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<ol class="abc-list"><li data-list-item-id="sec4-em-2025-yckss-p2-q1-b1-i1" data-list-item-path="sec4-em-2025-yckss-p2-q1-b1-i1"><div class="list-item-paragraph">Find all prime numbers satisfying $-5\leq2x-3\leq7$.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="sec4-em-2025-yckss-p2-q1-b1-i2" data-list-item-path="sec4-em-2025-yckss-p2-q1-b1-i2"><div class="list-item-paragraph">Simplify $\dfrac{18c^3d^3}{5f^3}\div\dfrac{3c^5d^2}{10f}$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="sec4-em-2025-yckss-p2-q1-b1-i3" data-list-item-path="sec4-em-2025-yckss-p2-q1-b1-i3"><div class="list-item-paragraph">Simplify $\left(\dfrac{16y^8}{81x^{12}}\right)^{-\frac34}$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="sec4-em-2025-yckss-p2-q1-b1-i4" data-list-item-path="sec4-em-2025-yckss-p2-q1-b1-i4"><div class="list-item-paragraph">Write $\dfrac{3x}{(2x-1)^2}-\dfrac2{2x-1}$ as a single fraction in its simplest form.<span class="inline-marks">[2]</span></div></li></ol>

Find all prime numbers satisfying $-5\leq2x-3\leq7$.

Simplify $\dfrac{18c^3d^3}{5f^3}\div\dfrac{3c^5d^2}{10f}$.

Simplify $\left(\dfrac{16y^8}{81x^{12}}\right)^{-\frac34}$.

Write $\dfrac{3x}{(2x-1)^2}-\dfrac2{2x-1}$ as a single fraction in its simplest form.

Multiplication and Division of Algebraic Fractions

Solving Simultaneous Linear Inequalities

Prime Numbers and Composite Numbers

Rational Indices

Addition and Subtraction of Algebraic Fractions

2025 YCKSS PRELIMS P2 Q1

Algebraic Expressions, Identities and Formulae

Indices

Linear Equations and Inequalities

Primes, HCF and LCM

<p>Solve the simultaneous inequalities $-4\le 3x+2&lt;17$.</p>

Solve the simultaneous inequalities $-4\le 3x+2<17$.

Sec 3/4 E Math T02-Q01 - Solving simultaneous linear inequalities

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Solve the inequality $-2(3 + x) \le \frac{2x - 3}{2} &lt; \frac{17 - 7x}{6}$ and represent the solution on a number line.</span><span class="inline-marks">[5]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence, state the minimum value of $x^2$, which satisfy the above inequality.</span><span class="inline-marks">[1]</span></div></li></ol>

Solve the inequality $-2(3 + x) \le \frac{2x - 3}{2} < \frac{17 - 7x}{6}$ and represent the solution on a number line.

Hence, state the minimum value of $x^2$, which satisfy the above inequality.

IP2 Class Test (May 2025) Q9 (2025 RGS Y3 CBA1 Q2)

<p>Given that the universal set is the set of positive even integers and that&nbsp;$A = \{x : 30 &lt; 3x &lt; 62\}$ and $B = \{x : x - 1 &lt; 17 &lt; x + 11\}$.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">List the elements of set&nbsp;$A$ and set&nbsp;$B$.</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Find $n(A' \cap B)$.</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Describe, as simply as possible, in words, the elements contained in the set&nbsp;$C$ where&nbsp;$C = \{8, 12, 16\}$.</div></li></ol>
<p>All sets in this question are subsets of the stated universal set&nbsp;$\xi$; every set-builder variable is restricted to that universe.</p>

Given that the universal set is the set of positive even integers and that $A = \{x : 30 < 3x < 62\}$ and $B = \{x : x - 1 < 17 < x + 11\}$.

List the elements of set $A$ and set $B$.

Describe, as simply as possible, in words, the elements contained in the set $C$ where $C = \{8, 12, 16\}$.

All sets in this question are subsets of the stated universal set $\xi$; every set-builder variable is restricted to that universe.

Introduction to Set Notations

Combined Operations on Sets

Analysis of Universal Sets and Subset Properties

Sets

<p>$\xi = \{x : x \text{ is an integer and}\hspace{0.5em} 1 &lt; x &lt; 18\}$</p>
<p>$A = \{x : x \text{ is a multiple of}\hspace{0.5em} 3\}$</p>
<p>$B = \{x : 9 \le 3x - 4 &lt; 32\}$</p>
<p style="margin-top: 1.5rem">Find the number of elements in the set&nbsp;$A \cup B'$.</p>
<p>All sets in this question are subsets of the stated universal set&nbsp;$\xi$; every set-builder variable is restricted to that universe.</p>

$\xi = \{x : x \text{ is an integer and } 1 < x < 18\}$

$A = \{x : x \text{ is a multiple of } 3\}$

Find the number of elements in the set $A \cup B'$.

Union and Complement of Sets Defined by Multiples and Inequalities

<p>List all the elements of the set&nbsp;$C = \{x : x \text{ is an integer such that\ } 4x - 7 &lt; x \le 2x + 3\}$.</p>

List all the elements of the set $C = \{x : x \text{ is an integer such that } 4x - 7 < x \le 2x + 3\}$.

Logical Operators and Element Identification in Finite Sets

<p>By solving the pair of inequalities $3(a-5)<2a-3$ and $2-a\le 5a$, find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the least possible value of $a$,</div></li><li><div class="list-item-paragraph">the greatest possible integer value of $a$,</div></li><li><div class="list-item-paragraph">the greatest possible perfect square value of $a$.</div></li></ol>

By solving the pair of inequalities $3(a-5)<2a-3$ and $2-a\le 5a$, find

Solving Simultaneous Inequalities and Identifying Special Values

<ol class="i-list"><li data-list-item-id="item-1765534907481-u2haqglba" data-list-item-path="item-1765534907481-u2haqglba"><div class="list-item-paragraph">Solve the inequality $x-1&lt;\frac{2x+1}{3}\le x+\frac{4}{3}$.</div></li><li data-list-item-id="item-1765534908313-z9r3xcx9z" data-list-item-path="item-1765534908313-z9r3xcx9z"><div class="list-item-paragraph">Write down the number of integers that satisfy the inequality in <strong>(i).</strong></div></li></ol>

Finding the Number of Integer Values Satisfying a Compound Inequality

<ol class="i-list"><li><div class="list-item-paragraph">Solve the inequality $4x-7<\frac{3x-1}{4}\le 5$.</div></li><li><div class="list-item-paragraph">State the largest prime number which satisfies the above inequality $4x-7<\frac{3x-1}{4}\le 5$.</div></li></ol>

Double Inequality with Rational Expressions and Prime Constraints

<p>Solve the inequality $\frac{x+2}{4}\le \frac{2x-1}{3}<3\frac{1}{2}$ and hence, find the largest prime number value of $x$ which satisfies the inequality.</p>

Solve the inequality $\frac{x+2}{4}\le \frac{2x-1}{3}<3\frac{1}{2}$ and hence, find the largest prime number value of $x$ which satisfies the inequality.

Three-Part Inequality with Rational Expressions and Prime Constraints

<p>Solve the inequality $\frac{a}{2}-3<\frac{2a-5}{3}\le 10-a$ and show your solution on a number line.</p>

Solve the inequality $\frac{a}{2}-3<\frac{2a-5}{3}\le 10-a$ and show your solution on a number line.

Three-Part Linear Inequality with Number Line Sketch

<p>Solve the inequality $\frac{2-x}{3}\le 3+x<4$ and represent your solution on a number line.</p>

Solve the inequality $\frac{2-x}{3}\le 3+x<4$ and represent your solution on a number line.

Linear Fractional Inequality with Graphical Representation

<p>Find the range of values of $x$ that satisfies $3x+1>2$ and $2x-10<5-x$.</p>

Find the range of values of $x$ that satisfies $3x+1>2$ and $2x-10<5-x$.

Finding the Range of Values Satisfying Multiple Inequalities

<ol class="i-list"><li><div class="list-item-paragraph">Solve the inequality $-2\le 2x+4<17$.</div></li><li><div class="list-item-paragraph">Show your solution on a number line.</div></li><li><div class="list-item-paragraph">Find the smallest prime number that satisfy the inequality $-2\le 2x+4<17$.</div></li></ol>

Solving a Compound Linear Inequality and Identifying Prime Solutions

<p>It is given that $\frac{3x-1}{4}\le \frac{7x+4}{3} < x+2\frac{2}{3}$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Solve the inequality.</div></li><li><div class="list-item-paragraph">Hence, list the integer values of $x$ that satisfy the inequality.</div></li></ol>

It is given that $\frac{3x-1}{4}\le \frac{7x+4}{3} < x+2\frac{2}{3}$.

Solving a Three-Part Compound Inequality Involving Algebraic Fractions

<ol class="i-list"><li><div class="list-item-paragraph">Solve the inequalities $-10\le 7-2x<1$.</div></li><li><div class="list-item-paragraph">Write down all the prime numbers that satisfy $-10\le 7-2x<1$.</div></li></ol>

Solving and Interpreting a Compound Inequality with Prime Number Constraints

<ol class="abc-list"><li><div class="list-item-paragraph">Find the range of values of $x$ for which</div><ol class="i-list"><li><div class="list-item-paragraph">$x-1>1-x$.</div></li><li><div class="list-item-paragraph">$6\le 10-x\le 10$</div></li></ol></li><li><div class="list-item-paragraph">Represent the solution to both inequalities in <strong>(a)(i)</strong> and <strong>(a)(ii)</strong> on a number line.</div></li><li><div class="list-item-paragraph">Hence, state the least integer that satisfies both inequalities in <strong>(a)(i)</strong> and <strong>(a)(ii)</strong>.</div></li></ol>

Solving and Interpreting a System of Inequalities with Number Line Representation

<ol class="i-list"><li><div class="list-item-paragraph">Solve the inequalities $-x\le 4x+5<\frac{6x+23}{3}$.</div></li><li><div class="list-item-paragraph">Hence, write down all the integer values of $x$ which satisfies $-x\le 4x+5<\frac{6x+23}{3}$.</div></li></ol>

Linear Compound Inequalities

<p>If $3k-1\le 21\le 5k-3$, write down</p>
<ol class="i-list"><li><div class="list-item-paragraph">the largest rational value of $k$,</div></li><li><div class="list-item-paragraph">the smallest integer value of $k$,</div></li><li><div class="list-item-paragraph">the largest value of $k$ if it is a prime number.</div></li></ol>

Linear Inequalities with Rational, Integer, and Prime Constraints

<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

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