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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.

Solving Simultaneous Linear Inequalities

Prime Numbers and Composite Numbers

Algebraic Fractions

Laws of Indices

2025 YCKSS PRELIMS P2 Q1

Algebraic Expressions, Identities and Formulae

Indices

Linear Equations and Inequalities

Primes, HCF and LCM

- Use prime factors to explain why 18 x 63 is not a perfect square. - The number 18p is a perfect cube. Find the smallest positive integer value of p.

Use prime factors to explain why $18\times63$ is not a perfect square.

The number $18p$ is a perfect cube. Find the smallest positive integer value of $p$.

Prime Factorisation and Its Applications

2025 SST PRELIMS P1 Q2

Sec 3/4 E Math T03-Q03 - Solving an exponential equation

<p>If&nbsp;$\frac{m^x}{n^y} \times \frac{n^{4-3x}}{(m^{y+1})^2} = \frac{n^7}{m^{10}}$, find the value(s) of $x$ and $y$.</p>

If $\frac{m^x}{n^y} \times \frac{n^{4-3x}}{(m^{y+1})^2} = \frac{n^7}{m^{10}}$, find the value(s) of $x$ and $y$.

Equality of Indices

Index Notation

Exponential and Logarithmic Functions

<ol class="i-list"><li><div class="list-item-paragraph">Given that&nbsp;$x={{16}^{18}}$ and $y={{18}^{16}}$, without using a calculator, determine whether $x&gt;y$,  showing your working clearly.</div></li><li><div class="list-item-paragraph">Arrange ${{3}^{312}}$, ${{6}^{234}}$ and ${{13}^{156}}$ in descending order.</div></li><li><div class="list-item-paragraph">Given that&nbsp;${{\left( {{x}^{2}}-x-1 \right)}^{x+2000}}=1$, find all the integer solutions.</div></li></ol>

IP2U9 HOT Q4

<p>Simplify the expression $\sqrt{\sqrt{3}-\sqrt{3-\sqrt{3}}} \times \sqrt{\sqrt{3}+\sqrt{3-\sqrt{3}}}$.</p>

Simplify the expression $\sqrt{\sqrt{3}-\sqrt{3-\sqrt{3}}} \times \sqrt{\sqrt{3}+\sqrt{3-\sqrt{3}}}$.

IP2U9 HOT Q3

<p>Given that&nbsp;$63^x = 35^y = 2205$, find the value of $\frac{x + 4xy + y}{2xy - x - y}$.</p>

Given that $63^x = 35^y = 2205$, find the value of $\frac{x + 4xy + y}{2xy - x - y}$.

IP2U9 HOT Q2

<p>Given that&nbsp;$5^x = 9^y = 2025$, find the value of $\frac{xy}{x + y}$.</p>

Given that $5^x = 9^y = 2025$, find the value of $\frac{xy}{x + y}$.

IP2U9 HOT Q1

<p>Given that&nbsp;$\frac{8\times {{2}^{x}}}{\sqrt{{{2}^{x}}}}=32$ , find the value of $x$.</p>

Given that $\frac{8\times {{2}^{x}}}{\sqrt{{{2}^{x}}}}=32$ , find the value of $x$.

Laws of Indices – Exponential Equation

<p>Given that&nbsp;${{2}^{x}}\times 7=56$, find the value of $x$.</p>

Given that ${{2}^{x}}\times 7=56$, find the value of $x$.

Use Factorisation to Solve for Powers

<p>Given that ${{3}^{27}}\div \frac{1}{9}={{3}^{k}}$, find $k$.</p>

Given that ${{3}^{27}}\div \frac{1}{9}={{3}^{k}}$, find $k$.

Laws of Indices: Division and Negative Powers

<p>Solve</p>
<ol class="i-list"><li><div class="list-item-paragraph">${{3}^{2x+1}}=1$</div></li><li><div class="list-item-paragraph">$\sqrt[3]{{{8}^{x}}}=0.125$</div></li></ol>

Solving Exponential Equations Involving Powers and Roots

<p>Simplify each of the following.</p>
<ol class="i-list"><li><div class="list-item-paragraph">${{\left( \frac{{{p}^{3}}}{q} \right)}^{4}}\times {{\left( \frac{3{{q}^{4}}}{{{p}^{3}}} \right)}^{2}}$</div></li><li><div class="list-item-paragraph">$\frac{{{(2{{x}^{5}}{{y}^{4}})}^{2}}}{2{{x}^{8}}{{y}^{2}}}$</div></li><li><div class="list-item-paragraph">${{(-2{{q}^{4}}{{p}^{3}})}^{3}}\div {{(4{{q}^{5}}{{p}^{3}})}^{2}}$ </div></li><li><div class="list-item-paragraph">$2{{a}^{\frac{1}{4}}}{{b}^{\frac{1}{3}}}\div {{(5a)}^{-2}}\times {{b}^{-\frac{2}{3}}}$</div></li></ol>

Simplifying Expressions Using Advanced Index Laws

<p>Given that&nbsp;${{a}^{5}}\times {{a}^{2}}\div \sqrt[3]{a}={{a}^{k}}$, find the value of $k$.</p>

Given that ${{a}^{5}}\times {{a}^{2}}\div \sqrt[3]{a}={{a}^{k}}$, find the value of $k$.

Laws of Indices: Solve for the Unknown Exponent

<p>Evaluate without the use of a calculator.		</p>
<ol class="i-list"><li><div class="list-item-paragraph">${{2}^{\frac{3}{2}}}\times \sqrt{8}\div 8$</div></li><li><div class="list-item-paragraph">${{\left( 11\frac{1}{9} \right)}^{-\frac{1}{2}}}$</div></li></ol>

Evaluate without the use of a calculator.		

Laws of Indices: Rational and Mixed Index Applications

<p>Expressing $\sqrt[3]{49}$ as a power of $7$.</p>

Expressing $\sqrt[3]{49}$ as a power of $7$.

Expressing Roots as Powers of a Given Base

<p>Simplify $2\div {{\left( \frac{2}{x} \right)}^{-3}}$.</p>

Simplify $2\div {{\left( \frac{2}{x} \right)}^{-3}}$.

Simplifying with Negative Indices and Fractions

Simplifying Expressions with Negative Indices

<p>Given that&nbsp;$\frac{x\times {{x}^{3}}}{{{x}^{p}}}=\sqrt{x}$ , find the value of $p$.</p>

Given that $\frac{x\times {{x}^{3}}}{{{x}^{p}}}=\sqrt{x}$ , find the value of $p$.

Rational Indices

Laws of Indices: Solve for the Unknown Power

<p>Given that&nbsp;${{2}^{27}}\div 32={{64}^{x}}$, find the value of $x$.</p>

Given that ${{2}^{27}}\div 32={{64}^{x}}$, find the value of $x$.

Math Question Bank