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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

<p>A pie chart shows the distribution of time (in hours) spent on different activities in a day.</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/1767772048028-yj04hp73lsl.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzIwNDgwMjgteWowNGhwNzNsc2wucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.IoHK0uhuXBhplHENv-hvWIoobaahJ5WeoEejZCABto4" 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">What percentage of the day is spent on work?</div></li><li><div class="list-item-paragraph">Which activity takes up the largest portion of the day?</div></li><li><div class="list-item-paragraph">What is the ratio of time spent on sleep to time spent on work?</div></li><li><div class="list-item-paragraph">If the time spent on leisure is reduced by $1$
 hour, what will be the new percentage of time spent on leisure?</div></li></ol>

A pie chart shows the distribution of time (in hours) spent on different activities in a day.

Pie Charts

Simplifying Ratios

Statistics

Ratio, Rate and Speed

<p>The pie chart below shows the share of brands A, B, C, D and all other brands in the smartphone market in region R.</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/1767763547153-cjbu4rqmb2m.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjM1NDcxNTMtY2pidTRycW1iMm0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.szfoMAYSHiE_A7iqITlpZCZDEQDXQzcSOCLEGQCw_hQ" 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 value of $x$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the ratio of the market share of each brand in the order of A : B : C : D : Others.</span></div></li><li><div class="list-item-paragraph">Due to operational problems, brand A was split into two sub-brands A1 and A2, each with a market share of $7.5%$. Assuming that the remaining market share (in percentage) of the original brand A is equally occupied by brands B, C, D and Others, find the ratio of the market share of each brand after the split of brand A in the order of A1 : A2 : B : C : D : Others.</div></li><li><div class="list-item-paragraph">Given that the ‘Others’ part of the pie chart consists of $10$ brands, state one disadvantage of a pie chart when a detailed market share of all brands needs to be studied. Hence suggest one statistical diagram that is more appropriate in this case and briefly state your reasons.</div></li></ol>

The pie chart below shows the share of brands A, B, C, D and all other brands in the smartphone market in region R.

Find the ratio of the market share of each brand in the order of A : B : C : D : Others.

Interpreting and Evaluating Statistical Representations

Changing Ratios

<p>Three companies, A, B, and C, cooperate with a technological university to develop a project. The investment ratio of companies A, B, and C is $a : b : c$ in the simplest form. The university does not invest money but will share $25%$ of the profits. The rest of the profits will be shared by companies A, B and C according to the ratio of their investments.</p>
<ol class="i-list"><li><div class="list-item-paragraph">The pie chart below shows the investment of the three companies. Find the values of $a$, $b$ and $c$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-22-i-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0yMi1pLWRpYWdyYW0tMS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNjU0LCJleHAiOjE3OTI2NjI5NTR9.jA04896WyogfvgMNv0kKFyVNhVIFW_YK0YBTr4SIK0A" alt="List item image" class="aligncenter custom-width" style="max-width: min(250px, 100%); height: auto;" /></div></li></ol>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Construct a pie chart using the figure below to illustrate the profit distribution among companies A, B, C, and the university, stating clearly the degree of each sector, profit distribution in percentage and the name of each entity.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-22-ii-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0yMi1paS1kaWFncmFtLTEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.8dzu137wASBkCdcjdguolwakynGlhAwAyW2WpyF1coA" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">Given that the project yields a total profit of $\$2\ 800\ 000$, find the amount of profit that companies A, B, C and the university receive, respectively.</div></li><li><div class="list-item-paragraph">Given that the profit rate of companies A, B and C is $40%$, find the investment of companies A, B and C, respectively.</div></li><li><div class="list-item-content"><span class="list-item-text">State one advantage of representing the investment of the companies and profit distribution in pie charts.</span></div></li></ol>

Three companies, A, B, and C, cooperate with a technological university to develop a project. The investment ratio of companies A, B, and C is $a : b : c$ in the simplest form. The university does not invest money but will share $25%$ of the profits. The rest of the profits will be shared by companies A, B and C according to the ratio of their investments.

The pie chart below shows the investment of the three companies. Find the values of $a$, $b$ and $c$.

Construct a pie chart using the figure below to illustrate the profit distribution among companies A, B, C, and the university, stating clearly the degree of each sector, profit distribution in percentage and the name of each entity.

State one advantage of representing the investment of the companies and profit distribution in pie charts.

Dividing Quantities in a Given Ratio

Percentages involving Finances: Profit and Loss

Percentages

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjExODMwNDAtMW1icGllNndnbGMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.7Q9qByLZtVy9s_o8HXHRBMWkCoYa_hM9U57eWrCiF4A" 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.

Percentage Increase and Decrease

<p>The pie chart below shows the composition of types of products that a factory produces, where the ratio of the number of Type A to the number of Type B to the number of Type E produced is $2:3:6$.</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/1767697388127-ghr4a24gwdo.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTczODgxMjctZ2hyNGEyNGd3ZG8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.yBjYtlHullyhKlLM2IiKM1u1brP3E3PHbTP6WGkFuEE" 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">Find the ratio of the number of Type C to the number of Type D produced.</span></div></li><li><div class="list-item-paragraph">Given that the factory produces $500$ Type D products, find the total number of all $5$ types of products that the factory produces.</div></li><li><div class="list-item-content"><span class="list-item-text">Hence find the number of Types A, B, C and E products that the factory produces, respectively.</span></div></li></ol>

The pie chart below shows the composition of types of products that a factory produces, where the ratio of the number of Type A to the number of Type B to the number of Type E produced is $2:3:6$.

Find the ratio of the number of Type C to the number of Type D produced.

Hence find the number of Types A, B, C and E products that the factory produces, respectively.

<p>The table below shows the number of students who go to school by bus, car, MRT or on foot.</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/1767696506183-vcco3ub80s.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTY1MDYxODMtdmNjbzN1Yjgwcy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNjU0LCJleHAiOjE3OTI2NjI5NTR9.bTFIqQNXQFedA3Lmf1nRixqWQb-kXiu0QCWJi3mzdX4" 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">Complete the pictogram.</div><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-1-i-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xLWktZGlhZ3JhbS0xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI2NTQsImV4cCI6MTc5MjY2Mjk1NH0.4b8TLdXThx3uMs3prAoW-7cU3n3vlZcXLFNCMXr6f1k" alt="List item image" class="alignleft custom-width" style="max-width: min(500px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">Find the ratio of the number of students who go to school by bus to the number of students who go to school by car.</div></li><li><div class="list-item-paragraph">
Express the number of students who go to school on foot as a percentage of the total number of students, correcting your answer to $3$
 significant figures.</div></li></ol>

The table below shows the number of students who go to school by bus, car, MRT or on foot.

Expressing One Quantity as a Percentage of Another

Pictograms

<p>Ali, David and Priya agree to invest $\$315\,000$, $\$420\,000$ and $\$285\,000$ respectively into a project, and they cooperate with a technological university to develop their project. The university does not invest money into the project but will share $20\%$ of the profit of this project. The rest of the profit will be shared by Ali, David and Priya according to the ratio of their investments.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the ratio of Ali, David and Priya’s investments in the simplest form.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the fraction of total profit that Ali, David and Priya share, respectively.</span></div></li></ol>
<p>Suppose the project yields a total profit of $\$2\,550\,000$.</p>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Find the amount of profit that Ali, David, Priya and the university received, respectively.</span></div></li></ol>

Ali, David and Priya agree to invest $\$315\,000$, $\$420\,000$ and $\$285\,000$ respectively into a project, and they cooperate with a technological university to develop their project. The university does not invest money into the project but will share $20\%$ of the profit of this project. The rest of the profit will be shared by Ali, David and Priya according to the ratio of their investments.

Find the ratio of Ali, David and Priya’s investments in the simplest form.

Find the fraction of total profit that Ali, David and Priya share, respectively.

Suppose the project yields a total profit of $\$2\,550\,000$.

Find the amount of profit that Ali, David, Priya and the university received, respectively.

Percentage of a Quantity

Ratio

<p>There are $600$ girls in a school, and the ratio of the number of girls to the number of boys is $1 : 0.96$. Find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the number of boys in this school,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the ratio of the number of girls to the total number of students in this school.</span></div></li></ol>

There are $600$ girls in a school, and the ratio of the number of girls to the number of boys is $1 : 0.96$. Find

the ratio of the number of girls to the total number of students in this school.

<p>Find the ratio of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$0.7\text{h}$ to $56 \text{ min}$ to $3960\text{s}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$1\frac{1}{4} \text{m}$ to $205\text{cm}$ to $1750\text{mm}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$500\mathrm{g}$ to $10.25\text{kg}$ to $0.04\text{tonnes}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$250\text{ml}$ to $7.50\text{litre}$ to $1500\text{ml}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\$27.20$ to $\$6.80$ to $40\text{¢}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{1}{125} \text{m}^{3}$ to $4\text{dm}^{3}$ to $7000\text{cm}^{3}$</span></div></li></ol>

$0.7\text{h}$ to $56 \text{ min}$ to $3960\text{s}$

$1\frac{1}{4} \text{m}$ to $205\text{cm}$ to $1750\text{mm}$

$500\mathrm{g}$ to $10.25\text{kg}$ to $0.04\text{tonnes}$

$250\text{ml}$ to $7.50\text{litre}$ to $1500\text{ml}$

$\frac{1}{125} \text{m}^{3}$ to $4\text{dm}^{3}$ to $7000\text{cm}^{3}$

Conversion between Cubic Units

 Ratio

Volume and Surface Area of Prisms

<p>Simplify each of the following ratios.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{12}{5} : \frac{64}{45}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$2\frac{16}{75} : \frac{2}{15}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$143\% : 13\%$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$512 : 640$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$25x^{2}y^{2} : 625xy$, where $x, y \neq 0$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$1.25a^{2}b : 3.75ab^{2}$, where $a, b \neq 0$</span></div></li></ol>

$25x^{2}y^{2} : 625xy$, where $x, y \neq 0$

$1.25a^{2}b : 3.75ab^{2}$, where $a, b \neq 0$

Solving Ratio Problems Using Algebra

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ0NjU0ODM5MzAtMDZ6Z29od3VjM203LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI2NTQsImV4cCI6MTc5MjY2Mjk1NH0.LhhCnR80qaWc8AZOjDPwtbTOaHs0K95K43FFEaGLGhU" 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 Graphs

Line Graph

<p>The pie chart shows the expenditure in a household. The total expenditure is $\$720$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><ol class="abc-list"><li data-list-item-id="item-1780823084502-sdqk832l8"><div class="list-item-paragraph">Find the amount spend on</div><ol class="i-list"><li data-list-item-id="subitem-1780823090919-ofsxl1r5e"><div class="list-item-paragraph">phone bills,</div></li><li data-list-item-id="subitem-1780823091063-wq4cbi09x"><div class="list-item-paragraph">food.</div></li></ol></li><li data-list-item-id="item-1780823085375-tdo0ht4t3"><div class="list-item-paragraph">Express the amount spent on phone bills as a fraction of the expenditure.</div></li><li data-list-item-id="item-1780823085814-zt9vgdtdu"><div class="list-item-paragraph">Find the ratio of expenditure on transport to utility bills.</div></li><li data-list-item-id="item-1780823086686-x5ie1c4ag"><div class="list-item-paragraph">Find the percentage of the total expenditure on food.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><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/1777984081942-f4arspii0yj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5ODQwODE5NDItZjRhcnNwaWkweWoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.vzeYR_E6Ki9w1EHLsbYe0N59ZGQ4EvNtftkdsHWyug8" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

The pie chart shows the expenditure in a household. The total expenditure is $\$720$.

Interpreting a Pie Chart: Household Expenditure

<p>The pie chart below shows the distribution of participants in a marathon.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><ol class="abc-list"><li data-list-item-id="item-1780822668529-x82fbq27u"><div class="list-item-paragraph">Find the ratio of the number of boys to the number of women taking part in the 	marathon.</div></li><li data-list-item-id="item-1780822669337-ts9w78hyz"><div class="list-item-paragraph">There are $621$ more men than boys. Find the total number of men and boys 	participating in the marathon.</div></li><li data-list-item-id="item-1780822669896-qg720mbki"><div class="list-item-paragraph">Calculate the angle of the sector representing the number of girls participating in the 	marathon.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><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/1777982995337-13iucjjw3v9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5ODI5OTUzMzctMTNpdWNqanczdjkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.OKsLWRK0EC7n_6Hz3kVmonVx7_Py3fteLk1ysKVjaKw" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

The pie chart below shows the distribution of participants in a marathon.

Pie Chart

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQ0MDk3ODgyODAtbTc1bHZoc3plcDkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjY1NCwiZXhwIjoxNzkyNjYyOTU0fQ.KEMzXnw4trSLC58Pa6GvvRvkhVhDtg96PHrZCUP0lkM" 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>Simplify each of the following ratios.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--3" data-layout="3"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">$350\mathrm{ \ m}l$ : $\frac{4}{5}l$ </div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">$3.1$ hours : $80$ minutes </div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="3"><li><div class="list-item-paragraph">$9500$ mm : $0.012$ km</div></li></ol></div></div></div>

Simplifying Ratios with Unit Conversion

<p>Simplify each of the following ratios.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--3" data-layout="3"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">$2\frac{7}{8}:1.8$</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">$6\frac{3}{5}:\frac{2}{8}$ </div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="3"><li><div class="list-item-paragraph">$2.5$ m  : $500$ cm</div></li></ol></div></div></div>

Convert and Simplify Ratios

<p>There are $200$ grams of flour and $45$ grams of starch in a kitchen.  Find the ratio of </p>
<ol class="i-list"><li><div class="list-item-paragraph">the mass of the flour to the mass of the starch,</div></li><li><div class="list-item-paragraph">the mass of the starch to the mass of the flour.</div></li></ol>

There are $200$ grams of flour and $45$ grams of starch in a kitchen.  Find the ratio of 

Ratio of Two Quantities

<p>Simplify each of the following ratios.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--3" data-layout="3"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">$\frac{4}{5}:1.2$</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="2"><li><div class="list-item-paragraph">$4\frac{3}{4}:\frac{2}{5}$ </div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list" start="3"><li><div class="list-item-paragraph">$0.84$ kg	: $150$ g</div></li></ol></div></div></div>

<p>There are $215$ boys and $245$ girls in a school.  Find the ratio of </p>
<ol class="i-list"><li><div class="list-item-paragraph">the number of boys to the number of girls,</div></li><li><div class="list-item-paragraph">the numbers of girls to the number of boys. </div></li></ol>

There are $215$ boys and $245$ girls in a school.  Find the ratio of 

Ratio of Boys to Girls

<p>Ali, David and Priya agree to invest $\$315\,000$, $\$420\,000$ and $\$285\,000$ respectively into a project, and they cooperate with a technological university to develop their project. The university does not invest money into the project but will share $20\%$ of the profit of this project. The rest of the profit will be shared by Ali, David and Priya according to the ratio of their investments.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the ratio of Ali, David and Priya’s investments in the simplest form.</div></li><li><div class="list-item-paragraph">Find the fraction of total profit that Ali, David and Priya share, respectively.</div></li></ol>
<p>Suppose the project yields a total profit of $\$2\,550\,000$.</p>
<ol class="i-list" start="3"><li><div class="list-item-paragraph">Find the amount of profit that Ali, David, Priya and the university received, respectively.</div></li></ol>

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