A Math

A Math (IGCSE)

E Math

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

<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.

Solving Simultaneous Linear Inequalities

Prime Numbers and Composite Numbers

Algebraic Fractions

Laws of Indices

2025 YCKSS PRELIMS P2 Q1

Algebraic Expressions, Identities and Formulae

Indices

Linear Equations and Inequalities

Primes, HCF and LCM

<p>Solve the simultaneous inequalities $-4\le 3x+2&lt;17$.</p>

Solve the simultaneous inequalities $-4\le 3x+2<17$.

Sec 3/4 E Math T02-Q01 - Solving simultaneous linear inequalities

Find the smallest possible integer value of $m$ that satisfies $\dfrac{3}{7}m+4>1$.

Find the greatest prime number that satisfies the inequality $18-4x>-61$.

Simple Inequalities

Sec 2 E Math Linear Inequalities Q07 - Extreme integer and prime solutions

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Solve the inequality $-2(3 + x) \le \frac{2x - 3}{2} &lt; \frac{17 - 7x}{6}$ and represent the solution on a number line.</span><span class="inline-marks">[5]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence, state the minimum value of $x^2$, which satisfy the above inequality.</span><span class="inline-marks">[1]</span></div></li></ol>

Solve the inequality $-2(3 + x) \le \frac{2x - 3}{2} < \frac{17 - 7x}{6}$ and represent the solution on a number line.

Hence, state the minimum value of $x^2$, which satisfy the above inequality.

IP2 Class Test (May 2025) Q9 (2025 RGS Y3 CBA1 Q2)

<p>Given that&nbsp;$x$ and $y$ are integers such that&nbsp;$-6 \le x &lt; 2$ and $-5 &lt; y \le -2$, find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the smallest value of $x^2 + y^2$,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $\frac{y}{x}$,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $x + xy$.</span><span class="inline-marks">[1]</span></div></li></ol>

Given that $x$ and $y$ are integers such that $-6 \le x < 2$ and $-5 < y \le -2$, find

IP2 Class Test (May 2025) Q7

<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">In a $3$-digit positive number, use algebra to show that if the sum of all $3$ digits is divisible by $9$, then the number is also divisible by $9$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Explain if this only applies to $3$-digit positive numbers.</span></div></li></ol>

In a $3$-digit positive number, use algebra to show that if the sum of all $3$ digits is divisible by $9$, then the number is also divisible by $9$.

Explain if this only applies to $3$-digit positive numbers.

Solving Linear Equations

<ol class="abc-list"><li><div class="list-item-paragraph">In a $4$-digit positive number, use algebra to show that if the sum of all $4$ digits is divisible by $3$, then the number is also divisible by $3$.</div></li><li><div class="list-item-paragraph">Explain if this only applies to $4$-digit positive numbers.</div></li></ol>

 Solving Linear Equations

<p>In a $2$-digit positive number, the digit in the ones place is half of the digit in the tens place. The sum of this number and the number when the digits are reversed is $99$. Find the number.</p>

In a $2$-digit positive number, the digit in the ones place is half of the digit in the tens place. The sum of this number and the number when the digits are reversed is $99$. Find the number.

<p>In a class of $35$ students, there are $17$ boys and $18$ girls. Some girls left the class. Find the number of girls who left the class such that the fraction of the remaining girls in the class becomes $\frac{14}{31}$.</p>

In a class of $35$ students, there are $17$ boys and $18$ girls. Some girls left the class. Find the number of girls who left the class such that the fraction of the remaining girls in the class becomes $\frac{14}{31}$.

Applications of Linear Equations in Real Life

<p>The diagram below shows a rectangular plot of land with a circular pond. It is known that the length is $3$ metres longer than twice of the width. The width of the land is $x$ m.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767600843964-s9ivokqew7i.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDA4NDM5NjQtczlpdm9rcWV3N2kucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4Nzc0NjQ1OSwiZXhwIjoxNzg3NzQ2NzU5fQ.6EvzFTAFuRLvcGX3laS1lMXmz0dEuHrP5vfjXn-YaV8" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down an expression, in terms of $x$, for the length of the land (in metres).</span></div></li><li><div class="list-item-paragraph">The perimeter of the land is $48$ meters and the radius of the pond is $3$ metres. Find the value of $x$.</div></li><li><div class="list-item-paragraph">Find the area of the land which is not covered by the pond, correct to $3$ significant figures.</div></li></ol>

The diagram below shows a rectangular plot of land with a circular pond. It is known that the length is $3$ metres longer than twice of the width. The width of the land is $x$ m.

Write down an expression, in terms of $x$, for the length of the land (in metres).

<p>A string which forms the rectangle $ABCD$ is used to form a square $PQRS$. The rectangle has length and width of $(2x + 7)$ cm and $(x + 5)$ cm respectively and the square has sides of length $(3x - 11)$ cm.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767600692494-ldvnf79p4d.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDA2OTI0OTQtbGR2bmY3OXA0ZC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzg3NzQ2NDU5LCJleHAiOjE3ODc3NDY3NTl9.vY82pwsXeWlxS8iWh_WkPVud54QdL68GRy0_KUTcTGg" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down an equation in $x$ and find the value of $x$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the area of the square $PQRS$.</span></div></li></ol>

A string which forms the rectangle $ABCD$ is used to form a square $PQRS$. The rectangle has length and width of $(2x + 7)$ cm and $(x + 5)$ cm respectively and the square has sides of length $(3x - 11)$ cm.

Write down an equation in $x$ and find the value of $x$.

 Applications of Linear Equations in Real Life

<p>A man drives from town $A$ to town $B$ at an average speed of $67$ km/h. Using the same route, he travels back from town $B$ to town $A$ at an average speed of $72$ km/h. If the total travelling time to complete the journey is $85$ minutes, find the distance travelled by the man from town $A$ to town $B$.</p>

A man drives from town $A$ to town $B$ at an average speed of $67$ km/h. Using the same route, he travels back from town $B$ to town $A$ at an average speed of $72$ km/h. If the total travelling time to complete the journey is $85$ minutes, find the distance travelled by the man from town $A$ to town $B$.

<p>The sum of two consecutive even numbers is $178$. Find the product of the two numbers.</p>

The sum of two consecutive even numbers is $178$. Find the product of the two numbers.

<p>The numerator of a fraction is $8$ less than its denominator. If $2$ is added to the numerator and $3$ is subtracted from the denominator, the new fraction is $\frac{5}{8}$. Find the fraction in its lowest terms.</p>

The numerator of a fraction is $8$ less than its denominator. If $2$ is added to the numerator and $3$ is subtracted from the denominator, the new fraction is $\frac{5}{8}$. Find the fraction in its lowest terms.

<p>The age of Alan’s father is $5$ years older than $3$ times that of Alan. Let $x$ be Alan’s age (in years).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Express the father’s age (in years) in terms of $x$.</span></div></li><li><div class="list-item-paragraph">After $35$ years, Alan will be as old as his father now. Write down an equation in $x$ and solve it to find Alan’s age.</div></li></ol>

The age of Alan’s father is $5$ years older than $3$ times that of Alan. Let $x$ be Alan’s age (in years).

Express the father’s age (in years) in terms of $x$.

<p>Alice has $3x$ marbles. Beatrice has $6$ more marbles than Alice. Candice has half as many marbles as Beatrice.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down an expression, in terms of $x$, for the number of marbles that Candice has.</span></div></li><li><div class="list-item-paragraph">The total number of marbles is $114$. Find the number of marbles that Beatrice has.</div></li></ol>

Alice has $3x$ marbles. Beatrice has $6$ more marbles than Alice. Candice has half as many marbles as Beatrice.

Write down an expression, in terms of $x$, for the number of marbles that Candice has.

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{a - 2}{3} - \frac{1 - a}{2} = \frac{1}{5}(5a - 4)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{3b + 3}{b - 1} = -\frac{7}{2}$</span></div></li></ol>

$\frac{a - 2}{3} - \frac{1 - a}{2} = \frac{1}{5}(5a - 4)$

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{6x - 2}{3} - \frac{x}{2} = -\frac{1}{3}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{2 - 3y}{1 - y} = \frac{2}{5}$</span></div></li></ol>

$\frac{6x - 2}{3} - \frac{x}{2} = -\frac{1}{3}$

<p>Given $x - y = 7x + 3y$, find the value of $\frac{5x}{4y}$.</p>

Given $x - y = 7x + 3y$, find the value of $\frac{5x}{4y}$.

<p>Given $3a - 5b = 6a - 2b$, find the value of $\frac{a}{2b}$.</p>

Given $3a - 5b = 6a - 2b$, find the value of $\frac{a}{2b}$.

Math Question Bank