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<p>Given that&nbsp;$p=-4$, evaluate $9p^{2}-p$.</p>

Evaluation of Algebraic Expressions

Evaluating an Expression with a Single Variable

Algebraic Expressions, Identities and Formulae

<p>Given that&nbsp;$a=3$ and $b=-4$, evaluate $\frac{b^{3}-2a}{5ab}$.</p>

Given that $a=3$ and $b=-4$, evaluate $\frac{b^{3}-2a}{5ab}$.

Evaluating an Algebraic Fraction Using Substitution

<p>Simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$5x-5(x-2)$</div></li><li><div class="list-item-paragraph">$3x-3(x+3)$</div></li><li><div class="list-item-paragraph">$2r-3(2-r)+4$</div></li></ol>

Simplify each of the following expressions.

Expansion of Linear Algebraic Expressions

Simplifying Expressions Involving Brackets

<p>Factorise each of the following expressions completely. </p>
<ol class="abc-list"><li><div class="list-item-paragraph">$36a-9$</div></li><li><div class="list-item-paragraph">$7ab-21ac$</div></li><li><div class="list-item-paragraph">$3mx-15x+6$</div></li></ol>

Factorise each of the following expressions completely. 

Factorization of Algebraic Expressions

<p>Simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$2k-3\left( 2-k \right)+4$</div></li><li><div class="list-item-paragraph">$3r-4s-3\left( r-2s \right)$</div></li><li><div class="list-item-paragraph">$2\left( x+1 \right)-3\left( 5-3x \right)$</div></li></ol>

Simplifying Algebraic Expressions with Brackets

<p>Expand each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\frac{1}{3}k-\frac{1}{4}m+\frac{2}{5}k-\frac{1}{2}m$</div></li><li><div class="list-item-paragraph">$\frac{4}{5}(15x-1)-\frac{2}{7}-(-7x+1)$</div></li></ol>

Expand each of the following expressions.

Expansion and Simplification involving Fractional Coefficients

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Subtract $9x^3 - 2x^2 + 5x - 3$ from $6x^3 - x^2 + 10$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Subtract $y^2 - y + 3$ from the sum of $5y^2 + 10y - 2$ and $1- 5y - y^2$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Subtract the product of $2$ and $v^2 - 2v + 3$ from the product of $-4$ and $2 - v^2$.</span></div></li></ol>

Expand and simplify each of the following expressions.

Subtract $9x^3 - 2x^2 + 5x - 3$ from $6x^3 - x^2 + 10$.

Subtract $y^2 - y + 3$ from the sum of $5y^2 + 10y - 2$ and $1- 5y - y^2$.

Subtract the product of $2$ and $v^2 - 2v + 3$ from the product of $-4$ and $2 - v^2$.

 Expansion of Linear Algebraic Expressions

<p>Simplify ${\frac{3p - 2q}{3} - \frac{4p - 5q}{4}}$.</p>

Simplify ${\frac{3p - 2q}{3} - \frac{4p - 5q}{4}}$.

Basic Algebra and Algebraic Manipulation - General

1EM Unit 4 SW I Q7

<p>Given that $x=15$ and $y=-6$, evaluate</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$8x-y$</div></li><li><div class="list-item-paragraph">$\frac{6x}{7y}$</div></li><li><div class="list-item-paragraph">$x^{2}-5y^{2}+\frac{1}{x}$</div></li></ol>

Evaluating Algebraic Expressions Using Given Values

<p>Simplify ${7x^2 - 4x - 5 - (5x^2 - 4x + 2)}$.</p>

Simplify ${7x^2 - 4x - 5 - (5x^2 - 4x + 2)}$.

1EM Unit 4 SW I Q3

<p>In a farmhouse, there are chickens and pigs.</p>
<p>Each chicken has ${2}$ legs and each pig has ${4}$ legs.</p>
<p>There are a total of ${88}$ heads and ${214}$ legs.</p>
<p>Let ${x}$ be the number of chickens in the farmhouse.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Express, in terms of ${x}$, the number of pigs in the farmhouse.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Express, in terms of ${x}$, the number of legs for the pigs in the farmhouse.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Show that the total sum of legs of chickens and pigs in the farmhouse can be written as ${352 - 2x = 214}$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Find the number of pigs in the farmhouse.</div><p style="text-align: right;">[1]</p></li></ol>

In a farmhouse, there are chickens and pigs.

Each chicken has ${2}$ legs and each pig has ${4}$ legs.

There are a total of ${88}$ heads and ${214}$ legs.

Let ${x}$ be the number of chickens in the farmhouse.

2023 ACSBR EM S1 EOY P2 Q5

<p>Ascend Hotel has a total of $27$ rooms.</p>
<p>Each room can be used as a single room or a double room.</p>
<p>The price for a single room is $\$159$ per night.</p>
<p>The price for a double room is $\$219$ per night.</p>
<p>On a particular night, all the rooms are occupied, and ${x}$ rooms are used as single rooms.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that the total price of all the rooms on the particular night is $\$\left(5913-60x\right)$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Given that the total price of all the rooms is $\$5013$, form an equation and find the value of ${x}$.</div><p style="text-align: right;">[2]</p></li></ol>

Each room can be used as a single room or a double room.

The price for a single room is $\$159$ per night.

The price for a double room is $\$219$ per night.

On a particular night, all the rooms are occupied, and ${x}$ rooms are used as single rooms.

2023 AISS EM S1 EOY P1 Q5

<p>Solve ${\frac{3}{7}x - 5 = \frac{1}{3}(x - 2)}$.</p><p style="text-align: right;">[3]</p>

Solve ${\frac{3}{7}x - 5 = \frac{1}{3}(x - 2)}$.

2023 ACSBR EM S1 EOY P1 Q5

<p>Simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$7y-11y$</div></li><li><div class="list-item-paragraph">$3y+(-6y)-4$</div></li><li><div class="list-item-paragraph">$10x-y-8x+8y$</div></li><li><div class="list-item-paragraph">$-3x-12y-(-3x)+(-7y)$</div></li></ol>

Additions and Subtractions of Linear Algebraic Expressions

Simplifying Algebraic Expressions

<p>Simplify ${\frac{1}{2}(6a) - [5a - (8b + a)]}$.</p>

Simplify ${\frac{1}{2}(6a) - [5a - (8b + a)]}$.

1EM Unit 4 SW I Q5

2023 ACSBR EM S1 EOY P1 Q2

Simplifying Expressions by Combining Like Terms

<p>Expand each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$-2\left( -5a+11 \right)$</div></li><li><div class="list-item-paragraph">$2\left( -3x+8y \right)$</div></li><li><div class="list-item-paragraph">$-3p\left( 4q-2r \right)$</div></li></ol>

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