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PSLE Foundation Mathematics

Given 2x-y=8 and xy=4, without solving for x and y, find 4x2+y2.

Given $2x-y=8$ and $xy=4$, without solving for $x$ and $y$, find $4x^2+y^2$.

Evaluating Expressions using Special Identities

2025 PHS PRELIMS P1 Q17

Quadratic Functions, Equations and Inequalities

Algebraic Expressions, Identities and Formulae

<ol class="abc-list"><li><div class="list-item-paragraph">The sum and product of $m$ and $n$ are $18$ and $77$ respectively. Find the value(s) of $m-n$.</div></li><li><div class="list-item-content"><span class="list-item-text">It is given that&nbsp;$x^2-6x+1=0$. Without using a calculator, find the value of $x^4+\frac{1}{x^4}$.</span></div></li></ol>

It is given that $x^2-6x+1=0$. Without using a calculator, find the value of $x^4+\frac{1}{x^4}$.

<p>In the diagram, $S_1$, $S_2$ represents the area of squares $ACDE$ and $CFGB$ with side length $a$ and $b$, respectively. Given that&nbsp;$A$, $B$, $C$ are on the same straight line, $a^2 + b^2 = 20$, $AB = a + b = 6$ cm, find the area of the shaded region.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1768901774503-zsck6asskvk.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njg5MDE3NzQ1MDMtenNjazZhc3NrdmsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg2Nzg2MCwiZXhwIjoxNzkyODY4MTYwfQ.Yn1TIsdeIaDx_MevJ73e6rskrgwARqbjW1Sn6p1lCJ0" style="max-width: min(170px, 100%); height: auto; display: block;" alt="Diagram showing two adjacent squares and shaded triangular regions." class="alignright custom-width" /></figure><div class="image-caption" style="text-align: right;">Diagram showing two adjacent squares and shaded triangular regions.</div></div>

In the diagram, $S_1$, $S_2$ represents the area of squares $ACDE$ and $CFGB$ with side length $a$ and $b$, respectively. Given that $A$, $B$, $C$ are on the same straight line, $a^2 + b^2 = 20$, $AB = a + b = 6$ cm, find the area of the shaded region.

Area of Triangle

IP1U4 SWII (Further App. of Alg. Id.) Q21

Trigonometry

<p>Given that $x+\frac{1}{x}=5$, find the values of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$x^2 + \frac{1}{x^2}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$x^4 + \frac{1}{x^4}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\left(x - \frac{1}{x}\right)^2$</span></div></li></ol>

Given that $x+\frac{1}{x}=5$, find the values of

IP1U4 SWII (Further App. of Alg. Id.) Q17

<p>Given that $a+b=1$, find the value of $2a^2 - 2b^2 + 4b$.</p>

Given that $a+b=1$, find the value of $2a^2 - 2b^2 + 4b$.

IP1U4 SWII (Further App. of Alg. Id.) Q16

<p>Given that $(2024-m)(2023-m)=2025$, find the value of $(2024-m)^2 + (2023-m)^2$.</p>

Given that $(2024-m)(2023-m)=2025$, find the value of $(2024-m)^2 + (2023-m)^2$.

IP1U4 SWII (Further App. of Alg. Id.) Q15

<p>Given that $a + b = 6$, $a - b = 4$, find the values of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$ab$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$a^2 + b^2$.</span></div></li></ol>

Given that $a + b = 6$, $a - b = 4$, find the values of

IP1U4 SWII (Further App. of Alg. Id.) Q14

<p>Given that $(a - b) = 5$, $ab = 3$, find the values of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$(a + b)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$3(a^2 + b^2)$.</span></div></li></ol>

Given that $(a - b) = 5$, $ab = 3$, find the values of

IP1U4 SWII (Further App. of Alg. Id.) Q13

<p>Given that $(a + b)^2 = 16$, $ab = 4$, find the values of</p>
<ol class="i-list"><li><div class="list-item-paragraph">$\frac{a^2 + b^2}{3}$</div></li><li><div class="list-item-content"><span class="list-item-text">$(a - b)^2$.</span></div></li></ol>

Given that $(a + b)^2 = 16$, $ab = 4$, find the values of

IP1U4 SWII (Further App. of Alg. Id.) Q12

<p>Given that $(a + b)^2 = 9$, $(a - b)^2 = 5$, find the values of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$a^2 + b^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$ab$.</span></div></li></ol>

Given that $(a + b)^2 = 9$, $(a - b)^2 = 5$, find the values of

IP1U4 SWII (Further App. of Alg. Id.) Q11

<p>Given that $a + b = 7$, $ab = 10$, find the values of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$a^2 + b^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(a - b)^2$.</span></div></li></ol>

Given that $a + b = 7$, $ab = 10$, find the values of

IP1U4 SWII (Further App. of Alg. Id.) Q10

<p>Given that $2a-b=5$, $ab=\frac{3}{2}$, find the value of $4a^2+b^2-1$.</p>

Given that $2a-b=5$, $ab=\frac{3}{2}$, find the value of $4a^2+b^2-1$.

IP1U4 SWII (Further App. of Alg. Id.) Q9

<p>Given that $x+y=2$, find the value of $\frac{1}{2}x^2+xy+\frac{1}{2}y^2$.</p>

Given that $x+y=2$, find the value of $\frac{1}{2}x^2+xy+\frac{1}{2}y^2$.

IP1U4 SWII (Further App. of Alg. Id.) Q8

<p>Given that $(m + n)^2 = 11$, $mn = 2$, find the value of $(m - n)^2$.</p>

Given that $(m + n)^2 = 11$, $mn = 2$, find the value of $(m - n)^2$.

IP1U4 SWII (Further App. of Alg. Id.) Q7

<ol class="i-list"><li><div class="list-item-paragraph">Simplify the following expression:</div><div class="list-item-paragraph" style="text-align: center"> $\frac{a^2 + b^2 + 2ab}{a^2 - b^2}$</div></li><li><div class="list-item-paragraph">Hence evaluate $\frac{55^2 + 45^2 + 2 \times 55 \times 45}{55^2 - 45^2}$</div></li></ol>

Hence evaluate \[\frac{55^2 + 45^2 + 2 \times 55 \times 45}{55^2 - 45^2}\]

Simplifying Algebraic Fractions involving Factorisation

IP1U4 SWII (Further App. of Alg. Id.) Q5

<p>Without using a calculator, find the value of $2024^2 - 4048 \times 2014 + 2014^2$.</p>

Without using a calculator, find the value of $2024^2 - 4048 \times 2014 + 2014^2$.

IP1U4 SWII (Further App. of Alg. Id.) Q4

<p>Without using a calculator, find the value of $(991)^2$.</p>

Without using a calculator, find the value of $(991)^2$.

IP1U4 SWII (Further App. of Alg. Id.) Q3

<p>Without using a calculator, find the value of $(1009)^2$.</p>

Without using a calculator, find the value of $(1009)^2$.

IP1U4 SWII (Further App. of Alg. Id.) Q2

<p>Given that&nbsp;${{x}^{2}}-5x-2025=0$, find the value of $\frac{{{\left( x-2 \right)}^{4}}+{{\left( x-1 \right)}^{2}}-1}{\left( x-1 \right)\left( x-2 \right)}$.</p>

Given that ${{x}^{2}}-5x-2025=0$, find the value of $\frac{{{\left( x-2 \right)}^{4}}+{{\left( x-1 \right)}^{2}}-1}{\left( x-1 \right)\left( x-2 \right)}$.

<p>Given that&nbsp;${{m}^{2}}+{{n}^{2}}=4mn$, where&nbsp;$m&gt;0$ and $n&gt;0$,  find the exact value of $\frac{{{m}^{2}}-{{n}^{2}}}{mn}$.</p>

Given that ${{m}^{2}}+{{n}^{2}}=4mn$, where $m>0$ and $n>0$,  find the exact value of $\frac{{{m}^{2}}-{{n}^{2}}}{mn}$.

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