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<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Showing your working clearly, evaluate $0.5\times \frac{(17^2 - 7^2) \div \sqrt{(-20)\times(-1.8)}}{0.74 - 3.24}$.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Showing your working clearly, evaluate $\frac{\frac{8}{5}\times \sqrt{\left(-2\frac{3}{4}\right)^2 - 6}}{-1\frac{1}{2} - 2\frac{3}{4}}$.</span><span class="inline-marks">[3]</span></div></li></ol>

Showing your working clearly, evaluate $0.5\times \frac{(17^2 - 7^2) \div \sqrt{(-20)\times(-1.8)}}{0.74 - 3.24}$.

Showing your working clearly, evaluate $\frac{\frac{8}{5}\times \sqrt{\left(-2\frac{3}{4}\right)^2 - 6}}{-1\frac{1}{2} - 2\frac{3}{4}}$.

IP1 Class Test (May 2025) Q6

Real Numbers

<p style="text-align: center">$1\frac{3}{4}, \frac{1}{2}\pi, -174, 0.14\dot{7}\dot{6}, \frac{\sqrt{36}}{7}, \sqrt[3]{64}, \sqrt{2}, \sqrt{121}\pi, -\sqrt{144}$</p>
<p>From the numbers given, list the numbers that are</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">rational numbers,</span></div></li><li><div class="list-item-content"><span class="list-item-text">irrational numbers,</span></div></li><li><div class="list-item-paragraph">integers.</div></li></ol>

$1\frac{3}{4}, \frac{1}{2}\pi, -174, 0.14\dot{7}\dot{6}, \frac{\sqrt{36}}{7}, \sqrt[3]{64}, \sqrt{2}, \sqrt{121}\pi, -\sqrt{144}$

From the numbers given, list the numbers that are

IP1 Class Test (May 2025) Q2

<p>Find the value of $5 - 6 + 7 - 8 + 9 - 10 + \dots + 199 - 200 + 201$.</p>

Find the value of $5 - 6 + 7 - 8 + 9 - 10 + \dots + 199 - 200 + 201$.

Real Numbers - General

<p>Find the value of $5 + 6 + 7 + 8 \dots + 202 + 203 + 204$.</p>

Find the value of $5 + 6 + 7 + 8 \dots + 202 + 203 + 204$.

<p>Without using a calculator, determine whether $\frac{333}{3333}$ or $\frac{3333}{33\ 333}$ is smaller.</p>

Without using a calculator, determine whether $\frac{333}{3333}$ or $\frac{3333}{33\ 333}$ is smaller.

Combined Operations of Numbers

<p>Evaluate $(1 + \frac{1}{2})(1 + \frac{1}{3})(1 + \frac{1}{4}) \dots (1 + \frac{1}{2024})$.</p>

Evaluate $(1 + \frac{1}{2})(1 + \frac{1}{3})(1 + \frac{1}{4}) \dots (1 + \frac{1}{2024})$.

<p>Given that $p$ and $q$ are such that $-\frac{13}{7} \leq p \leq 4$ and $\frac{11}{2} \leq q \leq 9\frac{1}{4}$, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $q - p$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p^2 + q^2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p^2 + q^2$.</span></div></li></ol>

Given that $p$ and $q$ are such that $-\frac{13}{7} \leq p \leq 4$ and $\frac{11}{2} \leq q \leq 9\frac{1}{4}$, find

the smallest possible value of $p^2 + q^2$,

the greatest possible value of $p^2 + q^2$.

Addition and Subtraction involving Negative Numbers

Multiplication and Division involving Negative Numbers

 Addition, Subtraction, Multiplication, and Division involving Negative Numbers

<p>Given that $p$ and $q$ are integers such that $-10 \leq p &lt; 2$ and $0 \leq q &lt; 7$, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $q - p$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p^2 + q^2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p^2 + q^2$.</span></div></li></ol>

Given that $p$ and $q$ are integers such that $-10 \leq p < 2$ and $0 \leq q < 7$, find

<p>Given that $p$ and $q$ are integers such that $-8 &lt; p \leq 5$ and $-3 \leq q &lt; 3$, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p - q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p - q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p^2 + q^2$.</span></div></li></ol>

Given that $p$ and $q$ are integers such that $-8 < p \leq 5$ and $-3 \leq q < 3$, find

the smallest possible value of $p^2 + q^2$.

<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 $G$.

Applications of Negative Numbers in Real Life

<p>The temperatures of a city during winter for a particular 5-day period were shown in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">Monday</th><th style="text-align: left; --cell-justify: flex-start">Tuesday</th><th style="text-align: left; --cell-justify: flex-start">Wednesday</th><th style="text-align: left; --cell-justify: flex-start">Thursday</th><th style="text-align: left; --cell-justify: flex-start">Friday</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">$-4.0$ °C</td><td style="text-align: left; --cell-justify: flex-start">$1.5$ °C</td><td style="text-align: left; --cell-justify: flex-start">$2.0$ °C</td><td style="text-align: left; --cell-justify: flex-start">$-2.5$ °C</td><td style="text-align: left; --cell-justify: flex-start">$-1.5$ °C</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">List the days when the temperature fell below $-2$ °C.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the average temperature during this period.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the difference in temperature between Monday and Wednesday.</span></div></li></ol>

The temperatures of a city during winter for a particular 5-day period were shown in the table below.

List the days when the temperature fell below $-2$ °C.

Find the average temperature during this period.

Find the difference in temperature between Monday and Wednesday.

 Applications of Negative Numbers in Real Life

<p>Express $0.4\dot{1}\dot{5}$ as a fraction.</p>

Express $0.4\dot{1}\dot{5}$ as a fraction.

<p>Express $0.\dot{6}\dot{3}$ as a fraction.</p>

Express $0.\dot{6}\dot{3}$ as a fraction.

<p>Without using a calculator, evaluate $\sqrt{\frac{49}{625}} \times (-2\frac{1}{3})^2 - \sqrt[3]{(-\frac{216}{125})} \div (1\frac{3}{4} - \frac{1}{6})$.</p>

Without using a calculator, evaluate $\sqrt{\frac{49}{625}} \times (-2\frac{1}{3})^2 - \sqrt[3]{(-\frac{216}{125})} \div (1\frac{3}{4} - \frac{1}{6})$.

<p>Without using a calculator, evaluate $\frac{5}{6} \div (-2\frac{1}{3}) - \sqrt[3]{(-\frac{8}{125})} \times [2 - (-1\frac{1}{4})]$.</p>

Without using a calculator, evaluate $\frac{5}{6} \div (-2\frac{1}{3}) - \sqrt[3]{(-\frac{8}{125})} \times [2 - (-1\frac{1}{4})]$.

<p>Without using a calculator, evaluate $\frac{1}{13} \times (-2\frac{3}{5}) - (-\frac{3}{2})^2 \times [-1 - (-\frac{1}{3})]$.</p>

Without using a calculator, evaluate $\frac{1}{13} \times (-2\frac{3}{5}) - (-\frac{3}{2})^2 \times [-1 - (-\frac{1}{3})]$.

<p>Without using a calculator, evaluate $-6\frac{4}{9} \times \left(-\frac{3}{5}\right) - \left(-1\frac{1}{3}\right)^2$.</p>

Without using a calculator, evaluate $-6\frac{4}{9} \times \left(-\frac{3}{5}\right) - \left(-1\frac{1}{3}\right)^2$.

<p>Without using a calculator, find the value of each of the following.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$3.6 \div 2.4$</div></li><li><div class="list-item-paragraph">$6.02 \div 0.05$</div></li><li><div class="list-item-paragraph">$1.75 \div 0.25$</div></li></ol>

Without using a calculator, find the value of each of the following.

<p>Without using a calculator, find the value of each of the following.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$3.65 \times 2.4$</div></li><li><div class="list-item-paragraph">$205.3 \times 0.83$</div></li><li><div class="list-item-paragraph">$0.011 \times 2.06$</div></li></ol>

<p>Without using a calculator, evaluate the following.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$-1\frac{5}{6} \div \frac{5}{18}$</div></li><li><div class="list-item-paragraph">$\frac{9}{8} \div \left(-2\frac{3}{14}\right)$</div></li><li><div class="list-item-paragraph">$-4\frac{4}{9} \div \left(-2\frac{3}{22}\right)$</div></li></ol>

Without using a calculator, evaluate the following.

$$\frac{9}{8} \div \left(-2\frac{3}{14}\right)$$

$$-4\frac{4}{9} \div \left(-2\frac{3}{22}\right)$$

Math Question Bank