A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

<p>The following bar graph shows the unit cost and unit selling price of six items in a store.</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/1767772322945-f68m9qxei6b.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzIzMjI5NDUtZjY4bTlxeGVpNmIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.aDdcCCBtEfNNnMCrAVdaOBtNLGykxEytU-OPpOmrJgE" 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">Using the data from the bar graph above, 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/migrated/2024/06/Extra-Practice-Q30-i-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1RMzAtaS1kaWFncmFtLTEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.zJdGuwP9bknWMkoweGm5u6n5nrdCydu9UUW5-EoWACo" alt="List item image" class="aligncenter custom-width" style="max-width: min(450px, 100%); height: auto;" /></div><div class="list-item-paragraph">The bar graph below shows the quantities sold (in hundreds) of the six items from July to September.</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/2024/06/Extra-Practice-Q30-i-diagram-2-624x362.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1RMzAtaS1kaWFncmFtLTItNjI0eDM2Mi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzYzLCJleHAiOjE3OTI2NjMwNjN9.i5m9LQPjR_lnTfP4HwZPdC55aZM1rKlftx7mbxz32jI" alt="List item image" class="aligncenter custom-width" style="max-width: min(450px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">Using the data above, complete the pie chart below by subdividing the grey part according to the sales of items D, E and F. Hence state clearly the quantity sold for each item and the degree of each sector.</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/2024/06/Extra-Practice-Q30-ii-diagram--624x396.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1RMzAtaWktZGlhZ3JhbS0tNjI0eDM5Ni5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzYzLCJleHAiOjE3OTI2NjMwNjN9.K6_Qv3Aemeeo4KUAsDpixsDzPfhtjyu7lDS-zjlsQII" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">Complete the table below, which shows the total profit earned by each of the six items from July to September.</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/2024/06/Extra-Practice-Q30-iii-diagram--624x91.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1RMzAtaWlpLWRpYWdyYW0tLTYyNHg5MS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzYzLCJleHAiOjE3OTI2NjMwNjN9.9Xarp18XbDm5T0HwmbzK4-Q115OWlYeLve0jObdloHM" alt="List item image" class="aligncenter" style="max-width: 100%; height: auto;" /></div></li><li><div class="list-item-paragraph">Based on your answers in (iii), state which item has the highest total profit and which item has the lowest total profit.</div></li><li><div class="list-item-paragraph">Given that from July to September, the item that has the highest total profit is fan, while the item that has the lowest total profit is scarf, give one suggestion for the store’s selling plan for the next quarter (October to December), based on the following assumptions, respectively:</div><ol class="abc-list"><li><div class="list-item-paragraph">without considering any other factors;

</div></li><li><div class="list-item-paragraph">considering the monthly average temperature of the region where the store is located, which is shown in the line graph 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/migrated/2024/06/Extra-Practice-Q30-v-diagram--624x332.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1RMzAtdi1kaWFncmFtLS02MjR4MzMyLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NjMsImV4cCI6MTc5MjY2MzA2M30.6g7sge7lnkBIKpKl6YH7QBxKJOETSBlWqFMgrUvbWyw" alt="Sub-item image" class="aligncenter custom-width" style="max-width: min(450px, 100%); height: auto;" /></div></li></ol></li></ol>

The following bar graph shows the unit cost and unit selling price of six items in a store.

Percentages involving Finances: Profit and Loss

Interpreting and Evaluating Statistical Representations

Pie Charts

Bar Graphs

Line Graphs

 Bar Graphs, Pie Charts, Line Graphs

Percentages

Statistics

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzIwNDgwMjgteWowNGhwNzNsc2wucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.bvumPlsUyf895l0077BOOmk42iePJUlXKmmgXL22n5A" 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.

Simplifying Ratios

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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjM1NDcxNTMtY2pidTRycW1iMm0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.THejsQTbw8gFtJUDeNIRLMqsjcTHpgHMWqw6H0n2v4E" 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.

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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0yMi1pLWRpYWdyYW0tMS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzYzLCJleHAiOjE3OTI2NjMwNjN9.Gj1YwU5bGdTuP1Jbw6Ce9pNcOFy-Edp1dEKN7Q1HYgI" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0yMi1paS1kaWFncmFtLTEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.7tWnzOIReh6PZ2gT4TTRRVcuBtwzZngvGkaHeQePxUo" 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

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjExODMwNDAtMW1icGllNndnbGMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.Ah1ckVcbuCu5Dqv49g7YZSS3butXZ7bZyjX7KNXyGek" 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 charts below show the composition of sales and costs of $4$ different products of a company in $2022$, respectively. Given that the total costs and the total sales of the company in $2022$ is $\$1.2$ million and $\$2.0$ million, find</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/1767760842044-smj4ezvy8l.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjA4NDIwNDQtc21qNGV6dnk4bC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzYzLCJleHAiOjE3OTI2NjMwNjN9.EcnAo5gsFSMFa7EPHlVJrGvAMJLH56XSHFgnAp7tBYs" 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">the values of $x$, $y$ and $z$, respectively,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the profit that the company earns from each of Product A, B, C and D, respectively, and</span></div></li><li><div class="list-item-paragraph">the profit rate of each of Product A, B, C and D, respectively, expressed by the profit as a percentage of the cost of each product, correcting your answers to $3$ significant figures.</div></li><li><div class="list-item-content"><span class="list-item-text">Based on your answers in (ii) and (iii), state one suggestion for the company to increase its total profit, assuming the fluctuations in costs and sales in the future is negligible.</span></div></li></ol>

The pie charts below show the composition of sales and costs of $4$ different products of a company in $2022$, respectively. Given that the total costs and the total sales of the company in $2022$ is $\$1.2$ million and $\$2.0$ million, find

the values of $x$, $y$ and $z$, respectively,

the profit that the company earns from each of Product A, B, C and D, respectively, and

Based on your answers in (ii) and (iii), state one suggestion for the company to increase its total profit, assuming the fluctuations in costs and sales in the future is negligible.

<p>The table below shows the age distribution of the researchers in an institute.</p>
<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">Age range</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$20 - 29$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$30 - 39$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$40 - 49$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$&gt; 49$</p></th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Number of researchers</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$35$</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$30$</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$20$</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$x$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">Given that $15%$ of the researchers are aged above $49$, find the value of $x$.</div></li><li><div class="list-item-paragraph">Determine which age range does each sector represents in the pie chart below, hence express each part as a percentage of the whole and find the angles of each sector.</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-12-ii-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMi1paS1kaWFncmFtLTEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.AmN7kCJpn2vi6P_zuyVt2xgJ_0ELCVaijXWlbDAE9Zo" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">Construct a bar graph using the grids below to illustrate the data.</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-12-iii-diagram-624x408.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMi1paWktZGlhZ3JhbS02MjR4NDA4LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NjMsImV4cCI6MTc5MjY2MzA2M30.iIaqpZ4z7tVsbaNFVfD1CxDb6K6HvOoh3YfyJHdzk_0" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>
<p>The institute then hires a certain number of researchers aged between $40$ and $49$, such that the new number of researchers aged between $40$ and $49$ is $\frac{1}{3}$ of the new total number of researchers of the institute.</p>
<ol class="i-list" start="4"><li><div class="list-item-paragraph">Given that there is no other change in the number of researchers of the institute, express the number of researchers aged between $30$ and $39$ as a percentage of the new total number of researchers of the institute.</div></li></ol>

The table below shows the age distribution of the researchers in an institute.

Determine which age range does each sector represents in the pie chart below, hence express each part as a percentage of the whole and find the angles of each sector.

Construct a bar graph using the grids below to illustrate the data.

The institute then hires a certain number of researchers aged between $40$ and $49$, such that the new number of researchers aged between $40$ and $49$ is $\frac{1}{3}$ of the new total number of researchers of the institute.

 Pie Charts, Line Graphs

<p>The table below shows the age distribution of the researchers in an institute.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">Age range</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$20 - 29$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$30 - 39$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$40 - 49$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$&gt; 49$</p></th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">Number of researchers</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$35$</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$30$</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$20$</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$x$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Given that&nbsp;$15\%$ of the researchers are aged above $49$, find the value of $x$.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Determine which age range does each sector represents in the pie chart below, hence express each part as a percentage of the whole and find the angles of each sector.</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-12-ii-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMi1paS1kaWFncmFtLTEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.AmN7kCJpn2vi6P_zuyVt2xgJ_0ELCVaijXWlbDAE9Zo" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">Construct a bar graph using the grids below to illustrate the data.</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-12-iii-diagram-624x408.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMi1paWktZGlhZ3JhbS02MjR4NDA4LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NjMsImV4cCI6MTc5MjY2MzA2M30.iIaqpZ4z7tVsbaNFVfD1CxDb6K6HvOoh3YfyJHdzk_0" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>
<p>The institute then hires a certain number of researchers aged between $40$ and $49$, such that the new number of researchers aged between $40$ and $49$ is $\frac{1}{3}$ of the new total number of researchers of the institute.</p>
<ol class="i-list" start="4"><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">Given that there is no other change in the number of researchers of the institute, express the number of researchers aged between $30$ and $39$ as a percentage of the new total number of researchers of the institute.</div></li></ol>

The institute then hires a certain number of researchers aged between $40$ and $49$, such that the new number of researchers aged between $40$ and $49$ is $\frac{1}{3}$ of the new total number of researchers of the institute.

Pie Charts, Line Graphs

<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">The table below shows the number of students who get an A, B, C and D in a test, respectively. Construct a bar graph using the grids below and the data from the table.</div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">Rating</th><th style="text-align: center; --cell-justify: center"><p>$A$</p></th><th style="text-align: center; --cell-justify: center"><p>$B$</p></th><th style="text-align: center; --cell-justify: center"><p>$C$</p></th><th style="text-align: center; --cell-justify: center"><p>$D$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Number of students</td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$28$</p></td><td style="text-align: center; --cell-justify: center"><p>$21$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td></tr></tbody></table></div></div>
<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/1767697968109-3auxxpz6tsi.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTc5NjgxMDktM2F1eHhwejZ0c2kucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.qXwMXJzFme7E2kXRPK4AvvC4pZ1FKFB-vc7M3dAGtBY" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list" start="2"><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">The table below shows the percentage of four types of products produced by a factory, respectively. Construct a pie chart using the figure below and the data from the table, stating clearly the degree of each sector, production in percentage and the type of each product.</div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr style="height: 43px;"><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Type</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">I</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">II</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">III</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">IV</th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Production in percentage</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$25\%$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$50\%$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$20\%$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$5\%$</p></td></tr></tbody></table></div></div>
<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/1767698069825-kc0bpuwrej.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTgwNjk4MjUta2MwYnB1d3Jlai5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzYzLCJleHAiOjE3OTI2NjMwNjN9.lDAINt0mLhUajOOMHUrW_AdyDLcbCMv_N_wJxyuN4GA" style="max-width: min(250px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list" start="3"><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">The table below shows the number of employees that a company hires from $1995$ to $2020$, respectively. </div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">Year</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$1995$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$2000$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$2005$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$2010$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$2015$</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>$2020$</p></th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Number of employees</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$36$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$49$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$60$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$55$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$63$</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>$72$</p></td></tr></tbody></table></div></div>
<p>Construct a line graph using the grids below and the data from the table.</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/1767698124528-4t9b2zhe8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTgxMjQ1MjgtNHQ5YjJ6aGU4LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NjMsImV4cCI6MTc5MjY2MzA2M30.bXGqf54qtmPHouTxdO_WBozOi5OZGvnFBfRfU9xq0SI" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Construct a line graph using the grids below and the data from the table.

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTczODgxMjctZ2hyNGEyNGd3ZG8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.1sTA3mINRDzmrbycvL3LucQIF7q2TdGp5R1Dy66tQq4" 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 pie chart below shows the composition of the employees’ nationalities of a company.</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/1767697294189-vsq9j66tfqj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTcyOTQxODktdnNxOWo2NnRmcWoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.9d92mOWekT_yCrtLMfCf70UjaIbZdIRSHbaTCivAjpY" 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">Given that the number of employees whose nationality is Malaysian is $50$, find the total number of employees of the company,</div></li><li><div class="list-item-content"><span class="list-item-text">the number of employees whose nationality is Singaporean, and</span></div></li><li><div class="list-item-content"><span class="list-item-text">the value of $x$. Hence express the number of employees whose nationality is Indian as a percentage of the total number of employees of the company.</span></div></li></ol>

The pie chart below shows the composition of the employees’ nationalities of a company.

the number of employees whose nationality is Singaporean, and

the value of $x$. Hence express the number of employees whose nationality is Indian as a percentage of the total number of employees of the company.

<p>The following data shows the number of hours $24$ students of a class spent studying per day.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$6$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$5$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Using the grid below, draw a dot diagram to represent the above data.	</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/1765431475759-62j12cvscbf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzE0NzU3NTktNjJqMTJjdnNjYmYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.VXOrOGoPDgHkS9BsNpqpP17tOS4JhvrpARhis7sVTDA" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">What is the modal number of hours the students spent studying?</div></li><li><div class="list-item-paragraph">Calculate the mean number of hours the students spent studying.</div></li><li><div class="list-item-paragraph">If the above data was presented on a pie chart, what is the size of the angle that represents the number of students who study at least $3$ hours a day?</div></li><li><div class="list-item-paragraph">What is the probability of a student studying $4$ hours a day?	</div></li></ol>

The following data shows the number of hours $24$ students of a class spent studying per day.

Mean of a Frequency Distribution

Constructing and Interpreting Frequency Tables

Probability of a Single Event

Mode

Dot Diagrams

Number of Hours Spent Studying: Mode, Mean, and Probability

Probability

<p>The following data shows the number of customers across $12$ restaurants at a given moment.</p>
<div class="content-block content-block--table"><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"><p>$15$</p></th><th style="text-align: center; --cell-justify: center"><p>$15$</p></th><th style="text-align: center; --cell-justify: center"><p>$18$</p></th><th style="text-align: center; --cell-justify: center"><p>$16$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$15$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$14$</p></td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Using the grid below, draw a dot diagram to represent the above data.	</div></li><li><div class="list-item-paragraph">Calculate the mean number of customers across the restaurants.</div></li><li><div class="list-item-paragraph">If the above data was presented on a pie chart, what is the size of the angle that represents the number of restaurants that have at most $14$ customers?</div></li><li><div class="list-item-paragraph">What is the probability of a restaurant having $15$ customers at a given moment?</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/1765356605664-r1hvseay03d.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNTY2MDU2NjQtcjFodnNlYXkwM2QucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.b7o9EXnoS9kNP0o3EGNJm4GOSaDCsLJfdB6Ch92ibPI" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

The following data shows the number of customers across $12$ restaurants at a given moment.

Number of Customers Across Restaurants

<p>The following data shows the number of hours $24$ students of a class spent studying per day.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 560px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$6$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$2$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$2$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Using the grid below, draw a dot diagram to represent the above data.	</div></li><li><div class="list-item-paragraph">Calculate the mean number of hours the students spent studying.</div></li><li><div class="list-item-paragraph">If the above data was presented on a pie chart, what is the size of the angle that represents the number of students who study at least $3$ hours a day?</div></li><li><div class="list-item-paragraph">What is the probability of a student studying $4$ hours a day?	</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/1765353365573-827m1wboxzo.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNTMzNjU1NzMtODI3bTF3Ym94em8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.Gjl96sdfwDXGSdx-UgGdDDHxs204ecW1aoY7QxAPW7U" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

Finding The Mean From A Dot Diagram

<p>A shopping mall has a few departments which are categorised as groceries, furniture, clothing, entertainment, and food. The pie chart shows the number of sales transactions done by each department in one month.  </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/1765276598900-sga1cfwy8hj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUyNzY1OTg5MDAtc2dhMWNmd3k4aGoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.5nwkU6xRRqWEJgKG7Jo7uA0c24R0qqln-Noes92sV-M" style="max-width: min(200px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>A sale transaction is selected at random from the above data collected. Find the probability that the transaction was made by </p>
<ol class="i-list"><li><div class="list-item-paragraph">the groceries department,</div></li><li><div class="list-item-paragraph">the food or furniture departments. </div></li></ol>

A shopping mall has a few departments which are categorised as groceries, furniture, clothing, entertainment, and food. The pie chart shows the number of sales transactions done by each department in one month.  

A sale transaction is selected at random from the above data collected. Find the probability that the transaction was made by 

Sales Transactions: Sector Diagram Probability

<p>A survey is conducted to find out what is the favourite fruit of each student in a class. The pie chart shows the results of the survey. A student is selected at random.<br>Find the probability that the student’s favourite fruit is</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="i-list"><li><div class="list-item-paragraph">mango,</div></li><li><div class="list-item-paragraph">not durian,</div></li><li><div class="list-item-paragraph">apple or orange.</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/1765275621756-afc8tgkmrr.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUyNzU2MjE3NTYtYWZjOHRna21yci5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzYzLCJleHAiOjE3OTI2NjMwNjN9.zTXaejruT67VOapuvZeq5Ooi8A_TM79cnn5-VGIOXWQ" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

A survey is conducted to find out what is the favourite fruit of each student in a class. The pie chart shows the results of the survey. A student is selected at random.
Find the probability that the student’s favourite fruit is

Complementary Events

Probability: Reading a Pie Chart

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5ODQwODE5NDItZjRhcnNwaWkweWoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.CZ_C6cWu7rixBv_nApHbbRRKuxLQl9VGiBN4mezWbhw" 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 shows the distribution of different age groups in a marathon with $1080$ participants.</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-1780822976749-7jmidtn0c"><div class="list-item-paragraph">Calculate the percentage of adults in the marathon.</div></li></ol><p>There are twice as many elderly participants as children’s participants.</p><ol class="abc-list" start="2"><li data-list-item-id="item-1780822980781-jaln9eiqm"><div class="list-item-paragraph">Find the size of the angle representing children’s participants in the pie chart.</div></li><li data-list-item-id="item-1780822981517-srjo6k31a"><div class="list-item-paragraph">Find the number of the elderly participants 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/1777983896787-a2xgpec9faj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5ODM4OTY3ODctYTJ4Z3BlYzlmYWoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.mRRUoDcnV-YTjYgm2XVZmIzdcqie8GuDwi6JvbwwLgg" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

The pie chart shows the distribution of different age groups in a marathon with $1080$ participants.

Pie Chart Analysis – Marathon Participants

<p>The pie chart below represents the favourite fruits of students in a class. Each student indicated one fruit as their favourite fruit.</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-1780822865987-a6zg0u3me"><div class="list-item-paragraph">Find the value of $x$.</div></li><li data-list-item-id="item-1780822866547-ax0bobd1y"><div class="list-item-paragraph">Find the percentage of students whose favourite fruit is apple.</div></li><li data-list-item-id="item-1780822867099-y0lvw2l4h"><div class="list-item-paragraph">Given that there is a total of $40$ students in the class, find the number of students 	whose favourite fruit is orange.</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/1777983737632-cn1vyeh2ooo.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5ODM3Mzc2MzItY24xdnllaDJvb28ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.84GZCyh_27IbcQGQt8SHUiKdMasixODi0zIZNAQqgnk" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The pie chart below represents the favourite fruits of students in a class. Each student indicated one fruit as their favourite fruit.

Pie Chart: Favourite Fruits of Students

<p>The table below shows the grades obtained by $500$ students who went for acting class.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 500px;"><colgroup><col style="width: 250px;"><col style="width: 250px;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Grade</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Number of students</th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Distinction</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$90$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Credit</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$165$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Pass</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$200$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Fail</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$a$</td></tr></tbody></table></div></div>
<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;"><p>Calculate</p><ol class="abc-list"><li data-list-item-id="item-1780822783226-w8f6pf9ja"><div class="list-item-paragraph">the value of $a$.</div></li><li data-list-item-id="item-1780822783739-p4z6ocp5d"><div class="list-item-paragraph">the percentage of students who did not fail.</div></li><li data-list-item-id="item-1780822784202-k3jq6k7rh"><div class="list-item-paragraph">This data was represented in the pie chart shown. Calculate the value of $b{}^\circ $.</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/1777983251206-5ap3vbqx0tl.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzc5ODMyNTEyMDYtNWFwM3ZicXgwdGwucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc2MywiZXhwIjoxNzkyNjYzMDYzfQ.feMkLQbDUnw3_x9sy6KdQ8qvUPZ98yUvyBADyD3qwtc" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

The table below shows the grades obtained by $500$ students who went for acting class.

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