><span class="list-item-text">The radius of a circle is increased by $20\%$. Find the percentage change in its perimeter and area, respectively.</span></div></li><li><div class="list-item-content"><span class="list-item-text">The base of a triangle is increased by $10\%$ and the perpendicular height from the base is decreased by $10\%$. Find the percentage change in its area.</span></div></li></ol>

The length of a rectangle is increased by $30\%$ and the breadth of the rectangle is increased by $40\%$. Find the percentage change in its area.

The radius of a circle is increased by $20\%$. Find the percentage change in its perimeter and area, respectively.

The base of a triangle is increased by $10\%$ and the perpendicular height from the base is decreased by $10\%$. Find the percentage change in its area.

<p>The line graph below shows Ben’s and John’s savings over a period of $6$ months.</p>
<p>Use the information provided to answer each of the following questions.</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/1764467719897-rna8qxnbkt.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ0Njc3MTk4OTctcm5hOHF4bmJrdC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTY5NTM5LCJleHAiOjE3OTM1Njk4Mzl9.LId3bzW8b5XNT4kqyrIfcHLlQMJGDAHv6FcVs1jCJX0" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Calculate Ben’s average savings for the $6$ months.</div></li><li><div class="list-item-paragraph">If John gets an allowance of $\$4.50$ a day, calculate the amount of money John spent per day in May. Give your answer to the nearest $10$ cents. (Take $1$ month$=31$ days)</div></li><li><div class="list-item-paragraph">In July, John saved $\frac{3}{5}$ as much as he saved in February, while Ben saved $15\%$ less than the amount he saved in April.</div><ol class="i-list"><li><div class="list-item-paragraph">Calculate the amount John saved in July.</div></li><li><div class="list-item-paragraph">Calculate the amount Ben saved in July.</div></li><li><div class="list-item-paragraph">Find their total savings in July.</div></li></ol></li></ol>

The line graph below shows Ben’s and John’s savings over a period of $6$ months.

Use the information provided to answer each of the following questions.

Mean of Ungrouped Data

Line Graph of Monthly Savings: Ben vs John

<p>The line graph below shows the change in body temperature of a male patient from $8.00$ am to $11$ pm.  The temperatures are taken every $3$ hours. The normal temperature of a person is approximately $37{}^\circ \mathrm{C}$.</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/1764466324545-xrqoyqagmu.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ0NjYzMjQ1NDUteHJxb3lxYWdtdS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTY5NTM5LCJleHAiOjE3OTM1Njk4Mzl9.6c8xiAweSbYrcnmXKsZuOybh5qw5IRPrlp-7kR_45aA" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="item-1764466329994-09ci9wr1w" data-list-item-path="item-1764466329994-09ci9wr1w"><div class="list-item-paragraph">State the period of decline of his temperature till it reaches normal.</div></li><li data-list-item-id="item-1764466330518-783brbg7o" data-list-item-path="item-1764466330518-783brbg7o"><div class="list-item-paragraph">State which is the $3$ hours period of highest increase in the temperature and state the 	percentage increase in the numerical Celsius reading.</div></li><li data-list-item-id="item-1764466331044-3v7c3zk79" data-list-item-path="item-1764466331044-3v7c3zk79"><div class="list-item-paragraph">Calculate the mean of the six recorded temperatures from $8$ am to $11$ pm.</div></li></ol>

The line graph below shows the change in body temperature of a male patient from $8.00$ am to $11$ pm.  The temperatures are taken every $3$ hours. The normal temperature of a person is approximately $37{}^\circ \mathrm{C}$.

Line Graph Showing Body Temperature Changes in a Patient

<p>The graph shows the average price of petrol per litre, in the first nine months of a particular year.</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/1764465483930-06zgohwuc3m7.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ0NjU0ODM5MzAtMDZ6Z29od3VjM203LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTM1Njk1MzksImV4cCI6MTc5MzU2OTgzOX0.4OvgddtVsLDi6d_OifzATpns8v76yTA0VE_e8lhLEHk" 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">State the month with the highest price of petrol.</div></li><li><div class="list-item-paragraph">Find the ratio of the price of petrol in the month of April to the month of September.</div></li><li><div class="list-item-paragraph">Express as a fraction of the first nine months, the number of months with petrol prices greater than $\$1.50$ per litre.<br></div></li><li><div class="list-item-paragraph">Find the percentage increase in the price of petrol between January and September.</div></li><li><div class="list-item-paragraph">Steven needs to go to Town $S$ in June which is $264$ km away.  Assuming his car is able to travel $12$ km on a litre of petrol, calculate the amount he will spend on petrol for the trip.</div></li><li><div class="list-item-paragraph">On a certain month, Sebastian went to a petrol kiosk and paid $\$50$ to fill his car with $40$ litres of petrol.  Find the month that Sebastian went to the petrol kiosk.</div></li></ol>

The graph shows the average price of petrol per litre, in the first nine months of a particular year.

Calculating Rates and Quantities

Line Graph

<p>The following graph shows the amount of money a company spent on training programmes for its employees in the first $4$ months of a particular year.</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/1764409788280-m75lvhszep9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ0MDk3ODgyODAtbTc1bHZoc3plcDkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU2OTUzOSwiZXhwIjoxNzkzNTY5ODM5fQ.BtK7lq_nddtLrypYfgD_w2fTAP_joQpURW4C-5gCi2U" 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">Compare the amount of money spent on training programmes in the four months.</div><div class="list-item-paragraph">Express your answer in simplest ratio form in the order Jan : Feb : Mar : Apr.</div></li><li><div class="list-item-paragraph">What is the percentage increase in the amount spent from Feb to Mar?</div></li><li><div class="list-item-paragraph">Find the total amount spent in the first quarter (Jan, Feb and Mar) of the year.<br><br></div></li></ol>

The following graph shows the amount of money a company spent on training programmes for its employees in the first $4$ months of a particular year.

Bar Graphs

Bar Graph: Company Training Expenditure

<p>A stack of ten $\$1$ coins forms a cylinder of base diameter $x$ cm and height $2.5$ cm.</p>
<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;"><ol class="abc-list"><li data-list-item-id="item-1777885643496-t446ih76i" data-list-item-path="item-1777885643496-t446ih76i"><div class="list-item-paragraph">If the volume of the stack is $11.9$ cm$^{3}$, find $x$.</div></li><li data-list-item-id="item-1777885644052-37e9y6po2" data-list-item-path="item-1777885644052-37e9y6po2"><div class="list-item-paragraph">Find the total surface area of the stack.</div></li><li data-list-item-id="item-1777885645025-57qpa0jtd" data-list-item-path="item-1777885645025-57qpa0jtd"><div class="list-item-paragraph">If six more of the identical $\$1$ coins are added to the stack, find the percentage increase of the total surface area of the stack.</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/1764399699672-8t21c3pspn.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQzOTk2OTk2NzItOHQyMWMzcHNwbi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTY5NTM5LCJleHAiOjE3OTM1Njk4Mzl9.v-TcgZN33bg6McgJdOdFAj8Une3F1XOhoeuuEZyjfRc" style="max-width: min(120px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

A stack of ten $\$1$ coins forms a cylinder of base diameter $x$ cm and height $2.5$ cm.

Volume and Surface Area of Cylinders

Cylinder Formed by a Stack of Coins

Volume and Surface Area of Prisms

<p>James ran $14$ km from his house in $1$ hour $45$ minutes.  He rested for&nbsp;$40$ minutes before walking home.  His walking speed was $40\%$ less than his running speed.<br>Calculate</p>
<ol class="abc-list"><li><div class="list-item-paragraph">his running speed, in km/h.</div></li><li><div class="list-item-paragraph">his walking time, in hours and minutes.</div></li><li><div class="list-item-paragraph">his average speed, in m/s, for the whole journey.</div></li></ol>

James ran $14$ km from his house in $1$ hour $45$ minutes.  He rested for $40$ minutes before walking home.  His walking speed was $40\%$ less than his running speed.
Calculate

Speed and Percentage Reduction Journey Problem

<p>The length of a rectangle is decreased by $5\%$ and its width is increased by $8\%$.</p>
<p>Calculate the percentage change in its area, stating clearly if there is an increase or decrease.</p>

The length of a rectangle is decreased by $5\%$ and its width is increased by $8\%$.

Calculate the percentage change in its area, stating clearly if there is an increase or decrease.

Percentage Change in Area

<p>The length of each side of a square is decreased by $10\%$.  Find the percentage decrease in the area of the square.</p>

The length of each side of a square is decreased by $10\%$.  Find the percentage decrease in the area of the square.

Percentage Change in Geometric Measures

<p>Mrs Lee bought a painting for&nbsp;$\$120$ and resold at $\$540$ one year later. </p>
<p>Find the percentage increase in its value.</p>

Mrs Lee bought a painting for $\$120$ and resold at $\$540$ one year later. 

Find the percentage increase in its value.

Percentage Increase in Value

<p>David scored $52$ marks for his first test and $75$ marks for his second test. </p>
<p>Find the percentage increase in his test score.</p>

David scored $52$ marks for his first test and $75$ marks for his second test. 

Find the percentage increase in his test score.

Calculating Percentage Increase

<p>The price of a mobile phone decreases from $\$825$ to $\$720$.  </p>
<p>Find the percentage decrease in price.</p>

The price of a mobile phone decreases from $\$825$ to $\$720$.  

Calculating Percentage Decrease

<p>The length of each side of a square is increased by $25\%$.  Find the percentage increase in the area of the square.</p>

The length of each side of a square is increased by $25\%$.  Find the percentage increase in the area of the square.

Math Question Bank