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<p>At a game show, Ming was given&nbsp;$20$ multiple-choice questions. He gets $5$ points if he answers a question correctly, gets a point if he does not answer a question and gets $2$ points deducted if he answers a question wrongly. If Ming answered at least a question wrongly and scored $52$ points at the game show, find the number of questions he answered wrongly.<span class="inline-marks">[4]</span></p>

At a game show, Ming was given $20$ multiple-choice questions. He gets $5$ points if he answers a question correctly, gets a point if he does not answer a question and gets $2$ points deducted if he answers a question wrongly. If Ming answered at least a question wrongly and scored $52$ points at the game show, find the number of questions he answered wrongly.

Linear Inequality

Systems of Linear Equations in up to Three Variables

Integer and Feasibility Constraints in Linear Models

Application of Simultaneous Equations in Real World Contexts

2026 HCI P1 Q1

System of Linear Equations

Inequalities

<p>Find the greatest prime number $q$ such that it satisfies the inequality 		</p>
<p style="text-align: center">$-4\left( \frac{1}{4}+q \right)>q-30$ .</p>

Find the greatest prime number $q$ such that it satisfies the inequality 		

Solving Complex Linear Inequalities with Prime Constraints

Linear Equations and Inequalities

<p>Find the largest perfect square of $p$ such that it satisfies the inequality 	</p>
<p style="text-align: center">$\frac{2(p-3)}{3}\le \frac{2p-5}{4}$ .</p>

Find the largest perfect square of $p$ such that it satisfies the inequality 	

Solving Linear Inequalities with a Perfect Square Condition

<ol class="i-list"><li><div class="list-item-paragraph">Find the <strong>largest integer</strong> $a$ for which $a+\frac{1}{4}(3a-8)\le 16$.</div></li><li><div class="list-item-paragraph">Represent the solution in <strong>(i)</strong> on a number line.</div></li></ol>

Solving Linear Inequalities Involving Fractions and Representing Integer Solutions on a Number Line

<p>Given that $15-3x\ge 2x-1$, find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the greatest value of $x$,</div></li><li><div class="list-item-paragraph">the greatest integer value of $x$.</div></li></ol>

Solving a Linear Inequality and Finding the Greatest (Integer) Solution

<ol class="i-list"><li><div class="list-item-paragraph">Solve $2-2x>9$.</div></li><li><div class="list-item-paragraph">Hence write down the greatest integer value of $x$ which satisfies $2-2x>9$.</div></li></ol>

Solving a Simple Linear Inequality and Finding the Greatest Integer Solution

<p>Solve the following inequalities, representing each solution on a number line.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$-2a+4>3$</div></li><li><div class="list-item-paragraph">$3\left( 1-b \right)\ge b$</div></li><li><div class="list-item-paragraph">$2\left( 3-c \right)\le 5\left( c+2 \right)$</div></li><li><div class="list-item-paragraph">$\frac{5}{3}d-13<3$</div></li><li><div class="list-item-paragraph">$\frac{1}{2}e+9\le \frac{1}{4}\left( 6e-7 \right)$</div></li><li><div class="list-item-paragraph">$\frac{f-2}{3}-\frac{f+5}{4}>1$</div></li></ol>

Solve the following inequalities, representing each solution on a number line.

Solving a Range of Linear Inequalities and Representing Solutions on a Number Line

<p>Solve the inequality $\frac{x-1}{2}-\frac{x+3}{4}&lt;\frac{1}{3}$.</p>
<p>List all possible values of $x$, given that&nbsp;$x$ is a positive integer.</p>

Solve the inequality $\frac{x-1}{2}-\frac{x+3}{4}<\frac{1}{3}$.

List all possible values of $x$, given that $x$ is a positive integer.

Solving a Linear Inequality with Positive Integer Solutions

<p>Find the greatest rational value of $x$ which satisfies the inequality</p>
<p style="text-align: center">$\frac{1}{5}\left( 2x+1 \right)\le \frac{1}{4}\left( x+7 \right)$.</p>

Find the greatest rational value of $x$ which satisfies the inequality

$\frac{1}{5}\left( 2x+1 \right)\le \frac{1}{4}\left( x+7 \right)$.

Linear Inequality with Rational Coefficients

<p>Find the smallest prime number $x$ which satisfies the inequality</p>
<p style="text-align: center">$\frac{7-x}{2}<\frac{x}{3}$.</p>

Find the smallest prime number $x$ which satisfies the inequality

Linear Inequality with a Prime Constraint

<p>Solve the following inequalities, illustrating the solution on a number line.</p>
<ol class="i-list"><li><div class="list-item-paragraph">$5x+3>7-x$</div></li><li><div class="list-item-paragraph">$\frac{2x-3}{5}>7+3x$</div></li><li><div class="list-item-paragraph">$\frac{1}{3}\left( \frac{1}{2}-x \right)\le \frac{1}{2}\left( 4x-1 \right)$</div></li></ol>

Solve the following inequalities, illustrating the solution on a number line.

Solving Linear Inequalities and Representing Solutions on a Number Line

<ol class="abc-list"><li><div class="list-item-paragraph">Solve the inequality $2x-4x\le 5$.</div></li><li><div class="list-item-paragraph">Draw a number line to represent the solution.</div></li><li><div class="list-item-paragraph">Hence write down the smallest integer value of $x$ such that&nbsp;$x$ satisfies $2x-4x\le 5$.</div></li></ol>

Solving and Representing Linear Inequalities

<ol class="abc-list"><li data-list-item-id="item-1763722687719-lbjp07zjo" data-list-item-path="item-1763722687719-lbjp07zjo"><div class="list-item-paragraph">Solve the inequality $4x-10\le x+6$.</div></li><li data-list-item-id="item-1763722688328-235e1w06m" data-list-item-path="item-1763722688328-235e1w06m"><div class="list-item-paragraph">Illustrate, on the number line given in the answer space below, the solution of the<br>inequality.<br></div><div class="graph-block" data-graph-config="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" data-width="381" data-height="54" style="width:381px;height:54px;max-width:100%;display:block;margin:0 auto;"></div></li><li data-list-item-id="item-1770628571172-bvprwrmxp" data-list-item-path="item-1770628571172-bvprwrmxp"><div class="list-item-paragraph">Hence, state the smallest prime number and the largest rational number in the solution. </div></li></ol>

<ol class="abc-list"><li><div class="list-item-paragraph">Solve the inequality $26&lt;-3x$.</div></li><li><div class="list-item-paragraph">Express the solution in <strong>(a)</strong> on the number line 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/pasted/1763722426575-ldnk9gkhac.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3MjI0MjY1NzUtbGRuazlna2hhYy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkxNzQ3MjEzLCJleHAiOjE3OTE3NDc1MTN9.Bw_KH0k2m3faEyqUVSLhpsIqxhWkF3VDxu5vkeh3lE8" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">Find the largest integer value of $x$ which satisfies $26&lt;-3x$.</div></li></ol>

<p>Solve the inequality $\frac{1}{2}x+\frac{1}{3}x&gt;-10$.</p>

Solve the inequality $\frac{1}{2}x+\frac{1}{3}x>-10$.

Solving a Linear Inequality with Fractions

<p>Solve the inequality $3x+2x\le -4$.</p>

Solving a Linear Inequality

<p>Given the inequality $9x\le 38$, find the greatest integer value of $x$. </p>

Given the inequality $9x\le 38$, find the greatest integer value of $x$. 

Inequality Problem Involving Integers

<p>Given the inequality $9x\le 38$, find the greatest prime number $x$. </p>

Given the inequality $9x\le 38$, find the greatest prime number $x$. 

Inequality Problem Involving Prime Numbers

<p>Find the greatest integer $y$ that satisfies the inequality $5y&lt;-10$.</p>

Find the greatest integer $y$ that satisfies the inequality $5y<-10$.

<p>Solve</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="abc-list"><li><div class="list-item-paragraph">$6x&lt;-18$</div></li></ol><ol class="abc-list" start="3"><li><div class="list-item-paragraph">$3x-3\ge 4$</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list" start="2"><li><div class="list-item-paragraph">$-4x&gt;34$</div></li></ol><ol class="abc-list" start="4"><li><div class="list-item-paragraph">$1-7x&gt;6$</div></li></ol></div></div></div>

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