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PSLE Foundation Mathematics

<ol class="i-list"><li><div class="list-item-paragraph">Simplify and express $\frac{2x}{2x^2 - x - 3} - \frac{3}{x + 1}$ as a single fraction in the simplest form.</div><div class="list-item-paragraph">Hence solve the equation $\frac{2x}{2x^2 - x - 3} - \frac{3}{x + 1} = 0$.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Simplify and express $\frac{1}{3 + 5x - 2x^2} - \frac{x + 3}{x - 3}$ as a single fraction in the simplest form.</div><div class="list-item-paragraph">Hence solve the equation $\frac{1}{3 + 5x - 2x^2} - \frac{x + 3}{x - 3} = 0$.<span class="inline-marks">[5]</span></div></li></ol>

Simplify and express $\frac{2x}{2x^2 - x - 3} - \frac{3}{x + 1}$ as a single fraction in the simplest form.

Simplify and express $\frac{1}{3 + 5x - 2x^2} - \frac{x + 3}{x - 3}$ as a single fraction in the simplest form.

Addition and Subtraction of Algebraic Fractions

Solving Equations involving Algebraic Fractions

Rational Equations Reducible to Quadratics

IP2 Class Test (May 2025) Q4

Algebraic Expressions, Identities and Formulae

Quadratic Functions, Equations and Inequalities

<p>Solve the equation \[\frac{{{x}^{2}}+x-2}{{{x}^{2}}-6x+5}+\frac{2+x}{4}=0.\]</p>

Solve the equation \[\frac{{{x}^{2}}+x-2}{{{x}^{2}}-6x+5}+\frac{2+x}{4}=0.\]

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

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

IP3U2 HOT PN1 Q5

<p>Solve $\frac{1}{x-6}-\frac{1}{x-4}=\frac{1}{x-3}-\frac{1}{x-5}$, leaving your answers in exact form.</p>

Solve $\frac{1}{x-6}-\frac{1}{x-4}=\frac{1}{x-3}-\frac{1}{x-5}$, leaving your answers in exact form.

IP3U2 HOT PN1 Q1

<p>Solve the following equations, giving your answers correct to 3 significant figures where necessary.</p>
<ol class="i-list"><li><div class="list-item-paragraph">$\frac{1}{{{x}^{2}}-4}+\frac{1}{2-x}=3$</div></li><li><div class="list-item-paragraph">$\frac{7x-2}{{{x}^{2}}-3x+2}-\frac{1}{x-1}=\frac{2}{3}$</div></li></ol>

Solve the following equations, giving your answers correct to 3 significant figures where necessary.

Rational Equations Requiring Quadratic Solutions

<ol class="i-list"><li><div class="list-item-paragraph">Express as a single fraction in its simplest form</div><div class="list-item-paragraph" style="text-align: center">$\frac{3}{x-2}-\frac{2}{x+1}$</div></li><li><div class="list-item-paragraph">Solve the equation $\frac{3}{x-2}-\frac{2}{x+1}=1$.</div></li></ol>

Expressing and Solving Rational Expressions

<p>Solve the following equations, giving your answers correct to $3$ significant figures where necessary.</p>
<ol class="i-list"><li><div class="list-item-paragraph">$\frac{5}{x-1}-\frac{4}{x+3}=7$</div></li><li><div class="list-item-paragraph">$\frac{2}{2x+1}+\frac{1}{2x-1}=\frac{2}{5}$</div></li><li><div class="list-item-paragraph">$\frac{2}{x+2}-\frac{x}{x+3}=1$</div></li><li><div class="list-item-paragraph">$\frac{3}{x-5}-5=\frac{2x}{3-x}$</div></li><li><div class="list-item-paragraph">$5x-3+\frac{7}{x-2}=19$</div></li></ol>

Solve the following equations, giving your answers correct to $3$ significant figures where necessary.

Solve Each Algebraic Fraction Equation

<p>Solve the following equations, giving your answers correct to $3$ significant figures where necessary.</p>
<ol class="i-list"><li><div class="list-item-paragraph">$3x-10=\frac{7}{x}$</div></li><li><div class="list-item-paragraph">$2x-\frac{3}{x}=-5$</div></li><li><div class="list-item-paragraph">$\frac{x+1}{4}=\frac{6}{x-1}$ </div></li><li><div class="list-item-paragraph">$\frac{8}{x+9}-2=x$</div></li><li><div class="list-item-paragraph">$\frac{x+4}{x}-\frac{7}{x-5}=0$</div></li></ol>

Solving Rational Equations and Rearranging Algebraic Fractions

<p>Solve the equation $\frac{1}{x-2}+\frac{2}{x-3}=5$.</p>

Solve the equation $\frac{1}{x-2}+\frac{2}{x-3}=5$.

Solving Equations Involving Algebraic Fractions

<p>Solve the equation $\frac{6}{x+4}=x+3$.</p>

Solving Equations Involving Fractions

<ol class="abc-list"><li><div class="list-item-paragraph">Factorise $6{{x}^{2}}+19x-36$.</div></li><li><div class="list-item-paragraph">Hence, solve $\frac{3x-1}{3x-4}-\frac{13}{6{{x}^{2}}+19x-36}=2$.</div></li></ol>

Factorisation of Quadratic Expressions

Algebra: Factorising and Using the Result to Solve an Equation

<ol class="abc-list"><li><div class="list-item-paragraph">Express $\frac{x+4}{x}-\frac{7}{x-5}$ as a fraction in its simplest form.</div></li><li><div class="list-item-paragraph">Hence solve the equation $\frac{x+4}{x}-\frac{7}{x-5}=0$.</div></li></ol>

Algebra: Fraction Manipulation and Equation Solving

<p>Solve the equation $\frac{3}{9{{x}^{2}}-6x+1}-\frac{1}{1-3x}=2$.</p>

Solve the equation $\frac{3}{9{{x}^{2}}-6x+1}-\frac{1}{1-3x}=2$.

Algebra: Solving Fractional Equations

<p>Solve the equation $\frac{x+2}{x+1}-\frac{18-7x}{(2x-3)(x+1)}=0$.</p>

Solve the equation $\frac{x+2}{x+1}-\frac{18-7x}{(2x-3)(x+1)}=0$.

Solving Rational Equations with Algebraic Fractions

<p>Solve the following equations, giving your answers to $3$ significant figures where necessary.</p>
<ol class="i-list"><li><div class="list-item-paragraph">${{\left( 3-x \right)}^{2}}=8$</div></li><li><div class="list-item-paragraph">$25{{x}^{2}}-5=31$</div></li><li><div class="list-item-paragraph">$4x-11=\frac{3}{x}$</div></li><li><div class="list-item-paragraph">$\frac{6}{x}+\frac{8}{x+2}=5$</div></li></ol>

Solve the following equations, giving your answers to $3$ significant figures where necessary.

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