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PSLE

PSLE Foundation Mathematics

<ol class="i-list"><li><div class="list-item-paragraph">Make $a$ the subject of the formula $\frac{1}{3b} = \frac{2}{3a} + \frac{1}{5c}$<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Make $x$ the subject of the formula $\sqrt{\frac{2}{y}} = \sqrt{\frac{5x + 3}{x - 5}}$<span class="inline-marks">[2]</span></div></li></ol>

Make $a$ the subject of the formula \[\frac{1}{3b} = \frac{2}{3a} + \frac{1}{5c}\]

Make $x$ the subject of the formula \[\sqrt{\frac{2}{y}} = \sqrt{\frac{5x + 3}{x - 5}}\]

Changing the Subject of a Formula

IP2 Class Test (May 2025) Q5

Algebraic Expressions, Identities and Formulae

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">It is given that $x = \sqrt{\frac{m+n}{m-n}}$. Express $n$ in terms of $x$ and $m$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">It is given that $d = v_{0}t + \frac{1}{2}at^2$. Express $v_{0}$ in terms of $d$, $a$ and $t$.</span><span class="inline-marks">[2]</span></div></li></ol>

It is given that $x = \sqrt{\frac{m+n}{m-n}}$. Express $n$ in terms of $x$ and $m$.

It is given that $d = v_{0}t + \frac{1}{2}at^2$. Express $v_{0}$ in terms of $d$, $a$ and $t$.

IP1 Class Test (May 2025) Q12

<ol class="abc-list"><li><div class="list-item-paragraph">Make $x$ the subject of the formula ${{\left( ax-1 \right)}^{2}}-a={{b}^{3}}$.</div></li><li><div class="list-item-paragraph">Make $k$ the subject of the formula $h=\frac{2\sqrt{k}}{3-\sqrt{k}}$.</div></li></ol>

<ol class="abc-list"><li><div class="list-item-paragraph">Make $a$ the subject of the formula $\frac{x}{y}=\sqrt{1-\frac{1}{{{a}^{2}}}}$.</div></li><li><div class="list-item-paragraph">Make $x$ the subject of the formula $\frac{c}{{{\left( x-3 \right)}^{2}}-a}={{b}^{3}}$.</div></li></ol>

<ol class="abc-list"><li><div class="list-item-paragraph">Make $t$ the subject of the formula $s=a+\sqrt{\frac{ab}{t}+{{a}^{2}}}$.</div></li><li><div class="list-item-paragraph">Hence, or otherwise, calculate $t$ when $a=-\frac{3}{4}$, $b=-20$ and $s=-8$.</div></li></ol>

Evaluation of Algebraic Expressions

Rearranging a Radical Formula to Make $𝑡$ the Subject

<ol class="abc-list"><li><div class="list-item-paragraph">Make $x$ the subject of the given formula $\sqrt{\frac{2}{y}}=\sqrt{\frac{5x+3}{x-5}}$.</div></li><li><div class="list-item-paragraph">Find $x$, when $y=0.02$.</div></li></ol>

Rearranging a Radical Equation to Make $𝑥$ the Subject

<ol class="abc-list"><li><div class="list-item-paragraph">Given that $m=\sqrt{\frac{nq}{p}-{{n}^{2}}}$, make $p$ the subject of the formula.</div></li><li><div class="list-item-paragraph">Given that $n=-4$, $m=3$ and $q=1$, find the value of $p$.</div></li></ol>

Rearranging a Radical Formula to Make $𝑝$ the Subject

<ol class="abc-list"><li><div class="list-item-paragraph">Make $T$ the subject of the formula $x=\sqrt[3]{\frac{4T}{2m-1}}$.</div></li><li><div class="list-item-paragraph">Hence, find the value of $T$ when $m=2$ and $x=1$.</div></li></ol>

Rearranging a Cube-Root Formula to Make $𝑇$ the Subject

<p>Make $y$ the subject of the formula $\sqrt{\frac{z-y}{y}}=\frac{1}{x}$.</p>

Make $y$ the subject of the formula $\sqrt{\frac{z-y}{y}}=\frac{1}{x}$.

Rearranging a Radical Formula to Make  $𝑦$ the Subject

<ol class="abc-list"><li><div class="list-item-paragraph">Make $x$ the subject of $y=\frac{2{{x}^{2}}+6x}{2{{x}^{2}}-18}$.</div></li><li><div class="list-item-paragraph">Hence, find the value of $x$ when $y=5$.</div></li></ol>

Subject Change in a Quadratic Rational Formula

<p>Given that $A=\frac{n\left( p-q \right)}{5}$,</p>
<ol class="abc-list"><li><div class="list-item-paragraph">find the value of $A$ when $n=20$, $p=6$ and $q=-7$,</div></li><li><div class="list-item-paragraph">express $p$ in terms of $A$, $n$ and $q$.</div></li></ol>

Given that $A=\frac{n\left( p-q \right)}{5}$,

Working with a Linear Formula: Evaluation and Rearrangement

<ol class="abc-list"><li><div class="list-item-paragraph">Make $b$ the subject of the formula, $a={{\left( b-c \right)}^{2}}+d$.</div></li><li><div class="list-item-paragraph">Find the value(s) of $b$ when $a=18$, $c=1$ and $d=2$.</div></li></ol>

Algebraic Rearrangement with Subsequent Numerical Solution

<p>Make $a$ the subject of the formula $\frac{1}{3b}=\frac{2}{3a}+\frac{1}{5c}$.</p>

Make $a$ the subject of the formula $\frac{1}{3b}=\frac{2}{3a}+\frac{1}{5c}$.

Rearranging a Fractional Formula to Make  $𝑎$ the Subject

<p>Given that&nbsp;$k=2\sqrt{3a-{{k}^{2}}}$, express $k$ in terms of $a$.</p>

Given that $k=2\sqrt{3a-{{k}^{2}}}$, express $k$ in terms of $a$.

Expressing  $𝑘$ in Terms of  $𝑎$ from a Square-Root Formula

<p>Make $s$ the subject of the formula $\frac{1}{r}+\frac{1}{s}=\frac{1}{t}$.</p>

Make $s$ the subject of the formula $\frac{1}{r}+\frac{1}{s}=\frac{1}{t}$.

Rearranging a Reciprocal Formula to Make  $𝑠$ the Subject

<p>Make $m$ the subject of the formula $k=\sqrt{\frac{3m}{2-gm}}$.</p>

Make $m$ the subject of the formula $k=\sqrt{\frac{3m}{2-gm}}$.

Rearranging a Radical Formula to Make  $𝑚$ the Subject

<p>Given that $b=\frac{2a-3}{4+a}$, express $a$ in terms of $b$.</p>

Given that $b=\frac{2a-3}{4+a}$, express $a$ in terms of $b$.

Rewriting a Rational Formula to Find  $𝑎$

<p>Make $y$ the subject of $ax+by=c$.</p>

Making  𝑦 y the Subject of a Linear Relationship

<p>It is given that&nbsp;$V=\frac{1}{3}\pi {{r}^{2}}h$.</p>
<ol class="abc-list"><li data-list-item-id="item-1764906672361-b7fgtnpay" data-list-item-path="item-1764906672361-b7fgtnpay"><div class="list-item-paragraph">Find the value of $V$ when&nbsp;$\pi =\frac{22}{7}$, $r=9$ and $h=21$.</div></li><li data-list-item-id="item-1764906672893-920rywd8m" data-list-item-path="item-1764906672893-920rywd8m"><div class="list-item-paragraph">Express $r$ in terms of $V$, $\pi $ and $h$.</div></li></ol>

It is given that $V=\frac{1}{3}\pi {{r}^{2}}h$.

Using the Formula for the Volume of a Cone

<p>Given that&nbsp;$\frac{1}{u}=\frac{1}{f}+\frac{1}{2v}$, express $v$ in terms of $u$ and $f$.</p>

Given that $\frac{1}{u}=\frac{1}{f}+\frac{1}{2v}$, express $v$ in terms of $u$ and $f$.

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