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PSLE

PSLE Foundation Mathematics

<p>Solve the equation ${{x}^{3}}+\frac{1}{{{x}^{3}}}-{{x}^{2}}-\frac{1}{{{x}^{2}}}+5x+\frac{5}{x}=10$, showing your working clearly.</p>

Solve the equation ${{x}^{3}}+\frac{1}{{{x}^{3}}}-{{x}^{2}}-\frac{1}{{{x}^{2}}}+5x+\frac{5}{x}=10$, showing your working clearly.

Cubic Expressions and Equations

Equations Reducible to Quadratics

Polynomials, Cubic Equations and Partial Fractions

Quadratic Functions, Equations and Inequalities

<ol class="abc-list"><li><div class="list-item-paragraph">Find $\mathrm{Q}\left( x \right)$ if&nbsp;${{x}^{4}}-6{{x}^{3}}+6{{x}^{2}}+7x+3=\left( {{x}^{2}}-5x+3 \right)\mathrm{Q}\left( x \right)+9$.</div></li><li><div class="list-item-paragraph">Solve ${{x}^{4}}-6{{x}^{3}}+6{{x}^{2}}+7x-6=0$. Hence sketch the curve $y={{x}^{4}}-6{{x}^{3}}+6{{x}^{2}}+7x-6$ and state the range of values of 	$x$ such that</div><ol class="i-list"><li><div class="list-item-paragraph">$y&gt;0$,</div></li><li><div class="list-item-paragraph">$\frac{1}{y}&lt;0$.</div></li></ol></li></ol>

Polynomial Inequalities and Sign Charts

Polynomial Division and Remainders

Polynomial Functions and Key Features

<p>It is given that&nbsp;$\mathrm{f}\left( x \right)={{x}^{4}}+a{{x}^{3}}+b{{x}^{2}}-2x+1$ and $\mathrm{g}\left( x \right)=3{{x}^{4}}-48$, where&nbsp;$a$ and $b$ are integers.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">If&nbsp;$\mathrm{f}\left( x \right)$ has a remainder of $2x-3$ when it is divided by ${{x}^{2}}-4$, find the value of $a$ and of $b$.</div></li><li><div class="list-item-paragraph">Factorise $\mathrm{g}\left( x \right)$ completely. Hence state the real values of $x$ if&nbsp;$\mathrm{g}\left( x \right)=0$.</div></li><li><div class="list-item-paragraph">Given further that&nbsp;$2\mathrm{f}\left( x \right)-3\mathrm{g}\left( x \right)=\mathrm{Q}\left( x \right)\left( x+2 \right)+\mathrm{R}\left( x \right)$, where&nbsp;$\mathrm{Q}\left( x \right)$ and $\mathrm{R}\left( x \right)$ are the quotient and remainder 	respectively, find $\mathrm{R}\left( x \right)$.</div></li></ol>

It is given that $\mathrm{f}\left( x \right)={{x}^{4}}+a{{x}^{3}}+b{{x}^{2}}-2x+1$ and $\mathrm{g}\left( x \right)=3{{x}^{4}}-48$, where $a$ and $b$ are integers.

Factorisation by Special Identities

Remainder and Factor Theorems

<p>Find the exact value of $1+\frac{1}{2+\frac{1}{2+\frac{1}{2+\cdots }}}$.<br></p>

Find the exact value of $1+\frac{1}{2+\frac{1}{2+\frac{1}{2+\cdots }}}$.


IP3U2 HOT PN1 Q6

<p>Solve $3{{\left( x-\frac{1}{x} \right)}^{2}}-13x+\frac{13}{x}-10=0$, leaving your answers in exact form.</p>

Solve $3{{\left( x-\frac{1}{x} \right)}^{2}}-13x+\frac{13}{x}-10=0$, leaving your answers in exact form.

IP3U2 HOT PN1 Q2

<p>Solve each of the following equations, leaving your answers in exact form.</p>
<ol class="abc-list"><li data-list-item-id="item-1766036039369-ytr3tt1ym" data-list-item-path="item-1766036039369-ytr3tt1ym"><div class="list-item-paragraph">${{\left( 4x-5 \right)}^{2}}={{\left( 3-5{{x}^{2}} \right)}^{2}}$</div></li><li data-list-item-id="item-1766036040160-2xjy1gp9f" data-list-item-path="item-1766036040160-2xjy1gp9f"><div class="list-item-paragraph">${{\left( {{y}^{2}}-y \right)}^{2}}-{{y}^{2}}+y=0$</div></li></ol>

Solve each of the following equations, leaving your answers in exact form.

IP3U2 HOT WE1

<p>Solve the equation $x\left( x+2 \right)\left( x+4 \right)\left( x+6 \right)=9$, leaving your answer in exact form.</p>

Solve the equation $x\left( x+2 \right)\left( x+4 \right)\left( x+6 \right)=9$, leaving your answer in exact form.

IP2U4 HOT Q7

<p>Solve the equation ${{x}^{2}}{{\left( x+1 \right)}^{2}}+{{x}^{2}}-8{{\left( x+1 \right)}^{2}}=0$, leaving your answer in exact form.</p>

Solve the equation ${{x}^{2}}{{\left( x+1 \right)}^{2}}+{{x}^{2}}-8{{\left( x+1 \right)}^{2}}=0$, leaving your answer in exact form.

IP2U4 HOT Q6

<p>Solve the equation $\frac{x-{{x}^{3}}}{{{\left( 1+{{x}^{2}} \right)}^{2}}}=\frac{1}{4}$, leaving your answer in exact form.</p>

Solve the equation $\frac{x-{{x}^{3}}}{{{\left( 1+{{x}^{2}} \right)}^{2}}}=\frac{1}{4}$, leaving your answer in exact form.

IP2U4 HOT Q5

<p>Solve the equation ${{x}^{4}}-2{{x}^{2}}-400x=9999$, showing your working clearly.</p>

Solve the equation ${{x}^{4}}-2{{x}^{2}}-400x=9999$, showing your working clearly.

IP2U4 HOT Q4

<p>Solve the equation ${{\left( x+2 \right)}^{4}}+{{\left( x+1 \right)}^{4}}=17$, showing your working clearly.</p>

Solve the equation ${{\left( x+2 \right)}^{4}}+{{\left( x+1 \right)}^{4}}=17$, showing your working clearly.

Math Question Bank