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 box-and-whisker plot represents a set of data with $80$ data points.</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/1769497950121-106nfxli3zxd.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njk0OTc5NTAxMjEtMTA2bmZ4bGkzenhkLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI2NzksImV4cCI6MTc5MjY2Mjk3OX0.UzcDXFMXqRfGUMrDa1FxvgXDGl708zfPjakJl_Oju0A" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Box-and-whisker plot showing data values at 7, 48, 65, 78, and 85." class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the greatest and the least possible number of data points with the value of $78$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the greatest and the least possible number of data points with values at least $78$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the greatest and the least possible number of data points with the value of $85$.</span></div></li></ol>

The box-and-whisker plot represents a set of data with $80$ data points.

Find the greatest and the least possible number of data points with the value of $78$.

Find the greatest and the least possible number of data points with values at least $78$.

Find the greatest and the least possible number of data points with the value of $85$.

Finding Unknowns from Averages and Spread

Box-and-Whisker Plots

IP2U15 HOT Q4

Statistics

<p>The number of minutes taken by four boys to complete a question is $x - y$, $8$, $10$ and $x + y$. The mean time taken is $9$ minutes.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Show that&nbsp;$x = 9$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given that the standard deviation is $5$ minutes, find the value of $y$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Four girls answered the same question and the mean time taken is also $9$ minutes but the standard deviation is $2$ minutes. Compare and comment on these two sets of data.</span></div></li></ol>

The number of minutes taken by four boys to complete a question is $x - y$, $8$, $10$ and $x + y$. The mean time taken is $9$ minutes.

Given that the standard deviation is $5$ minutes, find the value of $y$.

Four girls answered the same question and the mean time taken is also $9$ minutes but the standard deviation is $2$ minutes. Compare and comment on these two sets of data.

Comparing Distributions Using Centre and Spread

IP2U15 HOT Q3

<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 $G$.

Mean of Ungrouped Data

Median, Quartiles, Range and Interquartile Range

Applications of Negative Numbers in Real Life

Real Numbers

<p>During a health check-up, the weights of $20$ students of the same height were recorded. </p>
<p>The stem-and-leaf diagram below illustrates their results.</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/1765430994441-kl6y6j4p12.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzA5OTQ0NDEta2w2eTZqNHAxMi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNjc5LCJleHAiOjE3OTI2NjI5Nzl9.OFwtpXQvzOob9s3R5fD7A6q4C-v6Iw6EPkOK-LSaMAY" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-paragraph">If the median weight of the students is $56$ kg, write down the value of $w$.</div></li><li><div class="list-item-paragraph">A student is considered underweight when weighs less than $45$ kg. Find the percentage of students who are underweight.</div></li></ol>

During a health check-up, the weights of $20$ students of the same height were recorded. 

The stem-and-leaf diagram below illustrates their results.

Expressing One Quantity as a Percentage of Another

Stem-and-Leaf Diagrams

Student Weight Distribution: Median and Underweight Percentage

Percentages

<p>The following shows the number of books read by a group of students.</p>
<p style="text-align: center">$5$, $7$, $5$, $3$, $4$, $7$, $2$, $6$, $x$, $5$</p>
<ol class="i-list"><li><div class="list-item-paragraph">If there are $2$ values for mode, write down the value of $x$.	</div></li><li><div class="list-item-paragraph">Hence, calculate the mean.</div></li></ol>

The following shows the number of books read by a group of students.

$5$, $7$, $5$, $3$, $4$, $7$, $2$, $6$, $x$, $5$

Books Read Data: Mode Constraints and Mean Calculation

<p>The table below shows the marks of a science test scored by a group of students.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 150px;"><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><strong>Marks</strong></p></th><th style="text-align: center; --cell-justify: center"><p>$23$</p></th><th style="text-align: center; --cell-justify: center"><p>$24$</p></th><th style="text-align: center; --cell-justify: center"><p>$25$</p></th><th style="text-align: center; --cell-justify: center"><p>$26$</p></th><th style="text-align: center; --cell-justify: center"><p>$27$</p></th><th style="text-align: center; --cell-justify: center"><p>$28$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><strong>Number of students</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$14$</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>$x$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td></tr></tbody></table></div></div>
<p>Find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the smallest possible value of $x$ if the modal mark is $27$.</div></li><li><div class="list-item-paragraph">the largest possible value of $x$ if the median is $25$.	</div></li></ol>

The table below shows the marks of a science test scored by a group of students.

Science Test Marks: Frequency Table with Mode and Median Conditions

<p>The table below shows the total number of goals scored by soccer teams in a tournament.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 150px;"><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 style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Total number of goals</strong></p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$1$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$2$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$3$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$4$</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$5$</p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p><strong>Number of teams</strong></p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$20$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$x$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$6$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$5$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$5$</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the value of $x$ if&nbsp;$40$ teams took part in the tournament.</div></li><li><div class="list-item-paragraph">State the biggest possible value of $x$ if the mode is $0$ goal.	</div></li><li><div class="list-item-paragraph">Write down the smallest possible value of $x$ is the median is $1$ goal.</div></li></ol>

The table below shows the total number of goals scored by soccer teams in a tournament.

<p><strong>Total number of goals</strong></p>

Tournament Goal Data: Solving for  $𝑥$, Mode, and Median

<p>The table below shows the number of cars per household.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 360px;"><colgroup><col style="width: 110px;"><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><strong>Number of cars</strong></p></th><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$2$</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></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><strong>Number of households</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$x$</p></td><td style="text-align: center; --cell-justify: center"><p>$1$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">If the median number of cars is $1$, find the possible values of $x$.</div></li><li><div class="list-item-paragraph">If&nbsp;$x=5$,</div><ol class="i-list"><li><div class="list-item-paragraph">state the modal number of cars,</div></li><li><div class="list-item-paragraph">find the probability of choosing a household with at least $2$ cars.</div></li></ol></li></ol>

The table below shows the number of cars per household.

Probability of a Single Event

Mode

Household Car Ownership: Median, Mode, and Probability

Probability

<p>The number of hours per week spent in doing homework by some students is shown in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 200px;"><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><strong>No of hours per week</strong></p></th><th style="text-align: center; --cell-justify: center"><p>$5$</p></th><th style="text-align: center; --cell-justify: center"><p>$6$</p></th><th style="text-align: center; --cell-justify: center"><p>$7$</p></th><th style="text-align: center; --cell-justify: center"><p>$8$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><strong>Frequency</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$2$</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><td style="text-align: center; --cell-justify: center"><p>$x$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down the largest possible value of $x$ if the mode is $7$.</div></li><li><div class="list-item-paragraph">Write down the value of $x$ if the median is $6.5$.</div></li><li><div class="list-item-paragraph">Calculate the value of $x$ if the mean is $7$.</div></li><li><div class="list-item-paragraph">Write down the possible value(s) of $x$ if the median is $6$.</div></li><li><div class="list-item-paragraph">Write down the value of $x$ if the modes are $7$ and $8$. </div></li></ol>

The number of hours per week spent in doing homework by some students is shown in the table below.

<p><strong>No of hours per week</strong></p>

Homework Hours: Mode, Median, and Mean with Unknown Frequency

<p>The mean of nine numbers is $27$. Four of the numbers have a mean of $21$. The remaining five numbers are $23$, $15$, $35$, $5$ and $t$. Find the value of $t$.</p>

The mean of nine numbers is $27$. Four of the numbers have a mean of $21$. The remaining five numbers are $23$, $15$, $35$, $5$ and $t$. Find the value of $t$.

Mean Problem with Two Groups of Numbers

<p>The mean of nine numbers is $52$. Six of the numbers are $23$, $60$, $65$, $45$, $37$ and $34$. </p>
<p>The remaining three numbers are each equal to $t$. Find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the sum of the $9$ numbers,</div></li><li><div class="list-item-paragraph">the value of $t$.</div></li></ol>

The mean of nine numbers is $52$. Six of the numbers are $23$, $60$, $65$, $45$, $37$ and $34$. 

The remaining three numbers are each equal to $t$. Find

Mean of Nine Numbers with Unknown Values

<p>The mean of $\mathrm{25}$, $12$, $35$, $24$, $15$, $x$ and $y$  is $22$ .</p>
<p>Find the mean of $x$ and $y$.</p>

The mean of $\mathrm{25}$, $12$, $35$, $24$, $15$, $x$ and $y$  is $22$ .

Mean Calculation with Two Unknown Values

<p>The mean of $\mathrm{15}$, $37$, $22$, $x$ and $y$  is $55$ .</p>
<p>Find the mean of $x$ and $y$.</p>

The mean of $\mathrm{15}$, $37$, $22$, $x$ and $y$  is $55$ .

Finding the Mean of Two Unknown Numbers

<p>The mean of $\$50$, $\$64$, $\$57$, $\$82$, $\$25$ and $\$x$ is $\$58$.</p>
<p>Find the value of $x$.</p>

The mean of $\$50$, $\$64$, $\$57$, $\$82$, $\$25$ and $\$x$ is $\$58$.

Finding an Unknown Value from a Given Mean

<p>The mean of eight numbers is $-5$. Five of the numbers are $-10$, $3$, $8$, $-2$ and $9$. The remaining three numbers are each equal to $t$. Find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the sum of the $8$ numbers,</div></li><li><div class="list-item-paragraph">the value of $t$. </div></li></ol>

The mean of eight numbers is $-5$. Five of the numbers are $-10$, $3$, $8$, $-2$ and $9$. The remaining three numbers are each equal to $t$. Find

Finding an Unknown Number from a Given Mean

<p>The mean of $52$, $38$, $x$, $47$, $52$, $48$ is $50$. </p>
<p>Find the value of $x$. </p>

The mean of $52$, $38$, $x$, $47$, $52$, $48$ is $50$. 

Math Question Bank