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PSLE

PSLE Foundation Mathematics

<ol class="abc-list"><li data-list-item-id="cgs-p2-q1-q-0-content-items-0" data-list-item-path="cgs-p2-q1-q-0-content-items-0"><div class="list-item-paragraph">Show that the equation $3e^{2x} + 7e^x = 6$ has only one solution and find its value correct to 2 significant figures.<span class="inline-marks">[4]</span></div></li><li data-list-item-id="cgs-p2-q1-q-0-content-items-1" data-list-item-path="cgs-p2-q1-q-0-content-items-1"><div class="list-item-paragraph">Factorise $(3x + 1)^3 - 8$ completely.<span class="inline-marks">[2]</span></div></li></ol>

Show that the equation $3e^{2x} + 7e^x = 6$ has only one solution and find its value correct to 2 significant figures.

Solving Exponential Equations Using Substitution

Factorisation by Special Identities

2025 CGS PRELIMS P2 Q1

Polynomials, Cubic Equations and Partial Fractions

Exponential and Logarithmic Functions

<p>Factorise the following expression completely</p>
<p style="text-align: center">$64-49a^2-28ab-4b^2$</p>

Factorise the following expression completely

Quadratic Functions, Equations and Inequalities

Algebraic Expressions, Identities and Formulae

<p>Factorise the following expression completely</p>
<p style="text-align: center">$a^2-b^2+3b-3a$</p>

Factorisation by Grouping

<p>Factorise each of the following expressions completely.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$-10x^2 - 19x - 6$</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">$18 - 2(a + b)^2$</span><span class="inline-marks">[2]</span></div></li></ol>

Factorise each of the following expressions completely.

Factorisation of Quadratic Expressions

IP2 Class Test (May 2025) Q2

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$m^2 - 4n^2 - 4n - 1$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 - 2ab + b^2 - c^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$25 - x^2 - y^2 - 2xy$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$9m^2 - 6mn + n^2 - 81$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q20

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$4x^2 + 9y^2 - 12xy - 16$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$m^2 - 2mn + n^2 - r^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 + b^2 - 2ab - 1$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$9a^2 - b^2 + 4b - 4$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q19

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$a^4 - \frac{1}{b^4}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$75a^3b^2 - 108ab^4$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$25(x+y)^2 - 16(x-y)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$3a^5 - 48a^3$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q18

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$a^{12}b^4 - a^4b^{12}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$100(m-n)^2 - 121(x+y)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$2a - 50a^3$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{25}{a^2} - \frac{4a^2}{9}$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q17

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$16a^2 - 24a + 9$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$1 - 6a + 9a^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$x^2 y^2 - 6xyz + 9z^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 - 4ab + 4b^2$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q12

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$a^2 + a + \frac{1}{4}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 - 6a + 9$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 - 10a + 25$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$9a^2 - 12a + 4$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q11

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$m^2 + 6am + 9a^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$4a^2 + 20a + 25$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$36a^2 + 36a + 9$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$9a^2 + 24a + 16$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q10

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$a^2 + 8a + 16$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 + 14a + 49$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$1 + 2a + a^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$9 + 6c + c^2$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q9

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$(3m + 4n)^2 - (4m + 5n)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(a + b)^2 - (a - b)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$50x^2 - 72y^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$x^4 - (y + z)^4$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q8

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$a^4 - 1024$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$81m^2 - 49n^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 - (b - c)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$16a^2 - (3b + 2y)^2$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q7

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$m^4 - 256$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(a+b)^4 - c^4$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2b^2 - 16$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$81x^4y^4 - 256m^4n^4$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q6

<p>Factorise completely</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$144x^2 - 169y^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$1 - 0.09x^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$16m^2 - 121$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$-64x^2 + \left(\frac{9}{25}\right)y^2$</span></div></li></ol>

$-64x^2 + \left(\frac{9}{25}\right)y^2$

IP1U4 SWI (Algebraic Identities) Q5

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Factorise completely $6a^2 - 3ab + 8ba - 4b^2$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Factorise completely $10x^2 - 4xy - 5yx + 2y^2$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Factorise completely $64a^3 - 4a$,</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Factorise completely $25x^2 - 70xy + 49y^2$.</span><span class="inline-marks">[2]</span></div></li></ol>

Factorise completely $6a^2 - 3ab + 8ba - 4b^2$.

Factorise completely $10x^2 - 4xy - 5yx + 2y^2$.

Factorise completely $25x^2 - 70xy + 49y^2$.

IP1 Class Test (May 2025) Q10

<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Given that $64x^3 - 27y^3 = (4x - 3y)(16x^2 + axy + 9y^2)$, state the value of $a$.</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Express $\frac{7x^2 + x + 15}{x(x^2 + 3)}$ in partial fractions.</span><span class="inline-marks">[5]</span></div></li></ol>

Given that $64x^3 - 27y^3 = (4x - 3y)(16x^2 + axy + 9y^2)$, state the value of $a$.

Express $\frac{7x^2 + x + 15}{x(x^2 + 3)}$ in partial fractions.

Partial Fractions

2023 ACSBR AM S3 EOY Q8 

<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.

Polynomial Division and Remainders

Equations Reducible to Quadratics

Remainder and Factor Theorems

<p>It is given that&nbsp;$\sqrt[3]{x+5}-\sqrt[3]{x-5}=1$, find the value of ${{x}^{2}}$.</p>

It is given that $\sqrt[3]{x+5}-\sqrt[3]{x-5}=1$, find the value of ${{x}^{2}}$.

Math Question Bank