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PSLE

<p>Given that&nbsp;$x$ and $y$ are integers such that&nbsp;$-6 \le x &lt; 2$ and $-5 &lt; y \le -2$, find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the smallest value of $x^2 + y^2$,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $\frac{y}{x}$,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $x + xy$.</span><span class="inline-marks">[1]</span></div></li></ol>

Given that $x$ and $y$ are integers such that $-6 \le x < 2$ and $-5 < y \le -2$, find

Extreme Values under Integer Constraints

IP2 Class Test (May 2025) Q7

Linear Equations and Inequalities

<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

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

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

 Addition, Subtraction, Multiplication, and Division involving Negative Numbers

<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 $p^2 + q^2$.

Real Numbers

<p>Given that $x$ and $y$ are integers and $2\le x\le 5$ and $-8\le y\le -3$, find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the least possible value of ${{x}^{2}}+y$,</div></li><li><div class="list-item-paragraph">the largest possible value of $x-y$,</div></li><li><div class="list-item-paragraph">the largest possible value of $\frac{x}{y}$.</div></li></ol>

Given that $x$ and $y$ are integers and $2\le x\le 5$ and $-8\le y\le -3$, find

Finding Extremes of Algebraic Expressions Within Integer Constraints

<p>Find the value of $x$ if $x$ is an integer, such that $\frac{13}{262}<\frac{1}{x}<\frac{7}{134}$.</p>

Find the value of $x$ if $x$ is an integer, such that $\frac{13}{262}<\frac{1}{x}<\frac{7}{134}$.

[EPQ Vol 1A] Question 10

<p>Given that&nbsp;$p$ and $q$ are integers such that&nbsp;$-3\le p&lt;9$ and $-11\le q&lt;4$, find</p>
<ol class="abc-list"><li data-list-item-id="item-1765257811024-py0ag9ipf" data-list-item-path="item-1765257811024-py0ag9ipf"><div class="list-item-paragraph">the greatest possible value of $\frac{p}{q}$,</div></li><li data-list-item-id="item-1765257815637-cow0m09hq" data-list-item-path="item-1765257815637-cow0m09hq"><div class="list-item-paragraph">the greatest possible value of $\frac{q}{p}$,</div></li><li data-list-item-id="item-1765257821735-hhgam1j9i" data-list-item-path="item-1765257821735-hhgam1j9i"><div class="list-item-paragraph">the smallest possible value of $\frac{p}{q}$,</div></li><li data-list-item-id="item-1765257829069-o0usw6lft" data-list-item-path="item-1765257829069-o0usw6lft"><div class="list-item-paragraph">the smallest possible value of $\frac{q}{p}$.</div></li></ol>

<p>Exclude zero denominators when forming each ratio.</p>

Given that $p$ and $q$ are integers such that $-3\le p<9$ and $-11\le q<4$, find

Exclude zero denominators when forming each ratio.

[EPQ Vol 1A] Question 9

<p>Given that $a$ and $b$ are integers, $-4\le a\le \mathrm{4}$ and $2\le b < 8$, state the</p>
<ol class="abc-list"><li><div class="list-item-paragraph">smallest possible value of ${{a}^{2}}-{{b}^{2}}$.</div></li><li><div class="list-item-paragraph">largest possible value of $b-a$.</div></li></ol>

Given that $a$ and $b$ are integers, $-4\le a\le \mathrm{4}$ and $2\le b < 8$, state the

Integer Constraints and Maximum–Minimum Values

<p>Given that $\frac{2-x}{4}\le 3+x<11$ and $0 < y < 5$, where $x$ and $y$ are integers, find the</p>
<ol class="i-list"><li><div class="list-item-paragraph">range of values of $x$.</div></li><li><div class="list-item-paragraph">greatest possible value of ${{\left( x+y \right)}^{2}}$.</div></li><li><div class="list-item-paragraph">least possible value of $(x+y)(x-y)$.</div></li></ol>

Given that $\frac{2-x}{4}\le 3+x<11$ and $0 < y < 5$, where $x$ and $y$ are integers, find the

Solving Simultaneous Linear Inequalities

Inequalities Involving Integers

<p>Given that $x$ and $y$ are integers such that $-4\le x\le 3$ and $1\le y\le 5$, find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the largest possible value of $y-x$,</div></li><li><div class="list-item-paragraph">the smallest possible value of $\frac{x}{y}$,</div></li><li><div class="list-item-paragraph">the least possible value of ${{x}^{2}}-{{y}^{2}}$.</div></li></ol>

Given that $x$ and $y$ are integers such that $-4\le x\le 3$ and $1\le y\le 5$, find

Math Question Bank