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PSLE

PSLE Foundation Mathematics

Mark the following numbers on the number line: -(1)/(2), 3, -5, (4)/(7), 5. 9, -7(2)/(3), 6

Mark the following numbers on the number line:

$-\frac{1}{2}$, $3$, $-5$, $\frac{4}{7}$, $ 5.\dot{9}$, $-7\frac{2}{3}$, $6$

Plotting Mixed Numbers and Decimals on a Number Line

Real Numbers

-(6)/(11), sqrt(5), -3, 1(1)/(3), -3pi, sqrt(27), 0.2 4 1 From the given numbers, list the numbers that are - rational numbers, - irrational numbers, - integers.

$-\frac{6}{11}$, $\sqrt{5}$, $-3$, $1\frac{1}{3}$, $-3\pi $, $\sqrt{27}$, $0.2\dot{4}\dot{1}$

From the given numbers, list the numbers that are

Classifying Numbers as Rational, Irrational, and Integers

**Rational Numbers** A rational number can be expressed as p/q, where p,q are integers and q 0. The denominator must not be zero. **Irrational Numbers** An irrational number is a real number that cannot be expressed as p/q for integers p,q with q 0. Are the following numbers rational or irrational? 2(3)/(4), -1.72, 0.01, sqrt(2), pi, 0. 2, sqrt(49), -4

A rational number can be expressed as $p/q$, where $p,q$ are integers and $q\ne0$.

An irrational number is a real number that cannot be expressed as $p/q$ for integers $p,q$ with $q\ne0$.

Are the following numbers rational or irrational?

$2\frac{3}{4}$, $-1.72$, $0.01$, $\sqrt{2}$, $\pi $, $0.\dot{2}$, $\sqrt{49}$, $-4$

Classifying Rational and Irrational Numbers

Without using a calculator and showing your working clearly, evaluate ((3)/(4)-(5)/(6)) x 2 (-(2)/(3)+(1)/(2)).

Without using a calculator and showing your working clearly, evaluate $\left( \frac{3}{4}-\frac{5}{6} \right)\times 2\div \left( -\frac{2}{3}+\frac{1}{2} \right)$.

Fraction Operations Without a Calculator

Without the use of a calculator, evaluate 3 3(1)/(3) x (2)/(5). Show your working clearly.

Without the use of a calculator, evaluate $3\div 3\frac{1}{3}\times \frac{2}{5}$. Show your working clearly.

Fraction Division and Multiplication Without a Calculator

The temperature at the bottom of a mountain was 0 C. The temperature at the top was -20 C. Find the - difference between the two temperatures. - average of the two temperatures.

The temperature at the bottom of a mountain was $0^\circ \mathrm{C}$. The temperature at the top was $-20^\circ \mathrm{C}$.

Temperature Difference and Average

Without the use of a calculator, evaluate ((- 2)/(3)) x (2-1(4)/(5))(5)/(7) 4(2)/(7) by showing your working clearly.

Without the use of a calculator, evaluate $\frac{\left( -\frac{2}{3} \right)\times \left( 2-1\frac{4}{5} \right)}{\frac{5}{7}\div 4\frac{2}{7}}$ by showing your working clearly.

Evaluating Complex Fraction Expressions Without a Calculator

The freezing of a liquid is -7 C. The temperature difference between its freezing point and boiling point is 25 C. - Find the boiling point of the liquid. - An addition of a small quantity of salt into the liquid decreased its freezing point by 0.8 C and increased its boiling point by 0.7 C. Find the temperature difference between the freezing point and the boiling point of this liquid-salt mixture.

The freezing of a liquid is $-7^\circ \mathrm{C}$. The temperature difference between its freezing point and boiling point is $25^\circ \mathrm{C}$.

Temperature Changes and Effects of Adding Salt

Without the use of a calculator, evaluate (12.8 0.032)/(3.2-0.7).

Without the use of a calculator, evaluate $\frac{12.8\div 0.032}{3.2-0.7}$.

Evaluating Decimal Expressions Without a Calculator

<p>$5-2$ </p>
<p>$5-\left( -2 \right)$ </p>
<p>$-5-\left( -2 \right)$</p>

Addition and Subtraction involving Negative Numbers

Subtraction involving Negative Numbers

<p>The Number Line</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760777236067-bvb4a4kmsaf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA3NzcyMzYwNjctYnZiNGE0a21zYWYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzU1OTI4NSwiZXhwIjoxNzkzNTU5NTg1fQ.RHb4WbOqUtIyk1PwUmvOVCCaivVVQximHEz5csDPKY0" width="400" class="aligncenter" /></figure>
<p>Mark the following numbers on the number line:</p>
<p>$4$, $-6$, $-3$, $\frac{5}{7}$, $3\frac{1}{2}$, $-\frac{3}{4}$, $\pi$, $1.\dot{3}$</p>

$4$, $-6$, $-3$, $\frac{5}{7}$, $3\frac{1}{2}$, $-\frac{3}{4}$, $\pi$, $1.\dot{3}$

Ordering Real Numbers and the Number Line

Negative and Positive Numbers

<p>Consider the following sets:<br>The set of natural numbers, $\mathbb{N}$ ;<br>The set of integers, $\mathbb{Z}$ ;<br>The set of rational numbers, $\mathbb{Q}$ ;<br>The set of real numbers, $\mathbb{R}$ .</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Which of the above sets is/are such that&nbsp;$\left\{ 0,\frac{1}{3} \right\}$ is a subset of it?</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Give a description of the set&nbsp;$\mathbb{R} \setminus \mathbb{Q}$ , i.e., the set that contains all elements that are in $\mathbb{R}$ but not in $\mathbb{Q}$.<br>Hence write down a subset of $\mathbb{R} \setminus \mathbb{Q}$.</div></li></ol>

Consider the following sets:
The set of natural numbers, $\mathbb{N}$ ;
The set of integers, $\mathbb{Z}$ ;
The set of rational numbers, $\mathbb{Q}$ ;
The set of real numbers, $\mathbb{R}$ .

Classifying Real Numbers

Representing Relationships between Sets

IP2U10 HOT Q2

Sets

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Showing your working clearly, evaluate $0.5\times \frac{(17^2 - 7^2) \div \sqrt{(-20)\times(-1.8)}}{0.74 - 3.24}$.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Showing your working clearly, evaluate $\frac{\frac{8}{5}\times \sqrt{\left(-2\frac{3}{4}\right)^2 - 6}}{-1\frac{1}{2} - 2\frac{3}{4}}$.</span><span class="inline-marks">[3]</span></div></li></ol>

Showing your working clearly, evaluate $0.5\times \frac{(17^2 - 7^2) \div \sqrt{(-20)\times(-1.8)}}{0.74 - 3.24}$.

Showing your working clearly, evaluate $\frac{\frac{8}{5}\times \sqrt{\left(-2\frac{3}{4}\right)^2 - 6}}{-1\frac{1}{2} - 2\frac{3}{4}}$.

Operations with Fractions and Mixed Numbers

Combined Operations of Numbers

IP1 Class Test (May 2025) Q6

<p style="text-align: center">$1\frac{3}{4}, \frac{1}{2}\pi, -174, 0.14\dot{7}\dot{6}, \frac{\sqrt{36}}{7}, \sqrt[3]{64}, \sqrt{2}, \sqrt{121}\pi, -\sqrt{144}$</p>
<p>From the numbers given, list the numbers that are</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">rational numbers,</span></div></li><li><div class="list-item-content"><span class="list-item-text">irrational numbers,</span></div></li><li><div class="list-item-paragraph">integers.</div></li></ol>

$1\frac{3}{4}, \frac{1}{2}\pi, -174, 0.14\dot{7}\dot{6}, \frac{\sqrt{36}}{7}, \sqrt[3]{64}, \sqrt{2}, \sqrt{121}\pi, -\sqrt{144}$

From the numbers given, list the numbers that are

IP1 Class Test (May 2025) Q2

<p>Without using a calculator, determine whether $\frac{333}{3333}$ or $\frac{3333}{33\ 333}$ is smaller.</p>

Without using a calculator, determine whether $\frac{333}{3333}$ or $\frac{3333}{33\ 333}$ is smaller.

<p>Evaluate $(1 + \frac{1}{2})(1 + \frac{1}{3})(1 + \frac{1}{4}) \dots (1 + \frac{1}{2024})$.</p>

Evaluate $(1 + \frac{1}{2})(1 + \frac{1}{3})(1 + \frac{1}{4}) \dots (1 + \frac{1}{2024})$.

<p>Given that $p$ and $q$ are such that $-\frac{13}{7} \leq p \leq 4$ and $\frac{11}{2} \leq q \leq 9\frac{1}{4}$, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $q - p$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p^2 + q^2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p^2 + q^2$.</span></div></li></ol>

Given that $p$ and $q$ are such that $-\frac{13}{7} \leq p \leq 4$ and $\frac{11}{2} \leq q \leq 9\frac{1}{4}$, find

the smallest possible value of $p^2 + q^2$,

the greatest possible value of $p^2 + q^2$.

Extreme Values over Stated Real Intervals

 Addition, Subtraction, Multiplication, and Division involving Negative Numbers

<p>Given that $p$ and $q$ are integers such that $-8 &lt; p \leq 5$ and $-3 \leq q &lt; 3$, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p - q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p - q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p^2 + q^2$.</span></div></li></ol>

Given that $p$ and $q$ are integers such that $-8 < p \leq 5$ and $-3 \leq q < 3$, find

the smallest possible value of $p^2 + q^2$.

Extreme Values under Integer Constraints

<p>In a class quiz, the average time taken by seven candidates to complete the quiz is 1 hour and 17 minutes. The table below shows the difference between the time taken by each candidate and the average time.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">Candidates</th><th style="text-align: left; --cell-justify: flex-start">A</th><th style="text-align: left; --cell-justify: flex-start">B</th><th style="text-align: left; --cell-justify: flex-start">C</th><th style="text-align: left; --cell-justify: flex-start">D</th><th style="text-align: left; --cell-justify: flex-start">E</th><th style="text-align: left; --cell-justify: flex-start">F</th><th style="text-align: left; --cell-justify: flex-start">G</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">Difference (minutes)</td><td style="text-align: left; --cell-justify: flex-start">-8</td><td style="text-align: left; --cell-justify: flex-start">2</td><td style="text-align: left; --cell-justify: flex-start">-3</td><td style="text-align: left; --cell-justify: flex-start">-11</td><td style="text-align: left; --cell-justify: flex-start">$x$</td><td style="text-align: left; --cell-justify: flex-start">5</td><td style="text-align: left; --cell-justify: flex-start">13</td></tr></tbody></table></div></div>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the value of $x$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the difference between the greatest and smallest time taken to complete the quiz,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the average time taken to complete the quiz by candidate $C$, $D$ and $G$.</span></div></li></ol>

In a class quiz, the average time taken by seven candidates to complete the quiz is 1 hour and 17 minutes. The table below shows the difference between the time taken by each candidate and the average time.

the difference between the greatest and smallest time taken to complete the quiz,

the average time taken to complete the quiz by candidate $C$, $D$ and $G$.

Finding Unknowns from Averages and Spread

Mean of Ungrouped Data

Median, Quartiles, Range and Interquartile Range

Applications of Negative Numbers in Real Life

Statistics

<p>The temperatures of a city during winter for a particular 5-day period were shown in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">Monday</th><th style="text-align: left; --cell-justify: flex-start">Tuesday</th><th style="text-align: left; --cell-justify: flex-start">Wednesday</th><th style="text-align: left; --cell-justify: flex-start">Thursday</th><th style="text-align: left; --cell-justify: flex-start">Friday</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">$-4.0$ °C</td><td style="text-align: left; --cell-justify: flex-start">$1.5$ °C</td><td style="text-align: left; --cell-justify: flex-start">$2.0$ °C</td><td style="text-align: left; --cell-justify: flex-start">$-2.5$ °C</td><td style="text-align: left; --cell-justify: flex-start">$-1.5$ °C</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">List the days when the temperature fell below $-2$ °C.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the average temperature during this period.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the difference in temperature between Monday and Wednesday.</span></div></li></ol>

The temperatures of a city during winter for a particular 5-day period were shown in the table below.

List the days when the temperature fell below $-2$ °C.

Find the average temperature during this period.

Find the difference in temperature between Monday and Wednesday.

Math Question Bank