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PSLE

PSLE Foundation Mathematics

<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.

Multiplication and Division of Algebraic Fractions

Solving Simultaneous Linear Inequalities

Prime Numbers and Composite Numbers

Rational Indices

Addition and Subtraction of Algebraic Fractions

2025 YCKSS PRELIMS P2 Q1

Algebraic Expressions, Identities and Formulae

Indices

Linear Equations and Inequalities

Primes, HCF and LCM

Write 12-x- 3x+2x2-7x+10 as a single fraction in its simplest form.

Write $\dfrac1{2-x}-\dfrac{3x+2}{x^2-7x+10}$ as a single fraction in its simplest form.

2025 SJI PRELIMS P1 Q10

<p>The sum of $\frac{3}{5x+4}$, $\frac{7}{4-5x}$ and $\frac{px+q}{16-25x^2}$, where&nbsp;$p$ and $q$ are constants, is $\frac{Ax+B}{25x^2-16}$.</p>
<p>Find an expression, in terms of $p$ and / or $q$, for&nbsp;$A$ and $B$.</p>

The sum of $\frac{3}{5x+4}$, $\frac{7}{4-5x}$ and $\frac{px+q}{16-25x^2}$, where $p$ and $q$ are constants, is $\frac{Ax+B}{25x^2-16}$.

Find an expression, in terms of $p$ and / or $q$, for $A$ and $B$.

Comparing Coefficients in Polynomial Identities

<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.

Solving Equations involving Algebraic Fractions

Rational Equations Reducible to Quadratics

IP2 Class Test (May 2025) Q4

Quadratic Functions, Equations and Inequalities

<p>Express each of the following as a fraction in its simplest form.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$4m - n + \frac{5}{2}(4n - 3m) - \frac{m - 4n}{5}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{f - 3h}{5} - 6 \left[ h - 3 \left( \frac{4f - h}{7} \right) \right]$</span></div></li></ol>

Express each of the following as a fraction in its simplest form.

$4m - n + \frac{5}{2}(4n - 3m) - \frac{m - 4n}{5}$

$\frac{f - 3h}{5} - 6 \left[ h - 3 \left( \frac{4f - h}{7} \right) \right]$

<p>Express each of the following as a fraction in its simplest form.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$4(x - 5y) - \left[ \frac{2(x - y)}{9} + \frac{y - 7x}{6} \right]$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{5}{2}(a - 3b) - \frac{b - 4a}{5} + \frac{5}{8}(b - a)$</span></div></li></ol>

$4(x - 5y) - \left[ \frac{2(x - y)}{9} + \frac{y - 7x}{6} \right]$

$\frac{5}{2}(a - 3b) - \frac{b - 4a}{5} + \frac{5}{8}(b - a)$

 Addition and Subtraction of Algebraic Fractions

<p>Express each of the following as a single fraction.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{v - u}{2} - \frac{3v - 4u}{3} + \frac{v - u}{4}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{m + n}{3} - \frac{m - n}{5} - \frac{n - 2m}{6}$</span></div></li></ol>

Express each of the following as a single fraction.

$\frac{v - u}{2} - \frac{3v - 4u}{3} + \frac{v - u}{4}$

$\frac{m + n}{3} - \frac{m - n}{5} - \frac{n - 2m}{6}$

<p>Express each of the following as a single fraction.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{x + 2}{4} + \frac{2(4 - x)}{3}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{2(3 - y)}{4} - \frac{6}{5}(10 - y)$</span></div></li></ol>

$\frac{2(3 - y)}{4} - \frac{6}{5}(10 - y)$

<p>Express each of the following as a single fraction.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{2(4 - 3p)}{3} + \frac{3(p - 1)}{5}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{4 - t}{5} - \frac{1 - t}{3}$</span></div></li></ol>

$\frac{2(4 - 3p)}{3} + \frac{3(p - 1)}{5}$

<p>Express each of the following as a fraction in its simplest form.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{u - v}{2} - \frac{3v - 5u}{3} + \frac{u + v}{9}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{2a - b}{8} - \frac{4b - a}{6} - \frac{3(2a - 5b)}{12}$</span></div></li></ol>

$\frac{u - v}{2} - \frac{3v - 5u}{3} + \frac{u + v}{9}$

$\frac{2a - b}{8} - \frac{4b - a}{6} - \frac{3(2a - 5b)}{12}$

<p>Express each of the following as a fraction in its simplest form.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{3p - 2}{5} - \frac{2 - 3p}{2}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{3(q - 1)}{5} - \frac{5}{2}(3 - 2q)$</span></div></li></ol>

$\frac{3(q - 1)}{5} - \frac{5}{2}(3 - 2q)$

<p>Express each of the following as a fraction in its simplest form.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{3x - 1}{2} - \frac{x + 1}{4}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{5}{6}(1 - 2x) - \frac{4x + 2}{3}$</span></div></li></ol>

<p>Simplify the expression $\frac{2d\left( c+2 \right)}{\left( 3d-c \right)\left( c+1 \right)}-\frac{1}{c+1}\left( \frac{2d}{3d-c} \right)-\frac{3c\left( 3d+c \right)}{9{{d}^{2}}-{{c}^{2}}}$.</p>

Simplify the expression $\frac{2d\left( c+2 \right)}{\left( 3d-c \right)\left( c+1 \right)}-\frac{1}{c+1}\left( \frac{2d}{3d-c} \right)-\frac{3c\left( 3d+c \right)}{9{{d}^{2}}-{{c}^{2}}}$.

<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">$\frac{8}{x-2}-\frac{5}{4-2x}$</div></li><li><div class="list-item-paragraph">Solve the equation $\frac{8}{x-2}-\frac{5}{4-2x}=\frac{7}{4}$.</div></li></ol>

Simplifying and Solving Algebraic Fractions

<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>Express $\frac{4(x+3)}{5}-2+\frac{x-2}{3}$ as a fraction in its simplest form.</p>

Express $\frac{4(x+3)}{5}-2+\frac{x-2}{3}$ as a fraction in its simplest form.

[EPQ Vol 1A] Question 21

<ol class="abc-list"><li><div class="list-item-paragraph">Express $\frac{2y-3}{2{{y}^{2}}+7y-15}-\frac{3}{y+5}$ as a single fraction in its simplest form.</div></li><li><div class="list-item-paragraph">Find $y$ if&nbsp;$\frac{2y-3}{2{{y}^{2}}+7y-15}-\frac{3}{y+5}=2$.</div></li></ol>

Subtracting Rational Expressions and Finding the Solution

<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

<ol class="abc-list"><li><div class="list-item-paragraph">Express $\frac{4}{x-3}-\frac{x-27}{9-{{x}^{2}}}$ as a single fraction in its simplest form.</div></li><li><div class="list-item-paragraph">Hence, solve the equation $\frac{4}{x-3}-\frac{x-27}{9-{{x}^{2}}}=2$.</div></li></ol>

Algebra: Simplifying Rational Expressions and Solving Equations

<p>Express $\frac{x-2}{2{{x}^{2}}-x-6}+\frac{x}{2x+3}$ as a single fraction in its simplest form.</p>

Express $\frac{x-2}{2{{x}^{2}}-x-6}+\frac{x}{2x+3}$ as a single fraction in its simplest form.

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