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PSLE

<p>Given that $p = 25$, $q = -1$ and $r = 6$, evaluate each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$r + 2qr - \sqrt{p}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$q^2 - \sqrt{r - 3q}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{p - q}{3r - q} - \frac{r}{p + q}$</span></div></li></ol>

Given that $p = 25$, $q = -1$ and $r = 6$, evaluate each of the following expressions.

Evaluation of Algebraic Expressions

Algebraic Expressions, Identities and Formulae

<p>Given that $a = -3$, $b = 5$ and $c = -10$, evaluate each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$b^2 - 4ac$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$ab(c - a)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{1}{b+a} - \frac{1}{b-c}$</span></div></li></ol>

Given that $a = -3$, $b = 5$ and $c = -10$, evaluate each of the following expressions.

<p>Find the value of $m n^{2}+2(m-3n)$ when $m=2$ and $n=-3$.</p>

Find the value of $m n^{2}+2(m-3n)$ when $m=2$ and $n=-3$.

[EPQ Vol 1A] Question 18

<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>

Changing the Subject of a Formula

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

<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>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;$p=-4$, evaluate $9p^{2}-p$.</p>

Evaluating an Expression with a Single Variable

<p>Given that&nbsp;$a=3$ and $b=-4$, evaluate $\frac{b^{3}-2a}{5ab}$.</p>

Given that $a=3$ and $b=-4$, evaluate $\frac{b^{3}-2a}{5ab}$.

Evaluating an Algebraic Fraction Using Substitution

<p>Given that $a=2$, $b=-3$ and $c=-1$ evaluate $b^{2}-\frac{4(b+a)-c}{3c+b}$.</p>

Given that $a=2$, $b=-3$ and $c=-1$ evaluate $b^{2}-\frac{4(b+a)-c}{3c+b}$.

Evaluating an Algebraic Expression with Substitution

<p>Given that $x=-2$, $y=4$ and $z=5$, evaluate $\frac{y-x}{3}+x y^{2} z$.</p>

Given that $x=-2$, $y=4$ and $z=5$, evaluate $\frac{y-x}{3}+x y^{2} z$.

Evaluating an Expression Using Substitution

<p>Given that&nbsp;$x=-1$, $y=4$ and $z=3$, find the value of $\frac{xy}{z}-\frac{yz}{x}+\frac{xz}{y}$.</p>

Given that $x=-1$, $y=4$ and $z=3$, find the value of $\frac{xy}{z}-\frac{yz}{x}+\frac{xz}{y}$.

Evaluating an Expression Involving Fractions and Substitution

<p>Given that&nbsp;$e=3$ and $f=-2$, find the value of $\frac{3e f^{2}}{5e+f}$.</p>

Given that $e=3$ and $f=-2$, find the value of $\frac{3e f^{2}}{5e+f}$.

Evaluating an Algebraic Fraction with Substitution

<p>Find the value of $\frac{p^{3}+2q^{2}}{qr+p}$ when $p=2$, $q=-1$ and $r=-3$.</p>

Find the value of $\frac{p^{3}+2q^{2}}{qr+p}$ when $p=2$, $q=-1$ and $r=-3$.

Substituting Values into an Algebraic Fraction

<p>Evaluate $\frac{-2m+n}{m-n^{3}}$, given that $m=-2$ and $n=-1$.</p>

Evaluate $\frac{-2m+n}{m-n^{3}}$, given that $m=-2$ and $n=-1$.

<p>If $x=3$, $y=-1$ and $z=-4$, find the value of $x(y-1)+z^{2}x$.</p>

If $x=3$, $y=-1$ and $z=-4$, find the value of $x(y-1)+z^{2}x$.

Math Question Bank