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PSLE

PSLE Foundation Mathematics

<p>The frequency table below summarizes the volume of apple juice dispensed from vending machine $A$ for&nbsp;$50$ trials.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Volume from $A$ ($x$ ml)</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Frequency</th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$246 &lt; x \le 248$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$4$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$248 &lt; x \le 250$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$7$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$250 &lt; x \le 252$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$28$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$252 &lt; x \le 254$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$6$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$254 &lt; x \le 256$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$5$</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">For vending machine $A$, calculate</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the mean,</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the standard deviation.</span><span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Another vending machine $B$ is used to dispense apple juice. The mean and standard deviation of the volumes of apple juice dispensed by vending machine $B$ is $251.36$ ml and $2.22$ ml respectively. The nominal volume of each cup of apple juice dispensed from these vending machines is $250$ ml. If you run a vending machine business, which machine would you buy? Explain your choice.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">What is the range of volume dispensed by machine $A$?</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Why is the standard deviation preferred over the range as a measure of the spread of data?</span><span class="inline-marks">[1]</span></div></li></ol></li></ol>

The frequency table below summarizes the volume of apple juice dispensed from vending machine $A$ for $50$ trials.

Another vending machine $B$ is used to dispense apple juice. The mean and standard deviation of the volumes of apple juice dispensed by vending machine $B$ is $251.36$ ml and $2.22$ ml respectively. The nominal volume of each cup of apple juice dispensed from these vending machines is $250$ ml. If you run a vending machine business, which machine would you buy? Explain your choice.

Comparing Distributions Using Centre and Spread

Median, Quartiles, Range and Interquartile Range

Mean and Standard Deviation for Grouped Data

Statistics

<p>A survey is conducted to study the amount of daily pocket money (in dollars) of a group of students in a class. The results of the survey, in terms of $x$, is as given in the data set&nbsp;$\{x-3,\ x+2,\ x+7,\ x-6,\ x+4,\ x,\ x+5\}$, where&nbsp;$x\ge6$.</p>
<p>Write down an expression for its</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">range,<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">lower quartile.<span class="inline-marks">[2]</span></div></li></ol>

A survey is conducted to study the amount of daily pocket money (in dollars) of a group of students in a class. The results of the survey, in terms of $x$, is as given in the data set $\{x-3,\ x+2,\ x+7,\ x-6,\ x+4,\ x,\ x+5\}$, where $x\ge6$.

<p>A set of pollutant standards index (PSI) has been taken on different parts of Singapore as follows.</p>
<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">28</th><th style="text-align: center; --cell-justify: center">29</th><th style="text-align: center; --cell-justify: center">30</th><th style="text-align: center; --cell-justify: center">24</th><th style="text-align: center; --cell-justify: center">25</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">29</td><td style="text-align: center; --cell-justify: center">25</td><td style="text-align: center; --cell-justify: center">28</td><td style="text-align: center; --cell-justify: center">22</td><td style="text-align: center; --cell-justify: center">28</td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-content"><span class="list-item-text">Find the</span></div><ol class="i-list"><li data-list-item-id="item-a-i" data-list-item-path="item-a/item-a-i"><div class="list-item-content"><span class="list-item-text">median,</span></div></li><li data-list-item-id="item-a-ii" data-list-item-path="item-a/item-a-ii"><div class="list-item-content"><span class="list-item-text">interquartile range.</span></div></li></ol></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-content"><span class="list-item-text">Represent the data by a box-and-whisker plot.</span></div></li></ol>

A set of pollutant standards index (PSI) has been taken on different parts of Singapore as follows.

Represent the data by a box-and-whisker plot.

Box-and-Whisker Plots

PSI: Median, Interquartile Range and Box Plot

<p>The Mathematics Test results obtained by $11$ students are as follows:</p>
<p style="text-align: center">$52, 36, 67, 66, 37, 46, 70, 55, 50, 60, 61$</p>
<p>A box-and-whisker plot is drawn to represent the data.</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/1767945085451-x0x93gdsbbd.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDUwODU0NTEteDB4OTNnZHNiYmQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNSwiZXhwIjoxNzkyNjk2MTE1fQ._fBAxblOxiIWEws87cH7Puqa3E9TMjrDR0Nwm-XMFZk" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Box-and-whisker plot of Mathematics Test results" class="aligncenter custom-width" /></figure></div>
<p>State the values of $x$, $y$ and $z$.</p>

The Mathematics Test results obtained by $11$ students are as follows:

$52, 36, 67, 66, 37, 46, 70, 55, 50, 60, 61$

A box-and-whisker plot is drawn to represent the data.

State the values of $x$, $y$ and $z$.

Statistical Data Representation: Box-and-Whisker Plot Analysis

<p>The data below shows the marks obtained by $14$ students in a Mathematics test.</p>
<p>$36, 49, 49, 57, 60, 60, 60, 61, 69, 75, 76, 80, 86, 97$</p>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the median mark,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the lower quartile mark.</span></div></li></ol>

The data below shows the marks obtained by $14$ students in a Mathematics test.

$36, 49, 49, 57, 60, 60, 60, 61, 69, 75, 76, 80, 86, 97$

Data Summary: Median Identification and Variability Analysis

<p>Twenty boys took a Mathematics test. The marks are shown in the stem-and-leaf diagram.</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/1767939934439-2kxx1nlb6tn.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5Mzk5MzQ0MzktMmt4eDFubGI2dG4ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNSwiZXhwIjoxNzkyNjk2MTE1fQ.yO1i-xCNds7BEZnZtbu5VQXn9O_TUiRiEpku_7ccmJU" style="max-width: min(200px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down the median of the boy's marks.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Calculate the interquartile range of the boys' marks.</span></div></li></ol>

Twenty boys took a Mathematics test. The marks are shown in the stem-and-leaf diagram.

Write down the median of the boy's marks.

Calculate the interquartile range of the boys' marks.

Stem-and-Leaf Diagrams

Statistical Profiling of Student Commute Patterns

<p>$11$ students took a test and their results are shown below.</p>
<p style="text-align: center">$10, 15, 16, 16, 16, 17, 18, 20, 21, 23, 25.$</p>
<p>Find the median and the interquartile range.</p>

$11$ students took a test and their results are shown below.

$10, 15, 16, 16, 16, 17, 18, 20, 21, 23, 25.$

Find the median and the interquartile range.

Statistical Measures of Central Tendency and Dispersion

<p>The line graph below shows the temperature (in °C) recorded at noon over a week in a city.</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/1767772184081-8z1lw7pr1iw.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzIxODQwODEtOHoxbHc3cHIxaXcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNSwiZXhwIjoxNzkyNjk2MTE1fQ.nz5nGSGaJVjLaFll-A-2rc5JBDa6HjJEkWU_nT9yf0g" 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-content"><span class="list-item-text">Calculate the average temperature over the week.</span></div></li><li><div class="list-item-content"><span class="list-item-text">What was the difference in temperature between the hottest and the coldest day?</span></div></li><li><div class="list-item-content"><span class="list-item-text">If a day is considered "hot" when the temperature is above <strong>25°C</strong>, what is the fraction of hot days?</span></div></li><li><div class="list-item-content"><span class="list-item-text">What is the trend of the temperature over the week? Describe whether it is increasing, decreasing or fluctuating.</span></div></li></ol>

The line graph below shows the temperature (in °C) recorded at noon over a week in a city.

Calculate the average temperature over the week.

What was the difference in temperature between the hottest and the coldest day?

If a day is considered "hot" when the temperature is above **25°C**, what is the fraction of hot days?

What is the trend of the temperature over the week? Describe whether it is increasing, decreasing or fluctuating.

Mean of Ungrouped Data

Line Graphs

<p>A pictogram shows the number of apples sold at a fruit shop over a week. Each apple icon represents <strong>20</strong> apples.</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/1767771932127-6b46vpiisn4.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzE5MzIxMjctNmI0NnZwaWlzbjQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNSwiZXhwIjoxNzkyNjk2MTE1fQ.wYtAe4tTI9NEPPuMGdx3UiRFSjPfW88d0SjgiUnMbgY" 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-content"><span class="list-item-text">Which two days have the same number of apples sold?</span></div></li><li><div class="list-item-content"><span class="list-item-text">Which day has the most number of apples sold?</span></div></li><li><div class="list-item-content"><span class="list-item-text">Calculate the average number of apples sold per day.</span></div></li><li><div class="list-item-content"><span class="list-item-text">What is the difference in the number of apples sold between the day with the highest sale and the day with the lowest sale?</span></div></li></ol>

A pictogram shows the number of apples sold at a fruit shop over a week. Each apple icon represents **20** apples.

Which two days have the same number of apples sold?

Which day has the most number of apples sold?

Calculate the average number of apples sold per day.

What is the difference in the number of apples sold between the day with the highest sale and the day with the lowest sale?

Pictograms

<p>The line graph below shows the incomplete monthly average temperature of two regions in 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/1767766270632-gy8u3g0xjif.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NjYyNzA2MzItZ3k4dTNnMHhqaWYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNSwiZXhwIjoxNzkyNjk2MTE1fQ.Ktx954Va9SM84kbQvGh-ACBCw4GKdGz_PKu8BLacpDk" 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">Complete the line graph using the data in the table below.</span></div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">Month</th><th style="text-align: left; --cell-justify: flex-start">Jan</th><th style="text-align: left; --cell-justify: flex-start">Feb</th><th style="text-align: left; --cell-justify: flex-start">Mar</th><th style="text-align: left; --cell-justify: flex-start">Apr</th><th style="text-align: left; --cell-justify: flex-start">May</th><th style="text-align: left; --cell-justify: flex-start">Jun</th><th style="text-align: left; --cell-justify: flex-start">Jul</th><th style="text-align: left; --cell-justify: flex-start">Aug</th><th style="text-align: left; --cell-justify: flex-start">Sep</th><th style="text-align: left; --cell-justify: flex-start">Oct</th><th style="text-align: left; --cell-justify: flex-start">Nov</th><th style="text-align: left; --cell-justify: flex-start">Dec</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">Temp. in Region A (°C)</td><td style="text-align: left; --cell-justify: flex-start">0</td><td style="text-align: left; --cell-justify: flex-start">-1</td><td style="text-align: left; --cell-justify: flex-start">4</td><td style="text-align: left; --cell-justify: flex-start">11</td><td style="text-align: left; --cell-justify: flex-start">17</td><td style="text-align: left; --cell-justify: flex-start">23</td><td style="text-align: left; --cell-justify: flex-start">25</td><td style="text-align: left; --cell-justify: flex-start">25</td><td style="text-align: left; --cell-justify: flex-start">21</td><td style="text-align: left; --cell-justify: flex-start">16</td><td style="text-align: left; --cell-justify: flex-start">9</td><td style="text-align: left; --cell-justify: flex-start">4</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">Temp. in Region B (°C)</td><td style="text-align: left; --cell-justify: flex-start">-22</td><td style="text-align: left; --cell-justify: flex-start">-14</td><td style="text-align: left; --cell-justify: flex-start">-2</td><td style="text-align: left; --cell-justify: flex-start">6</td><td style="text-align: left; --cell-justify: flex-start">13</td><td style="text-align: left; --cell-justify: flex-start">16</td><td style="text-align: left; --cell-justify: flex-start">24</td><td style="text-align: left; --cell-justify: flex-start">23</td><td style="text-align: left; --cell-justify: flex-start">17</td><td style="text-align: left; --cell-justify: flex-start">6</td><td style="text-align: left; --cell-justify: flex-start">-5</td><td style="text-align: left; --cell-justify: flex-start">-15</td></tr></tbody></table></div></div>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Find</div><ol class="abc-list"><li><div class="list-item-paragraph">the difference between the highest and lowest monthly average temperature in Region A and Region B, respectively, and </div></li><li><div class="list-item-paragraph">the number of months when the monthly average temperature is above 10°C in Region A and Region B.</div></li></ol></li><li><div class="list-item-paragraph">A kind of crop needs to grow in an environment with an average temperature higher than $10$°C for more than $6$ consecutive months. State, with clear reasons, which region is more suitable for growing this crop.</div></li><li><div class="list-item-content"><span class="list-item-text">A skating team plans to use outdoor venues for training in either Region A or Region B. State, with clear reasons, which region can provide the skating team with a longer and more stable training time.</span></div></li></ol>

The line graph below shows the incomplete monthly average temperature of two regions in a year.

Complete the line graph using the data in the table below.

A skating team plans to use outdoor venues for training in either Region A or Region B. State, with clear reasons, which region can provide the skating team with a longer and more stable training time.

Interpreting and Evaluating Statistical Representations

<p>In a class quiz, the average time taken by seven candidates to complete the quiz is 1 hour and 17 minutes. The table below shows the difference between the time taken by each candidate and the average time.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">Candidates</th><th style="text-align: left; --cell-justify: flex-start">A</th><th style="text-align: left; --cell-justify: flex-start">B</th><th style="text-align: left; --cell-justify: flex-start">C</th><th style="text-align: left; --cell-justify: flex-start">D</th><th style="text-align: left; --cell-justify: flex-start">E</th><th style="text-align: left; --cell-justify: flex-start">F</th><th style="text-align: left; --cell-justify: flex-start">G</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">Difference (minutes)</td><td style="text-align: left; --cell-justify: flex-start">-8</td><td style="text-align: left; --cell-justify: flex-start">2</td><td style="text-align: left; --cell-justify: flex-start">-3</td><td style="text-align: left; --cell-justify: flex-start">-11</td><td style="text-align: left; --cell-justify: flex-start">$x$</td><td style="text-align: left; --cell-justify: flex-start">5</td><td style="text-align: left; --cell-justify: flex-start">13</td></tr></tbody></table></div></div>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the value of $x$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the difference between the greatest and smallest time taken to complete the quiz,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the average time taken to complete the quiz by candidate $C$, $D$ and $G$.</span></div></li></ol>

In a class quiz, the average time taken by seven candidates to complete the quiz is 1 hour and 17 minutes. The table below shows the difference between the time taken by each candidate and the average time.

the difference between the greatest and smallest time taken to complete the quiz,

the average time taken to complete the quiz by candidate $C$, $D$ and $G$.

Finding Unknowns from Averages and Spread

Applications of Negative Numbers in Real Life

Real Numbers

<p style="margin-top: 1rem">The table shows the temperature of six cities at midnight on a particular day.</p>
<div class="table-container"><table><thead><tr><th>City</th><th>Stockholm</th><th>Nuuk</th><th>Toronto</th><th>Wellington</th><th>Singapore</th><th>Reykjavík</th></tr></thead><tbody><tr><td>Temperature $\left( {}^\circ \mathrm{C} \right)$</td><td>$-4\mathrm{ }{}^\circ \mathrm{C}$</td><td>$-8\mathrm{ }{}^\circ \mathrm{C}$</td><td>$9\mathrm{ }{}^\circ \mathrm{C}$</td><td>$14\mathrm{ }{}^\circ \mathrm{C}$</td><td>$\mathrm{24 }{}^\circ \mathrm{C}$</td><td>$-5\mathrm{ }{}^\circ \mathrm{C}$</td></tr></tbody></table></div>
<ol class="abc-list"><li><div class="list-item-paragraph">List down all six cities in the ascending order of their temperature.

</div></li><li><div class="list-item-paragraph">Find the difference between the greatest temperature and smallest temperature.</div></li><li><div class="list-item-paragraph">Find the average temperature of Stockholm, Nuuk and Singapore.

</div></li></ol>

The table shows the temperature of six cities at midnight on a particular day.

Math Question Bank