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IB MYP Mathematics Syllabus (Grade 1-5)

July 1, 2024
IB MYP Syllabus
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Table of Contents

1 Assessment Criteria, as stated in IB MYP Subject Brief:
2 Criterion A: Knowing and understanding
- 2.1 Students should be able to:
- 2.2 Learning Progression
3 Criterion B: Investigating patterns
- 3.1 Students should be able to:
- 3.2 Learning Progression
4 Criterion C: Communicating
- 4.1 Students should be able to:
- 4.2 Learning Progression
5 Criterion D: Applying mathematics in real-life contexts
- 5.1 Students should be able to:
- 5.2 Learning Progression
6 KEY CONCEPTS
7 Related Concepts
8 ATL Skills
9 The concepts under MYP mathematics can be categorised under four branches:
10 Assessment Tasks in MYP mathematics
11 Assessment criteria Overview
12 MYP eAssessment
- 12.1 EXAMINATION BLUEPRINT
13 MYP 1
14 MYP 2
15 MYP 3
16 MYP 4
17 MYP 5

Assessment Criteria, as stated in IB MYP Subject Brief:

Each mathematics objective corresponds to one of four equally weighted assessment criteria. Each criterion has eight possible achievement levels (1–8), divided into four bands with unique descriptors that teachers use to make judgments about students’ work.

Criterion A: Knowing and understanding

Students select and apply mathematics to solve problems in both familiar and unfamiliar situations in a variety of contexts, demonstrating knowledge and understanding of the framework’s branches (number, algebra, geometry and trigonometry, statistics and probability).

Students should be able to:

Use appropriate mathematical concepts when tackling issues in both known and unfamiliar contexts.
Effectively use the chosen maths to solve issues accurately.
Tackle issues in a range of situations.

Learning Progression

Year 1	Year 3	Year 5
Criterion A: Knowing and Understanding
Use appropriate mathematical concepts when tackling issues in both known and unfamiliar contexts. Effectively use the chosen maths to solve issues accurately. Tackle issues in a range of situations.	Use appropriate mathematical concepts when tackling issues in both known and unfamiliar contexts. Effectively use the chosen maths to solve issues accurately. Tackle issues in a range of situations.	Use appropriate mathematical concepts when tackling issues in both known and unfamiliar contexts. Effectively use the chosen maths to solve issues accurately. Tackle issues in a range of situations.

Criterion B: Investigating patterns

Students work through investigations to become risk-takers, inquirers and critical thinkers.

Students should be able to:

Choose and use mathematical problem-solving strategies to identify intricate patterns.
Characterize patterns as broad guidelines that align with findings.
Demonstrate, or confirm and support, general laws.

Also Read: Comprehensive IB Maths AA SL & HL Syllabus

Learning Progression

Year 1	Year 3	Year 5
Criterion B: Communicating
Use mathematical techniques to solve problems and identify trends. Characterize patterns as connections or overarching guidelines that align with findings. Check to see if the pattern holds true for other instances.	Choose and use mathematical problem-solving strategies to identify intricate patterns. Characterize patterns as connections and/or broad guidelines that align with the results. Validate and explain connections and/or basic guidelines.	Choose and use mathematical problem-solving strategies to identify intricate patterns. Characterize patterns as broad guidelines that align with findings. Demonstrate, or confirm and support, general laws.

Criterion C: Communicating

Students use appropriate mathematical language and different forms of representation when communicating mathematical ideas, reasoning and findings, both orally and in writing.

Students should be able to:

Employ suitable notation, symbols, and vocabulary from mathematics in both written and spoken explanations.
Communicate information using suitable mathematical representations.
Switch between several mathematical representations.
Provide thorough, logical, and succinct mathematical arguments.
Information should be arranged logically.

Learning Progression

Year 1	Year 3	Year 5
Criterion C: Communicating
In both written and spoken remarks, employ proper mathematical terminology, symbols, and notation. Present information using suitable mathematical representations. Communicate logical mathematical arguments. Information should be arranged logically.	Employ suitable mathematical notation, symbols, and vocabulary when providing explanations verbally or in writing. When presenting facts, use the appropriate mathematical representations. Switch between various mathematical representations. Express comprehensive and logical mathematical arguments. Information should be arranged logically.	When explaining mathematical concepts or procedures, use suitable notation, symbols, and vocabulary. When presenting facts, use the appropriate mathematical representations. Switch between various mathematical representations. Present thorough, logical, and succinct mathematical arguments. Information should be arranged logically.

Criterion D: Applying mathematics in real-life contexts

Students transfer theoretical mathematical knowledge into real-world situations and apply appropriate problem-solving strategies, draw valid conclusions and reflect upon their results.

Students should be able to:

Determine pertinent components of real-world scenarios that are authentic.
Choose the right mathematical techniques to solve genuine real-world problems.
Effectively use the chosen mathematical techniques to arrive at a solution
Explain the level of precision of a solution.
Explain if a solution makes sense in light of the actual, real-world circumstances.

Learning Progression

Year 1	Year 3	Year 5
Criterion D: Applying mathematics in real-life contexts
Determine pertinent components of genuine, real-world scenarios. When tackling real-world problems, use the proper mathematical techniques. Utilize the chosen mathematical techniques effectively to arrive at a resolution. Describe the level of precision of a solution. Explain if a solution makes sense within the actual, authentic context of the circumstance.	Determine pertinent components of genuine, real-world scenarios. When tackling real-world problems, use the proper mathematical techniques. Utilize the chosen mathematical techniques effectively to arrive at a resolution. Describe the level of precision of a solution. Justify a solution’s viability given the actual, real-world circumstances.	Determine pertinent components of genuine, real-world scenarios. When tackling real-world problems, use the proper mathematical techniques. Utilize the chosen mathematical techniques effectively to arrive at a resolution. Describe the level of precision of a solution. Justify a solution’s level of precision. Justify a solution’s viability given the actual, real-world circumstances.

KEY CONCEPTS

FORM

Form is the external appearance, organization, and fundamental essence of an object or work, as well as its shape and underlying structure. In MYP mathematics, form refers to the knowledge that an entity’s attributes distinguish its underlying structure and shape. Students can learn to recognize the aesthetic quality of the constructions utilized in a discipline through form.

LOGIC

Logic is an approach to reasoning and a set of rules that are utilized to formulate claims and draw inferences. In MYP mathematics, judgments regarding variables, numbers, and forms are made via a method known as logic. Students have a way to justify the validity of their conclusions utilizing this line of reasoning. This is not to be confused with the mathematical branch known as “symbolic logic” inside the MYP.

RELATIONSHIPS

The links and linkages that exist between characteristics, items, persons, and ideas are known as relationships. These include the bonds that the human community has with the environment in which we live. Any alteration in a relationship has repercussions, some of which can be localized and impact human cultures and the global ecology, while other effects might be extensive and impact massive networks and systems. In MYP mathematics, relationships are defined as the links that exist between quantities, qualities, or concepts. These connections can be stated as assertions, models, or rules. Students can investigate patterns in the world around them through relationships. Establishing links between the actual world application of mathematics and the student is crucial for fostering a deeper understanding.

Related Concepts

Approximation
Generalisation
Quantity
Space
Change
Models
Representation
Systems
Equivalence
Patterns
Simplification
Validity

ATL Skills

Thinking skills

When solving problems, apply priority and sequence of precedence.

Social skills

As you work in groups, assist others in becoming successful.

Communication skills

Utilize both analog and digital tools to arrange and evaluate data.

Self-management skills

While tackling several issues at once, work on your concentration and focus.

Research skills

Utilize a range of media platforms and technology, such as social media and internet networks, to find information.

The concepts under MYP mathematics can be categorised under four branches:

The following table showcases different MYP concerts from MYP 1 to MYP 5 under each branch.

NUMERICAL AND ABSTRACT REASONING
MYP 1-3	MYP 4-5	MYP 4-5 EXTENDED
Operations Integers Fractions Decimals Percentage Transformation of form of numbers Estimation Rounding off Approximation Significant figures Recurring decimals Time zones Clocks Timetables Number line Inequalities Square and square roots Exponents Ratios Sequences and rules. Forming equations Algebraic expressions Substitution Expansion of brackets Factorisation of algebraic expressions Rearranging and solving equations Formulae Flowcharts Algorithms	Number system Notation Absolute values Inequalities Number sequences Surds Roots Radicals Laws of exponent Scientific notation Direct and inverse proportion Sequences Simultaneous equations (algebra and graphs) Solving inequalities Quadratic expressions Quadratic equations Formulae	Lower and upper bounds Logarithms Laws of logarithms Laws of exponents (fractional and rational) Notation and formulae for geometric and arithmetic sequence
THINKING WITH MODELS
MYP 1-3	MYP 4-5	MYP 4-5 EXTENDED
Not age appropriate	Mapping Function notation Linear functions Parallel and perpendicular lines Simultaneous equations (algebra and graphs) Quadratic equations Exponential functions Asymptotes Algorithms	Domain Range Rational functions Linear programming Inequalities Transformation of quadratic functions Translation Reflection Dilation Cubic, rationals, trigonometric and logarithmic function and asymptotes Networks
SPATIAL REASONING
MYP 1-3	MYP 4-5	MYP 4-5 EXTENDED
Shapes and angles Properties of angles Angles in intersecting and parallel lines Perimeter Volume Surface area Coordinates Symmetry Reflection	Metric conversions Circle geometry Perimeter Volume Surface area Gradients and intercepts Gradient of parallel lines Coordinate geometry Rotation Similarity Congruence Plane Properties of triangle Bearings Pythagoras’ theorem Trigonometric ratios Right angled triangles	Capacity Gradient and perpendicular lines Enlargement Identical representation of transformations Converse of pythagoras’ theorem Sine rule Cosine rule
REASONING WITH DATA
MYP 1-3	MYP 4-5	MYP 4-5 EXTENDED
Discrete data Continuous data Data collection and generation Limitations Graphical representation Data visualisations Infographics Mean, median and mode for discrete and grouped data Dispersion Range Qualitative probability Probability of simple events Sample space Probability scale Theoretical probability Experimental probability	Sampling techniques Response rates Data manipulation Interpretation Graphical representation Line of best fit Mean, median and mode for continuous data and quartiles and percentiles for discrete and continuous data Dispersion including interquartile range Correlation Sets Probability using Venn diagrams, tree diagrams and sample spaces Mutually exclusive events Combined events Relative frequency	Histograms Dispersion including standard deviation Correlation Probability of independent and dependent events

Assessment Tasks in MYP mathematics

Criterion	Typical assessment tasks
Knowing and understanding	Classroom tests Examinations Assignments
Investigating patterns	Mathematical investigations
Communicating	Investigations and real life problems that require logical structure, multiple forms of representation
Applying mathematics in real-life contexts	Opportunities to use maths concepts to solve real-life problems

Assessment criteria Overview

Four equally weighted assessment criteria form the basis of the criterion-related assessment used for mathematics courses across all program years.

Criterion	ACHIEVEMENT LEVEL
A- KNOWING AND UNDERSTANDING	MAXIMUM 8
B- INVESTIGATING PATTERNS	MAXIMUM 8
C- COMMUNICATING	MAXIMUM 8
D- APPLYING MATHEMATICS IN REAL-LIFE CONTEXTS	MAXIMUM 8

MYP eAssessment

EXAMINATION BLUEPRINT

TASK	MARKS	DESCRIPTION	CRITERION ASSESSED	CRITERION MARKS
Knowing and understanding	31-35*	Students’ knowledge and comprehension of mathematics are evaluated in the first assignment, but when applicable to the abilities employed to answer a question, marks may be given based on additional factors. For instance, students might have to switch between various mathematical representations in order to answer a question that evaluates their knowledge and comprehension.	A C	25 6-10*
Applying mathematics in real-life contexts	31-35*	The second task evaluates students’ application of mathematics in a real-world setting, usually one that is related to the session’s global context. It can be necessary for students to write longer essays in order to assess and defend the accuracy of mathematical models.	D C	25 6-10*
Investigating patterns	31-35	The final task will evaluate mathematical investigative ability. In order to accommodate students with varying skills, the abstract questions in this work will have more scaffolding than would be suitable in a classroom setting.	B C	25 6-10
	100

Please find the detailed syllabus for each grade from MYP 1-5 given below.

MYP 1

There are a total 19 units under mathematics MYP 1.

Unit 1: Number Systems

Subtopic	Description
Different Number Systems	Exploration of various ways to write and use numbers, such as Roman Numerals and Binary Code.
The Hindu-Arabic Number System	Learning about the common number system, including place value, for a better understanding of numbers.
Big Numbers	Handling extremely large or small numbers using scientific notation for easier representation.

Unit 2: Whole Numbers

Subtopic	Description
Addition and Subtraction	Basic operations of combining numbers (addition) or finding the difference between them (subtraction).
Multiplication and Division	Understanding multiplication as repeated addition and division as sharing into equal groups.
Two-Step Problem Solving	Solving problems involving multiple steps, incorporating addition, subtraction, multiplication, and division.
Index Notation	Expressing numbers as a base raised to an exponent, providing a concise representation.
Order of Operations	Following a set of rules to determine the sequence of calculations in complex problems.
Number Lines	Utilizing number lines to visualize and compare numbers, enhancing understanding of their relationships.
Rounding Numbers	Simplifying numbers by rounding them to the nearest whole number, ten, or hundred.

Unit 3: Points, Lines and Angles

Subtopic	Description
Points and Lines	Introduction to points (tiny dots) and lines (paths connecting points) as fundamental elements.
Angles	Understanding angles as the spaces between two lines meeting at a point.
Angles at a Point or on a Line	Exploration of angles formed when lines meet at a point or are in a straight line.
Vertically Opposite Angles	Identifying pairs of angles formed when two lines cross, directly opposite each other, and are equal.
Bisecting Angles	Learning the concept of bisecting angles, cutting an angle into two equal parts.

Unit 4: Number Properties

Subtopic	Description
Zero and One	Recognizing the special nature of zero (nothing) and one (a single item) as foundational numbers.
Square Numbers	Grasping the concept of square numbers, which result from multiplying a number by itself.
Cubic Numbers	Understanding cubic numbers as the result of multiplying a number by itself three times.
Divisibility	Exploring the concept of divisibility, determining whether one number can be evenly divided by another.
Divisibility Tests	Learning specific rules (divisibility tests) to quickly check if a number is divisible by another number.
Factors	Understanding factors as numbers that can be multiplied together to produce another number.
Prime and Composite Numbers	Differentiating between prime numbers (only two factors) and composite numbers (more than two factors).
Highest Common Factor	Grasping the concept of the highest common factor as the largest number that can evenly divide two or more numbers.
Multiples	Understanding multiples as numbers obtained by multiplying a number by other whole numbers.

Unit 5: Geometric Shapes

Subtopic	Description
Polygons	Flat shapes with straight sides, encompassing various forms such as triangles and pentagons.
Triangles	Three-sided polygons with distinct types and sizes.
Quadrilaterals	Four-sided polygons, including examples like squares and rectangles.
Circles	Round shapes with no corners, defined by a centre and a constant radius.
Solids	Three-dimensional shapes like cubes and spheres, possessing length, width, and height.
Drawing Solids	Creating 3D shapes on a 2D surface, a method to represent real-world objects.
Nets of Solids	Two-dimensional patterns that, when folded, produce three-dimensional shapes.

Unit 6: Fractions

Subtopic	Description
Fractions	Representation of a part of a whole with a numerator and a denominator.
Fractions as Division	Utilizing fractions to signify division or sharing, such as 1/2 representing equal parts.
Proper and Improper Fractions	Proper fractions (less than 1) and improper fractions (equal to or greater than 1).
Fractions on a Number Line	Visualizing fractions on a number line to understand their placement relative to whole numbers.
Equal Fractions	Fractions that represent the same portion of a whole despite different numerators or denominators.
Lowest Terms	Simplifying fractions to their lowest terms by dividing both numerator and denominator by their GCF.
Comparing Fractions	Comparing fractions to determine their relative sizes, often facilitated by common denominators.
Adding and Subtracting Fractions	Performing addition and subtraction with fractions, requiring a common denominator for accurate results.
Multiplying a Fraction by a Whole Number	Multiplying a fraction by a whole number involves repeating the fraction by the whole number.
A Fraction of a Quantity	Determining a fraction of a given quantity, representing a portion or division of the total.

Unit 7: Decimals

Subtopic	Description
Decimal Numbers	Numbers with a decimal point, similar to fractions, used for precise representation of parts.
Decimal Numbers on a Number Line	Displaying decimal numbers on a number line for a visual understanding of their magnitudes.
Ordering Decimal Numbers	Sequencing decimal numbers by comparing digits from left to right.
Rounding Decimal Numbers	Simplifying decimal numbers by rounding them to the nearest whole number or specified place value.
Converting Decimals to Fractions	Transforming decimal numbers into fractional form.
Converting Fractions to Decimals	Converting fractional representations into decimal numbers.
Adding and Subtracting Decimal Numbers	Performing addition and subtraction with decimal numbers, ensuring proper alignment of decimal points.
Multiplying by Powers of 10	Shifting the decimal point to the right or left when multiplying by powers of 10.
Dividing by Powers of 10	Adjusting the size of a number by shifting the decimal point when dividing by powers of 10.
Multiplying Decimals by a Whole Number	Ignoring the decimal point initially and reintroducing it in the result after multiplication.
Dividing Decimals by a Whole Number	Employing long division while considering the decimal point in the quotient.

Unit 8: Measurements: Introduction

Subtopic	Description
Units	Labels used to measure and comprehend quantities, such as metres, grams, litres, etc.
Reading Scales	Interpretation of numbers and units on measuring instruments like rulers or thermometers to derive accurate measurements.
Mass	Measurement of the amount of matter in an object, typically expressed in units like grams and kilograms.

Unit 9: Measurement: Length

Subtopic	Description
Units of Length	Different labels used to measure the length of objects, including metres, centimetres, and kilometres.
Operations with Lengths	Involves adding, subtracting, multiplying, and dividing lengths to solve problems.
Perimeter	The total distance around a shape or object, calculated by adding the lengths of its sides.
Scale Diagrams	Drawings using a scale to represent real-world objects or spaces, aiding in visualising sizes and proportions.

Unit 10: Measurement: Area, Volume, and Capacity

Subtopic	Description
Area	The amount of space inside a flat shape, measured in square units.
The Area of a Rectangle	Calculating the space inside a rectangle by multiplying its length and width.
The Area of a Triangle	Calculating the space inside a triangle by multiplying its base and height, then dividing by 2.
Volume	The amount of space inside a three-dimensional shape, measured in cubic units.
The Volume of a Rectangular Prism	Calculating the space inside a rectangular box by multiplying its length, width, and height.
Capacity	The maximum amount a container can hold, often measured in units like milliliters or liters.

Unit 11: Time

Subtopic	Description
Time Lines	Visual tools illustrating the sequence of events or moments in time.
Units of Time	Labels used to measure time intervals, such as seconds, minutes, and hours.
The Calendar Year	Dividing time into 12 months, starting from January and ending in December.
Time Calculations	Performing mathematical operations to find the duration or difference between two time points.
24-Hour Time	Expressing time using a 24-hour clock format, ranging from 00:00 (midnight) to 23:59 (11:59 PM).
Timetables	Schedules or plans displaying events, activities, or appointments at set times.

Unit 12: Percentage

Subtopic	Description
Percentage	Expressing a part of a whole in terms of 100.
Converting Percentages into Fractions	Turning a percentage into a fraction by placing it over 100 and simplifying.
Converting Fractions into Percentages	Transforming a fraction into a percentage by multiplying it by 100.
Converting Percentages into Decimals	Changing a percentage into a decimal by moving the decimal point two places to the left.
Converting Decimals into Percentages	Transforming a decimal into a percentage by moving the decimal point two places to the right and adding a “%” sign.
Number Lines	Visual tools representing percentages and their relationships to whole numbers.
Expressing One Quantity as a Percentage of Another	Determining what percentage one quantity represents in comparison to another.
Finding a Percentage of a Quantity	Calculating the portion of a quantity represented by a percentage.
Percentage Increase or Decrease	Calculating the change in a value relative to its original value, expressed as a percentage.

Unit 13: Positive and Negative Numbers

Subtopic	Description
The Number Line	A visual tool displaying numbers in order, with positive numbers to the right and negative numbers to the left.
Ordering Numbers	Organizing numbers from smallest to largest or vice versa.
Words Indicating Positive and Negative	Words providing clues about whether a number is positive or negative.
Addition and Subtraction on the Number Line	Performing addition or subtraction by moving along the number line to understand changes in position.
Adding and Subtracting Negative Numbers	Combining or subtracting negative numbers by moving to the left on the number line.
Multiplying Negative Numbers	The process of multiplying two negative numbers resulting in a positive product.
Dividing Negative Numbers	Dividing negative numbers can yield either a positive or negative result based on the numbers involved.

Unit 14: Sequences

Subtopic	Description
Generating a Sequence	Creating a list of numbers following a specific pattern or rule.
Finding a Rule for a Sequence	Determining how the numbers in a sequence are connected and using this rule to generate more numbers.
Patterns	Recurring designs or sequences that follow a regular, repeating order.

Unit 15: Location

Subtopic	Description
Grid References	Using numbers and letters on a map or grid to precisely find the location of a point.
Locating Points	Determining the precise position of a point on a map, grid, or coordinate system.
Coordinates	Pairs of numbers (x, y) used to describe the location of a point in relation to a reference point.
Positive and Negative Coordinates	Indicating whether a point is situated to the right (positive) or left (negative) of the reference point.
Compass Points	The cardinal directions (north, south, east, west) and intermediate directions used for orientation and navigation.

Unit 16: Line Graphs

Subtopic	Description
Line Graphs	Visual representations of data using lines to connect data points, showing changes or relationships over time or between variables.
Travel Graphs	Line graphs illustrating the motion or travel of an object or person over time, indicating changes in speed, distance, or time.
Conversion Graphs	Line graphs demonstrating the relationship between two different units of measurement or scales, aiding in conversion.

Unit 17: Probability

Subtopic	Description
Describing Probability	Expressing the chances of an event occurring through words or phrases indicating how certain or likely the event is.
Using Numbers to Describe Probabilities	Assigning numerical values, such as fractions, decimals, or percentages, to represent the likelihood of an event occurring.
Outcomes	The various results or possibilities of an event, encompassing all the different things that could occur.
Calculating Probabilities	Using mathematical techniques to find the chances of specific events happening, typically expressed as a ratio of successful outcomes to all potential outcomes.

Unit 18: Statistics

Subtopic	Description
Categorical Data	Information that can be organized into distinct categories or groups based on characteristics like types, names, or labels.
Dot Plots	Basic graphs using dots to show individual data points distributed along a number line, helping visualize data patterns.
Pictograms	Charts or graphs that utilize pictures or symbols to depict data or information, making it more visually appealing and comprehensible.
Column Graphs	Graphs employing rectangular bars or columns to display and compare data, particularly beneficial for categorical data.
Pie Charts	Circular graphs that divide a whole into sectors to illustrate the proportions of different data categories.
Numerical Data	Information represented using numbers, which can be used for various calculations. This type of data includes measurements, counts, or any data with numeric values.
Measuring the Center of a Data Set	Determining a representative value that describes the concentration of most data points in a dataset, such as the mean (average) or median.

Unit 19: Transformations

Subtopic	Description
Translations	Operations in geometry that shift or move objects from one position to another, preserving their shape and size. It’s like sliding an object in a straight line without changing its orientation.
Reflections	Transformations in geometry that create a mirrored or flipped image of an object over a line, often referred to as the mirror line. This results in a symmetrical image with respect to the line of reflection.
Rotations	Transformations in geometry that revolve or spin objects around a fixed point called the centre of rotation. This changes the orientation of the object by a specific angle.
Combinations of Transformations	Involves applying a series of transformation techniques like translations, reflections, or rotations in a specific order to alter an object’s position and orientation.

MYP 2

There are a total 19 units under mathematics MYP 2.

Unit 1: Whole Numbers

Subtopic	Description
Place Value	Fundamental concept defining the value of each digit based on its position in a number.
Rounding Numbers	The process of approximating a number to a specific place value or digit.
Operations	Fundamental mathematical processes, including addition, subtraction, multiplication, and division, applied to whole numbers.
Exponent Notation	Compact representation using exponents to indicate repeated multiplication of identical base number.

Unit 2: Number Properties

Subtopic	Description
Square Numbers	Numbers obtained by multiplying an integer by itself.
Cubic Numbers	Product of three identical numbers.
Divisibility	The property of one number being evenly divisible by another without leaving a remainder.
Even and Odd Numbers	Even numbers are divisible by 2, while odd numbers are not.
Divisibility Tests	Rules to determine if a number is divisible by another or not.
Factors	Numbers that can be multiplied together to obtain a specific product.
Prime and Composite Numbers	Prime numbers have exactly two distinct factors, while composite numbers have more than two.
Highest Common Factor (HCF)	The largest number that can evenly divide two or more integers without leaving a remainder.
Multiples	Numbers generated by multiplying an integer by another number.
Lowest Common Multiple (LCM)	The smallest multiple shared by two or more integers.

Unit 3: Lines and Angles

Subtopic	Description
Lines	Straight, continuous arrangements of points extending infinitely, categorized as horizontal, vertical, or slanted.
Angles	Formed when two lines, rays, or line segments meet at a point, measured in degrees.
Parallel and Perpendicular Lines	Parallel lines never intersect, while perpendicular lines intersect at right angles.
Angle Properties	Relationships and characteristics of angles, including complementary, supplementary, and vertical angles.
Vertically Opposite Angles	Pairs of angles formed when two lines intersect, equal in measure and opposite each other.
Angle Pairs	Different types of angle relationships, such as co-interior angles, corresponding angles, and alternate angles.
Angle Pairs on Parallel Lines	Specific angle relationships occur when two lines are parallel, including alternate, corresponding, and interior angles.
Tests for Parallelism	Methods to determine if two lines are parallel, like corresponding angles test or alternate angles test.
Geometric Construction	Using tools like a compass and straightedge to create geometric shapes and angles accurately.

Unit 4: Number Strategies and Order of Operations

Subtopic	Description
Addition Strategies	Methods for efficiently adding numbers, including mental maths, counting on, and regrouping.
Subtraction Strategies	Techniques for effectively subtracting numbers, such as mental maths, counting back, and borrowing.
Multiplication Strategies	Various methods for multiplying numbers, including using properties like distributive, commutative, and associative.
Division Strategies	Methods for dividing numbers, such as long division, short division, and using multiplication to check division.
Estimation	The process of making a guess about the result of a mathematical operation or the size of a quantity by rounding off.
Order of Operations	A set of rules determining the sequence in which mathematical operations should be performed. For instance, BEDMAS.
Problem Solving	Using mathematical skills and strategies to solve real-world or mathematical problems.

Unit 5: Positive and Negative Numbers

Subtopic	Description
The Number Line	A visual representation displaying numbers, including positive and negative integers, zero, and fractions, in order.
Words Indicating Positive and Negative	Terms describing numbers in relation to position on number line or direction they are moving on the number line.
Addition and Subtraction on the Number Line	Utilizing the number line as a visual aid for performing addition and subtraction, particularly with positive and negative integers.
Adding and Subtracting Negative Numbers	Operations involving understanding rules and techniques for working with negative integers in addition and subtraction.
Multiplying Negative Numbers	Determining the sign of the product based on the number of negative factors involved in multiplication.
Dividing Negative Numbers	Understanding division rules with negative integers and determining the sign of the quotient.
Order of Operations	Rules specifying the sequence for performing mathematical operations to solve expressions or equations.
Calculator Use	Employing calculators for accurate arithmetic operations and various mathematical tasks.

Unit 6: Fractions

Subtopic	Description
Fractions	Numerical representations describing parts of a whole, with a numerator indicating the part and a denominator signifying the total parts.
Fractions as Division	Viewing fractions as division problems, where the numerator represents the dividend, and the denominator is the divisor.
Proper and Improper Fractions	Proper fractions have smaller numerators than denominators, while improper fractions have numerators equal to or greater than denominators.
Fractions on a Number Line	Representing fractions on a number line to illustrate their position relative to whole numbers and other fractions.
Equal Fractions	Fractions that represent the same quantity, even with different numerators and denominators.
Lowest Terms	Fractions in their lowest terms have no common factors between the numerator and denominator other than 1.
Cancelling Common Factors	Simplifying fractions by dividing both the numerator and denominator by their greatest common factor.
One Quantity as a Fraction of Another	Expressing one quantity as a fraction of another to show the relationship and represent the parts of a whole.
Comparing Fractions	Determining which fraction is larger or smaller by finding a common denominator or converting fractions to decimals.
Adding and Subtracting Fractions	Operations involving finding a common denominator to combine or subtract fractions, essential in various mathematical contexts.
Multiplying a Fraction by a Whole Number	Scaling a fraction by a whole number, indicating how many parts of the whole are considered.
Multiplying Fractions	Performing multiplication operations on fractions by multiplying numerators and denominators.
Reciprocals	Pairs of numbers that, when multiplied, result in 1; for fractions, the reciprocal is obtained by swapping the numerator and denominator.
Dividing Fractions	Involves multiplying by the reciprocal of the second fraction, determining how many times one fraction is contained within another.

Unit 7: Decimals

Subtopic	Description
Decimal Numbers	A numerical system including both whole and fractional parts, separated by a decimal point.
Decimal Numbers on a Number Line	Representing decimal numbers on a number line for visual comparisons of magnitudes and positions.
Ordering Decimal Numbers	Arranging decimal numbers in ascending or descending order to compare their values.
Rounding Decimal Numbers	Simplifying decimal numbers to a specified place value for ease of calculation while maintaining an approximate value.
Converting Decimals to Fractions	Expressing decimal numbers as ratios of two integers.
Converting Fractions to Decimals	Representing fractional values as decimal numbers.
Adding and Subtracting Decimal Numbers	Mathematical operations for combining or finding the difference between decimal values.
Multiplying by Powers of 10	Multiplying decimal numbers by powers of 10 involves shifting the decimal point, changing their magnitude.
Dividing by Powers of 10	Dividing decimal numbers by powers of 10 also shifts the decimal point, changing their magnitude.
Multiplying Decimal Numbers	Performing multiplication operations on numbers with decimal fractions.
Dividing Decimal Numbers	Performing division operations on numbers with decimal fractions.

Unit 8: Algebra

Subtopics	Description
Building Expressions	Building expressions means creating mathematical expressions by combining numbers, variables, and operations.
Product Notation	Product notation is a mathematical representation used to express multiplication operations with parentheses and symbols.
Exponent Notation	Exponent notation includes using powers or indices to represent repeated multiplication, where a base is raised to an exponent.
Reading Expressions	Reading expressions involves comprehending and interpreting mathematical expressions by identifying the roles of numbers, variables, and operations.
Terms and Coefficients	Terms are the individual parts of an algebraic expression, and coefficients are the numerical factors that multiply those terms.
Equal Expressions	Equal expressions are algebraic expressions that yield the same value for all valid input values of variables.
Collecting Like Terms	Collecting like terms means organizing and simplifying algebraic expressions by grouping terms with identical variables and exponents.
Algebraic Substitution	Algebraic substitution involves substituting variables in an expression with particular values to calculate the expression’s result.
Formulae	Formulae are mathematical expressions or equations that define relationships between various variables and are utilized to solve particular problems.

Unit 9: Percentage

Subtopics	Description
Percentage	A percentage is a means of representing a part of a whole as a fraction of 100, typically denoted by the “%” symbol.
Converting Percentages into Decimals and Fractions	Converting percentages into decimals and fractions entails representing percentages as equivalent decimal numbers or fractions for different mathematical operations.
Converting Decimals and Fractions into Percentages	Converting decimals and fractions into percentages involves representing decimal numbers or fractions as equivalent percentages.
Expressing One Quantity as a Percentage of Another	Expressing one quantity as a percentage of another demonstrates the relationship between a specific quantity and the whole or another quantity, typically expressed as a percentage.
Finding a Percentage of a Quantity	Finding a percentage of a quantity involves determining a particular portion or fraction of a total amount.
Percentage Increase or Decrease	Percentage increase or decrease signifies the alteration in a quantity relative to its initial value, typically presented as a percentage.
Discount	A discount is a decrease in the original cost of a product or service, usually represented as a percentage.
Finding a Percentage Change	Finding a percentage change involves determining the difference between two values and representing it as a percentage.

Unit 10: Equations

Subtopics	Description
Equations	Equations are mathematical statements that indicate equality between two expressions, frequently involving variables to determine an unknown value.
Solving by Inspection	Solving equations by inspection means discovering the solution through quick observation and recognizing the answer without extensive calculations.
Maintaining Balance	In equations, maintaining balance is the practice of keeping both sides of the equation equal throughout the solving process by performing consistent operations.
Inverse Operations	Inverse operations are mathematical procedures that reverse the effects of one another, such as addition and subtraction or multiplication and division.
Algebraic Flowcharts	Algebraic flowcharts are visual diagrams that depict the sequential steps in solving equations, simplifying the solution process.
Solving Equations	Solving equations is the process of determining the values of variables that satisfy the equation, typically accomplished through a series of algebraic steps.
Equations with a Repeated Variable	These are equations in which the same variable appears multiple times, necessitating specific solving techniques.
Geometry Problems	Geometry problems entail the application of equations to resolve geometric situations and determine measurements, angles, or side lengths.
Writing Equations	Writing equations is the process of converting verbal or situational problems into mathematical expressions that can be solved.
Word Problems	Word problems are mathematical questions framed as written scenarios, demanding the use of equations to find solutions.

Unit 11: Polygons

Subtopics	Description
Polygons	Polygons are two-dimensional shapes with straight sides that are closed, and they vary in the number of sides.
Triangles	Triangles are polygons with three sides, and they can be categorized as equilateral, isosceles, or scalene.
Angle Sum of a Triangle	The angle sum of a triangle is consistently 180 degrees, irrespective of the triangle’s type.
Exterior Angles of a Triangle	Exterior angles of a triangle are created by extending one side of the triangle, and their total adds up to 360 degrees.
Isosceles Triangles	Isosceles triangles possess two sides of the same length and two corresponding angles that are equal.
Quadrilaterals	Quadrilaterals are polygons with four sides, encompassing various types such as rectangles, squares, parallelograms, and more.
Angle Sum of a Quadrilateral	The angle sum of a quadrilateral is always 360 degrees, irrespective of the particular type of quadrilateral.

Unit 12: Measurement: Length and Area

Subtopics	Description
Length	Length refers to the measurement of an object from one end to the other in one dimension.
Perimeter	Perimeter is the total distance around the boundary of a two-dimensional shape.
Area	Area is the measure of the surface enclosed by a two-dimensional shape.
Area of a Rectangle	The area of a rectangle is found by multiplying its length and width.
Area of a Triangle	The area of a triangle is determined by multiplying its base and height and then dividing by 2.
Area of a Parallelogram	The area of a parallelogram is calculated by multiplying its base and height.
Area of a Trapezium	The area of a trapezium is determined by taking the average of its two parallel sides (bases) and then multiplying by its height.

Unit 13: Solids

Subtopics	Description
Solids	Solids refer to three-dimensional objects that have volume and occupy space.
Nets of Solids	Nets are two-dimensional representations of three-dimensional solids. They are flat patterns that, when folded, create a specific solid shape.
Oblique and Isometric Projections	Oblique projection shows one face of a solid in true shape, while isometric projection shows the object from multiple angles.

Unit 14: Measurements: Volume, Capacity, and Mass

Subtopics	Description
Volume	Volume is the measure of the amount of three-dimensional space an object occupies.
Volume of a Prism	The volume of a prism is calculated by multiplying the area of its base by its height.
Capacity	Capacity represents the maximum amount of a substance, usually a liquid, that a container can hold.
Connecting Volume and Capacity	This explores the relationship between volume and capacity, emphasizing that capacity reflects the volume a container can hold.
Mass	Mass is the measure of the amount of matter in an object and is commonly expressed in units like grams or kilograms.
Relationship Between Units	This focuses on the conversion and relationships between different units of measurement within the context of volume, capacity, and mass.

Unit 15: Coordinate Geometry

Subtopics	Description
Coordinates	Coordinates represent the position of a point in a two-dimensional space and are expressed as (x,y) (x,y).
Positive and Negative Coordinates	Positive coordinates are in the right or upper half, while negative coordinates are in the left or lower half.
Plotting Points from a Table of Values	Plotting points involves marking corresponding points on a coordinate plane based on sets of x and y values.
Equation of a Line	The equation of a line is in the form y=mx+b y=mx+b, representing a straight line on a coordinate plane.

Unit 16: Ratio and Rates

Subtopics	Description
Ratio	A ratio is a comparison of two quantities or numbers and is often expressed as a fraction or using a colon.
Ratio and Fractions	Ratios can be represented as fractions, such as ab b a , allowing for precise mathematical operations.
Equal Ratios	Equal ratios represent the same relationship between quantities and can be simplified to the same value.
Lowest Terms	Reducing a ratio to its lowest terms involves dividing both the numerator and denominator by their GCF.
Proportions	Proportions state that two ratios are equal and can be written as fractions or equations. Cross-multiplication is often used.
Using Ratios to Divide Quantities	Ratios are used to divide quantities into parts based on the relationship between the quantities in the ratio.
Rates	Rates involve a change in one variable with respect to another, often expressed as a unit of time.
Unit Cost	Unit cost is the cost associated with a single unit of a product or service, calculated by dividing the total cost by the number of units.

Unit 17: Probability

Subtopics	Description
Describing Probability	Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1.
Using Numbers to Describe Probabilities	Probabilities range from 0 (impossible) to 1 (certain), with 0≤P(A)≤1 0≤P(A)≤1.
Sample Space	The sample space is the set of all possible outcomes of an experiment or a random process.
Theoretical Probability	Theoretical probability is calculated based on mathematical principles and the nature of the event.
Experimental Probability	Experimental probability is calculated based on actual observations or experiments.
Accuracy of Experimental Probabilities	The accuracy of experimental probabilities improves with more trials, approaching theoretical probability.

Unit 18: Statistics

Subtopics	Description
Data Collection	Data collection is the process of gathering information or observations for analysis.
Categorical Data	Categorical data consists of categories or labels that can be divided into distinct groups.
Displaying Categorical Data	Displaying categorical data involves presenting information visually using methods like bar charts or pie charts.
Comparing Categorical Data	Comparing categorical data involves analyzing and contrasting different categories within a dataset.
Numerical Data	Numerical data consists of numbers representing measurable quantities, such as temperature or test scores.
Stem-and-LePlots	A stem-and-leaf plot is a graphical representation of numerical data, preserving the order of individual data points.
Measuring the Centre	Measures of central tendency (mean, median, mode) help identify the typical or central value in a dataset.
Measuring the Spread	Measures of spread (range, interquartile range, variance, standard deviation) determine the variability of values.

Unit 19: Transformations

Subtopics	Description
Translations	Translations move an object from one position to another without changing its orientation or shape.
Reflections	Reflections create a mirror image of an object over a line of reflection, preserving distances.
Line Symmetry	Line symmetry occurs when a figure can be folded over a line (line of symmetry) and both sides match.
Rotations	Rotations turn an object around a fixed point (center of rotation), maintaining its shape and size.
Rotational Symmetry	Rotational symmetry allows an object to appear unchanged after a rotation of less than 360 degrees.
Enlargements and Reductions	Enlargements increase the size, and reductions decrease the size of an object while maintaining its shape.
Combinations of Transformations	Combinations involve applying multiple transformations, such as translations, rotations, and reflections, in sequence.

MYP 3

There are a total 21 units under mathematics MYP 3.

Unit 1: Number

Subtopic	Description
Operations with Negative Numbers	Involves addition, subtraction, multiplication, and division of numbers less than zero. Understanding rules for negative numbers is fundamental.
Exponent Notation	Represents repeated multiplication using a base number raised to an exponent. For example, a^b where ‘a’ is the base and ‘b’ is the exponent.
Factors	Numbers that multiply to obtain a product. Understanding factors is crucial for prime factorization and simplifying fractions.
Prime and Composite Numbers	Prime numbers have only two factors (1 and itself), while composite numbers have more. Recognizing them is essential in various contexts.
Highest Common Factor (HCF)	Largest positive integer dividing two or more numbers without remainder. Used for simplifying fractions and problem-solving.
Multiples	Numbers obtained by multiplying a given number by other integers. Crucial in arithmetic and algebraic concepts.
Order of Operations	Set of rules determining the sequence in which operations are performed. Standard order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Problem Solving	Involves applying mathematical concepts to real-life situations. Requires critical thinking, logical reasoning, and mathematical skills.

Unit 2: Sets and Venn Diagrams

Subtopic	Description
Sets	Collections of objects or elements, defined by listing elements inside curly braces. Example: {1, 2, 3}.
Complement of a Set	The complement, denoted as A’, contains elements not in set A within a larger universal set (A’ = U – A).
Intersection and Union	Intersection (∩) contains elements in both sets A and B. Union (∪) contains elements in either set A or set B.
Venn Diagrams	Graphical representations illustrating relationships between sets. Overlapping circles show intersections.
Numbers in Regions	In Venn diagrams, numbers in regions indicate the count of elements, aiding in quantifying set intersections.
Problem Solving with Venn Diagrams	Powerful tool for solving problems related to set theory, logic, and probability. Organises and visualises information.

Unit 3: Real Numbers

Subtopic	Description
Fractions	Represent a part of a whole, consisting of a numerator and denominator.
Equal Fractions	Fractions representing the same value.
Adding and Subtracting Fractions	Operations with fractions, straightforward with the same denominators; common denominators needed for different ones.
Multiplying Fractions	Multiply numerators and denominators.
Dividing Fractions	Divide by multiplying by the reciprocal.
Decimal Numbers	Fractions expressed in base 10.
Rounding Decimal Numbers	Approximating decimal numbers to a certain number of decimal places.
Adding and Subtracting Decimal Numbers	Operations similar to whole numbers, aligning decimal points.
Multiplying and Dividing by Powers of 10	Shifting decimal points when multiplying/dividing by powers of 10.
Multiplying Decimal Numbers	Ignore decimals, perform multiplication, then place the decimal point based on the original numbers.
Dividing Decimal Numbers	Convert to whole numbers, perform division, and adjust the decimal point.
Square Roots	Value that, when multiplied by itself, gives the original number.
Cube Roots	Value that, when multiplied by itself three times, gives the original number.
Rational Numbers	Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Decimals that repeat or terminate are also rational.
Irrational Numbers	Numbers not expressible as fractions with non-repeating, non-terminating decimals. Examples: Π and √2. .

Unit 4: Algebraic Expressions

Subtopic	Description
Product Notation	Product notation is a way to express the multiplication of a series of terms. It uses the Π (pi) symbol to represent multiplication.
Exponent Notation:	Exponent notation is used to represent repeated multiplication.
Writing Expressions	Involves representing mathematical ideas using symbols, variables, operations, and parentheses.
Generalizing Arithmetic	Identifying patterns and creating algebraic expressions to represent them.
Algebraic Substitution	Replacing variables in an expression with specific values to evaluate the expression.
The Language of Algebra	Understanding and using algebraic symbols, terms, variables, coefficients, constants, and operators.
Collecting Like Terms	Simplifying algebraic expressions by grouping terms with similar variables.
Algebraic Products	Expressions formed by multiplying algebraic terms or expressions.
Algebraic Fractions	Expressions with algebraic terms in the numerator and denominator.
Multiplying Algebraic Fractions	Multiply numerators to get the new numerator and denominators for the new denominator.
Dividing Algebraic Fractions	Divide by multiplying the first fraction by the reciprocal of the second.
Algebraic Common Factors	Terms that can be factored out from multiple expressions.

Unit 5: Percentage

Subtopic	Description
Converting Percentages into Decimals and Fractions	Convert percentages to decimals by dividing by 100. Convert to fractions using the percentage as the numerator and 100 as the denominator.
Converting Decimals and Fractions into Percentages	Convert decimals to percentages by multiplying by 100. Convert fractions to percentages by converting the fraction to a decimal and multiplying by 100.
Expressing One Quantity as a Percentage of Another	Calculate the percentage representation of one quantity compared to another.
Finding a Percentage of a Quantity	Multiply the quantity by the percentage as a decimal to find the portion represented by the percentage.
The Unitary Method for Percentages	Solve percentage problems by finding the value of one unit and scaling it accordingly.
Percentage Increase or Decrease	Measure the change relative to the original value.
Finding a Percentage Change	Calculate the percentage change between two quantities using the percentage increase or decrease formula.
Finding the Original Amount	Calculate the original amount when given the final amount and the percentage change.
Profit and Loss	Calculate profit or loss percentage in a business transaction.
Discount	Determine the discount percentage by finding the reduction from the original price. Express the discount as a percentage of the original price.
VAT and GST	Value Added Tax (VAT) and Goods and Services Tax (GST) are calculated as a percentage of the final price, representing the tax amount.

Unit 6: Laws of Algebra

Subtopic	Description
Exponent Laws	Rules for simplifying expressions with exponents, covering multiplication, division, power of a power, zero exponents, and negative exponents.
Expansion Laws	Techniques for expanding algebraic expressions, especially those with multiple terms, using the distributive law.
The Zero Exponent Law	States that any nonzero number raised to the power of zero is equal to 1.
The Negative Exponent Law	Explains how to handle expressions with negative exponents, involving taking the reciprocal of the base raised to the positive exponent.
The Distributive Law	Fundamental rule explaining how to simplify expressions by distributing a value across terms inside parentheses or brackets.
Factorization	Process of expressing an algebraic expression as a product of its factors, finding common factors and breaking down the expression.

Unit 7: Equations

Subtopic	Description
Solutions of an Equation	Values or expressions that, when substituted into the equation, make it true. Solutions satisfy the equation.
Maintaining Balance	Both sides of an equation must remain equal. Operations on one side should be mirrored on the other to maintain equality.
Inverse Operations	Pairs of operations that “undo” each other, like addition and subtraction, multiplication and division. Essential for solving equations.
Algebraic Flowcharts	Diagrams guiding the step-by-step solution of equations. Visual representations aid in understanding the solving process.
Solving Equations	The process of finding values or expressions that satisfy an equation. It involves simplifying, rearranging, and using inverse operations to isolate the unknown variable.
Equations with a Repeated Unknown	Equations with the same variable appearing multiple times. Solving requires combining like terms and simplifying to isolate the variable.
Power Equations	Equations involving variables raised to specific powers. Solving often requires understanding exponent rules.

Unit 8: Lines and Angles

Subtopic	Description
Angles	Geometric shapes formed by two rays or line segments sharing a common endpoint (vertex).
Parallel and Perpendicular Lines	Parallel lines never intersect and remain equidistant, while perpendicular lines intersect at a 90-degree angle.
Angle Properties	Include different angle relationships and theorems, such as complementary angles (sum up to 90 degrees) and supplementary angles (sum up to 180 degrees).
Lines Cut by a Transversal	When a transversal intersects two parallel lines, it forms various angles like corresponding, alternate interior, and alternate exterior angles.

Unit 9: Plane Geometry

Subtopic	Description
Circles	Closed curved shapes with all points equidistant from a central point called the center.
Triangles	Three-sided polygons with types including equilateral (all sides and angles equal), isosceles (two sides and angles equal), and scalene (no sides or angles equal).
Triangle Theorems	Essential properties and relationships within triangles, such as the Pythagorean theorem and the Law of Sines and Cosines.
Isosceles Triangles	Triangles with two sides and two angles equal. Understanding their properties and related theorems is crucial.
Quadrilaterals	Four-sided polygons, including squares, rectangles, parallelograms, rhombuses, and trapezoids.
Angle Sum of a Quadrilateral	The sum of the interior angles of a quadrilateral is always equal to 360 degrees.
Angle Sum of an n-Sided Polygon	For any n-sided polygon, the sum of its interior angles can be found using the formula (n-2) * 180 degrees.

Unit 10: Algebra: Formulae

Subtopic	Description
Number Crunching Machines	Understanding how calculators and computers perform complex calculations, especially those involving formulas.
Finding the Formula	Determining a mathematical formula or equation that represents a particular relationship, pattern, or set of data.
Substituting into Formulae	Substituting values into given formulas, involving replacing variables with known values to calculate a result.
Geometric Patterns	Analyzing recurring shapes and arrangements in a predictable manner, leading to the discovery of formulas and relationships.
Practical Problems	Using algebraic formulas to solve real-world problems, such as calculating areas, volumes, or other quantities.

Unit 11: Measurement: Length and Area

Subtopic	Description
Length	Measurement of distance between two points, typically in units like meters or inches.
Perimeter	Total length of the boundary or outline of a two-dimensional shape.
Circumference	Distance around the edge of a circle.
Area	Measurement of the space enclosed by a two-dimensional shape, expressed in square units.
Area Formula	Exploring formulas to calculate the area of geometric shapes like rectangles, triangles, parallelograms, and trapezoids.
The Area of a Circle	Area of a circle calculated using the standard formula.
Areas of Composite Figures	Composite figures made up of multiple basic geometric shapes. Finding area involves breaking them down and calculating individual areas.

Unit 12: Measurement: Surface Area, Volume and Capacity

Subtopic	Description
Surface Area	Total area covering the outer surface of a 3D object, measured in square units.
Surface Area of a Cylinder	Calculation involves the sum of areas of two circular bases and the lateral surface.
Surface Area of a Sphere	Finding surface area of the sphere using its standard formula.
Volume	Measurement of space occupied by a 3D object, measured in cubic units.
Volume of a Solid with Uniform Cross-Section	Volume is found by multiplying the area of the cross-section by the length.
Volume of a Tapered Solid	For tapered solids like cones or pyramids.
Volume of a Sphere	Finding volume of the sphere using its standard formula.
Capacity	Amount of space inside a container, used to measure liquid volume (liters or milliliters).
Connecting Volume and Capacity	Examines the relationship between volume and capacity, especially concerning liquid measurement in containers.

Unit 13: Time

Subtopic	Detailed Description
Units of Time	Covers various time units (seconds, minutes, hours, days, etc.) used for measuring time durations.
Time Calculations	Involves adding, subtracting, multiplying, or dividing time durations. Essential for scheduling and time management.
24-Hour Time	Utilizes a 24-hour clock format to express time, eliminating AM and PM.
Time Zones	Different regions on Earth with the same standard time to account for variations. Important for coordinating activities and understanding time differences.

Unit 14: Coordinate Geometry

Subtopic	Detailed Description
The Cartesian Plane	Two-dimensional grid formed by x-axis and y-axis to represent and locate points.
Straight Lines	Fundamental concept where points are connected to form the shortest distance.
Gradient	Measures a line’s steepness, calculated as the change in y over the change in x.
The Gradient-Intercept Form	Represents a line’s equation as y=mx+c y=mx+c using gradient (m) and y-intercept (c).
Graphing a Line from Its Gradient-Intercept Form	Graphing a line using the equation y=mx+c y=mx+c by identifying gradient and y-intercept.
The x-Intercept of a Line	The point where a line crosses the x-axis, with y equal to zero.
Graphing a Line from Its Axes Intercepts	Graphing a line when given both x and y-intercepts.
Finding the Equation from the Graph of a Line	Determining the equation of a line from its graph by identifying gradient and y-intercept.

Unit 15: Ratio

Subtopic	Detailed Description
Ratio	Comparison of two quantities expressed as a fraction (a/b).
Equal Ratios	Ratios that represent the same comparison between quantities.
Lowest Terms	Expressing a ratio in its simplest form by dividing by the greatest common factor.
Proportions	Statements that two ratios are equal (a/b = c/d).
Using Ratios to Divide Quantities	Dividing quantities into parts using ratios (e.g., boys to girls ratio).
Scale Diagrams	Diagrams where measurements are proportionally reduced or enlarged.

Unit 16: Rates and Line Graphs

Subtopic	Detailed Description
Rates	Measures how one quantity changes in relation to another, often over time.
Speed	Indicates how fast an object is moving, usually expressed in distance per time units (e.g., m/s or km/h).
Density	Represents the amount of mass within a given volume (e.g., kg/m³ or g/cm³).
Converting Rates	Involves changing the units of a rate while maintaining its proportional value.
Line Graphs	Graphical representations showing the relationship between two continuous variables over time or another continuous range.

Unit 17: Probability

Subtopic	Description
Probability	Measure of the likelihood of an event occurring, expressed as a number between 0 and 1.
Sample Space	The set of all possible outcomes of a random experiment.
Theoretical Probability	Calculated using the ratio of favorable outcomes to total possible outcomes.
Independent Events	Events where the occurrence of one does not affect the occurrence of the other.
Experimental Probability	Calculated from actual observations or experiments, based on real-world data.
Probabilities from Tabled Data	Finding probabilities from tables, like frequency or contingency tables.
Probabilities from Two-way Tables	Calculating probabilities from data organized in two-way tables.
Probabilities from Venn Diagrams	Determining probabilities using Venn diagrams that represent relationships between sets.
Expectation	A measure of the long-term average value or outcome in probability.

Unit 18: Statistics

Subtopic	Description
Data Collection	Involves gathering information or observations from various sources.
Categorical Data	Consists of distinct categories or groups, representing qualitative characteristics.
Numerical Data	Consists of numbers, measurable quantitatively and analyzed mathematically.
Grouped Data	Organizing numerical data into intervals or groups for simplified analysis.
Stem-and-Leaf Plots	A graphical representation of numerical data, separating data into stems and leaves.
Measures of Centre	Provide a summary of the central or typical value in a dataset.
Measures of Spread	Describe how data points vary and include range, variance, and standard deviation.
Measures from Frequency Table	Summarizing and analyzing data from frequency tables.

Unit 19: Congruence and Similarity

Subtopic	Description
Congruence	Two shapes or objects being identical in shape and size.
Congruent Triangles	Triangles with the same shape and size, proven using criteria like SSS or SAS.
Proof Using Congruence	Demonstrating that corresponding parts of congruent shapes are equal.
Enlargements and Reductions	Transformations changing the size of a shape while preserving its shape.
Similarity	Two shapes having the same shape but different sizes; corresponding angles are equal.
Similar Triangles	Triangles with the same shape but potentially different sizes, proven using criteria like AA or SSS.
Problem Solving	Applying congruence and similarity concepts to solve practical problems.

Unit 20: Pythagoras’ Theorem

Subtopic	Description
Pythagoras’ Theorem	Fundamental principle in geometry stating that in a right-angled triangle, sum of square of altitude and square of base is equal to square of hypotenuse.
Problem Solving	Applying Pythagoras’ theorem to find missing side lengths or solve real-world problems involving right-angled triangles.
The Converse of Pythagoras’ Theorem	States that if the sum of square of altitude and square of base is equal to square of hypotenuse in a triangle, then it is a right-angled triangle.

Unit 21: Problem Solving

Subtopic	Description
Writing Problems as Equations	Involves translating real-world problems into mathematical equations, identifying key information and variables.
Problem Solving with Algebra	Utilizing algebraic equations and expressions to find solutions to various mathematical and real-world problems.
Solution by Search	Problem-solving methods that systematically explore possibilities or test different values to find a solution.
Solutions by Working Backwards	A problem-solving technique where you start with the desired outcome and determine the steps or values leading to that outcome.
Miscellaneous Problems	Covering a variety of miscellaneous problems requiring problem-solving skills, including mathematical or real-world scenarios.
Lateral Thinking	A problem-solving approach that encourages creative thinking and considering alternative perspectives for innovative solutions.

MYP 4

There are a total of 30 units under mathematics MYP 4.

Unit 1: Number

Subtopic	Description
Exponent notation	Exponent notation is a representation of repeated multiplication, written as a^b.
The fundamental theorem of arithmetic	Every positive integer > 1 can be uniquely represented as a product of prime numbers.
Order of operations	Rules (PEMDAS) to determine the sequence of arithmetic calculations.
Absolute value	Absolute value is the magnitude of a number without considering its sign, denoted as

Unit 2: Algebra: Expressions

Subtopic	Description
Algebraic notation	Symbolic language using variables, numbers, and mathematical symbols.
Writing expressions	Translating word problems into algebraic expressions.
Algebraic substitution	Replacing variables with values to simplify algebraic expressions.
The language of Algebra	Set of terms, expressions, equations, and symbols in algebra.
Collecting like terms	Simplifying algebraic expressions by combining similar terms.
Algebraic products	Expressions involving the multiplication of algebraic terms or variables.
Algebraic quotients	Expressions where one algebraic term is divided by another.
Algebraic common factors	Expressions where terms share a common factor that can be factored out.

Unit 3: Exponents

Subtopic	Description
Exponent laws	Rules governing manipulation of expressions with exponents.
Zero and negative exponents	Special cases in exponent notation.
Standard form (scientific notation)	Representing large/small numbers using powers of 10.
International system (SI) units	Modern form of the metric system used for measuring physical quantities.

Unit 4: Algebra: Expansion

Subtopic	Description
The distributive law	Property stating the product of a sum and another expression.
The product (a+b)(c+d)	Expanding the product of two binomials.
The difference between two squares	Factoring the difference between two squares.
The perfect squares expansion	Factoring perfect squares.
Further expansion	Expanding more complex expressions.

Unit 5: Sets

Subtopic	Description
Sets	A collection of well-defined objects.
Complement of a set	The set of all elements not in A.
Intersection and union	Combining elements of two sets.
Special number sets	Commonly used number sets like natural numbers, integers, and real numbers.
Interval notation	Representing sets of numbers on a number line.

Unit 6: Linear equations and inequalities

Subtopic	Description
Linear equations	Equation of the form ax + b = 0, where a and b are constants, and a is not equal to 0.
Equations with fractions	Solving equations with fractions by multiplying both sides by the least common multiple of denominators.
Problem solving	Solving problems by setting up and solving linear equations.
Linear inequalities	Inequality of the form ax + b < 0, ax + b > 0, ax + b ≤ 0, or ax + b ≥ 0, where a and b are constants, a is not equal to 0.
Solving linear inequalities	Steps to solve linear inequalities: add/subtract constant, divide by coefficient, reverse inequality if coefficient is negative, express solution in interval notation.

Unit 7: Venn diagrams

Subtopic	Description
Venn diagrams	A Venn diagram uses overlapping circles to depict relationships between sets.
Venn diagram regions	Venn diagram regions illustrate different combinations of sets. The number of regions is 2^n, where n is the number of sets.
Numbers in regions	Counting rules for elements in Venn diagram regions: elements in a region = sum of elements in constituent sets, overlap = common elements in both sets, empty region always has 0 elements.
Problem solving with Venn diagrams	Venn diagrams can solve counting, probability, and logic problems.

Unit 8: Surds and other radicals

Subtopic	Description
Square roots	Understanding the concept of square roots and their calculation.
Properties of radicals	Properties for simplifying and manipulating radical expressions.
Simplest surd form	Expressing surd expressions in simplest form by removing perfect squares.
Cube and higher roots	Introduction to cube roots and simplifying higher roots using principles.
Power equations	Solving equations involving powers of numbers, such as quadratic equations.
Operations with radicals	Performing addition, subtraction, multiplication, and division with radicals.
Division with surds	Dividing surds using steps like rationalising the denominator.

Unit 9: Pythagoras’ theorem

Subtopic	Description
Pythagoras’ theorem	Fundamental principle in geometry stating that in a right-angled triangle, sum of square of altitude and square of base is equal to square of hypotenuse.
Pythagorean triples	Identifying sets of three positive integers satisfying Pythagoras’ theorem.
Problem solving	Applying Pythagoras’ theorem to find missing side lengths or solve real-world problems involving right-angled triangles.

Unit 10: Formulae

Subtopic	Description
Formula construction	Understanding and creating mathematical expressions (formulae).
Substituting into formulae	Replacing variables in formulae with known values.
Rearranging formulae	Solving problems by rearranging and substituting in formulae.
Rearrangement and substitution	Replacing variables in formulae with known values and solving problems by rearranging and substituting in formulae.

Unit 11: Financial Mathematics

Subtopic	Description
Percentage increase or decrease	A percentage increase or decrease is the amount by which a quantity increases or decreases as a percentage of its original value.
Business calculations	Business calculations involve using mathematical concepts such as percentage, profit and loss, and simple and compound interest to solve problems related to business activities.
Appreciation and depreciation	Appreciation is the increase in the value of an asset over time. Depreciation is the decrease in the value of an asset over time.
Simple interest	Simple interest is calculated by multiplying the principal (amount borrowed or invested), the interest rate, and the time period.
Compound interest	Compound interest is calculated on the principal amount plus the accumulated interest from previous periods.

Unit 12: Measurement: Length and Area

Subtopic	Description
Units of length	Units of length are used to measure the distance between two points.
Perimeter	The perimeter of a shape is the total length of all the sides of the shape.
Units of area	Units of area are used to measure the size of a surface.
Area of polygons	The area of a polygon is the size of the surface enclosed by the polygon.
Area of circles and sectors	The area of a circle is the size of the surface enclosed by the circle. The area of a sector is the size of the surface enclosed by a sector of a circle.

Unit 13: Measurement: Surface Area, Volume and Capacity

Subtopic	Detailed Description
Surface area of a solid with planar faces	The surface area of a solid with planar faces is the total area of all the faces of the solid.
Surface area of a cylinder	The surface area of a cylinder is the total area of the top, bottom, and sides of the cylinder.
Surface area of a cone	The surface area of a cone is the total area of the base and the sides of the cone.
Surface area of a sphere	The surface area of a sphere is the total area of the surface of the sphere.
Units of volume	Units of volume are used to measure the size of a three-dimensional space.
Volume of a solid of uniform cross-section	The volume of a solid of uniform cross-section is the area of the cross-section multiplied by the length of the solid.
Volume of a tapered solid	The volume of a tapered solid is calculated using the following formula:(1/3)(area of larger base + area of smaller base + √(area of larger base x area of smaller base)) x height
Volume of a sphere	The volume of a sphere is the amount of space enclosed by the sphere (4/3)πr³
Capacity	Capacity is the amount of liquid that a container can hold.

Unit 14: Algebra: Factorisation

Subtopic	Detailed Description
Common factors	Factorising by common factors involves finding the greatest common factor (GCD) of all the terms in the expression and then factoring it out. The greatest common factor (GCD) of two or more numbers is the largest number that is a factor of all the numbers.
Difference between two squares factorisation	Factorising the difference between two squares using a^2 – b^2 = (a + b)(a – b)
Factoring x^2+bx+c	Factorising using (a + b)^2 = a^2 + 2ab + b^2
Miscellaneous factorisation	There are a number of other methods that can be used to factorise expressions. Mostly the method of factorisation to be used is not mentioned and students have to choose one that suits the question on the basis of prior knowledge and practice.
Expressing with four terms	To factorise an expression with four terms, we can use the following steps: Find two common factors, one of which is linear and the other of which is quadratic. Factor out the common factors. Factor the quadratic expression.
Factorising ax^2+bx+c. a is not equal to 1	To factorise an expression of the form ax^2 + bx + c, where a ̸= 1, we can use the following steps: Divide the expression by a. Factor the resulting expression using the methods described above. Multiply the factored expression by a.

Unit 15: Algebraic fractions

Subtopic	Detailed Description
Evaluating algebraic fractions	Evaluating an algebraic fraction involves substituting values for the variables in the fraction and then simplifying.
Simplifying algebraic fractions	Simplifying an algebraic fraction involves finding the greatest common factor (GCD) of the numerator and denominator and then factoring it out.
Multiplying algebraic fractions	Multiplying algebraic fractions involves multiplying the numerators and the denominators.
Dividing algebraic fractions	Dividing algebraic fractions involves inverting the divisor and then multiplying.
Adding and subtracting algebraic fractions	To add or subtract algebraic fractions with different denominators, we first need to find a common denominator. This can be done by finding the least common multiple (LCM) of the denominators. Once we have found the common denominator, we can then add or subtract the numerators and simplify the fraction.

Unit 16: Coordinate Geometry

Subtopic	Detailed Description
The distance between two points	Calculating the distance between two points using the distance formula.
Midpoints	Finding the midpoint of a line segment using the midpoint formula.
Gradient	Understanding the concept of the gradient (slope) of a line.
Parallel and perpendicular lines	Identifying relationships between lines.
Using coordinate geometry	Graphical representations showing the relationship between two continuous variables over time or another continuous range.

Unit 17: Straight lines

Subtopic	Description
Vertical and horizontal lines	A vertical line is a line that is parallel to the y-axis. A horizontal line is a line that is parallel to the x-axis.
Points on a line	A point is on a line if its coordinates satisfy the equation of the line.
Axes intercepts	The x-intercept of a line is the point where the line crosses the x-axis. The y-intercept of a line is the point where the line crosses the y-axis.
Graphing from a table of values	To graph a line from a table of values, we simply plot the points in the table and then connect them with a line.
Gradient-intercept form	The gradient-intercept form of the equation of a line is of the form y = mx + b, where m is the gradient of the line and b is the y-intercept of the line.
General form	The general form of the equation of a line is of the form Ax + By + C = 0, where A, B, and C are constants.
Find the equation of a line	There are a few different ways to find the equation of a line, depending on the information that is given.

Unit 18: Simultaneous Equations

Subtopic	Description
Solution by trial and error	The solution by trial and error method is a simple method for solving simultaneous equations. It involves substituting different values for the variables until we find a combination of values that satisfies both equations.
Graphical solution	The graphical solution method involves plotting the graphs of both equations and finding the point of intersection of the two graphs. The point of intersection is the solution to the simultaneous equations.
Solution by equating values of y	The solution by equating values of y method involves solving both equations for y and then equating the two expressions for y. The solution to the simultaneous equations is the value of x that satisfies both equations.
Solution by substitution	The solution by substitution method involves solving one of the equations for one of the variables and then substituting the expression for the variable into the other equation. The solution to the simultaneous equations is the value of the other variable.
Solution by elimination	The solution by elimination method involves eliminating one of the variables from the two equations and then solving the remaining equation for the other variable. The solution to the simultaneous equations is the value of the variable that satisfies both equations.
Problem solving	Simultaneous equations can be used to solve a variety of real-world problems. For example, we can use simultaneous equations to find the distance between two points, the price of two items, or the number of people in two groups.

Unit 19: Transformation Geometry

Subtopic	Description
Translations	A translation is a transformation that moves every point on a shape by the same distance in the same direction.
Reflections	A reflection is a transformation that flips a shape over a line of reflection.
Rotations	A rotation is a transformation that turns a shape about a centre of rotation.
Enlargements and reductions	An enlargement is a transformation that makes a shape bigger or smaller. A reduction is a transformation that makes a shape smaller.
Stretches	A stretch is a transformation that makes a shape longer or shorter in one direction.
Combinations of transformations	Transformations can be combined to create more complex transformations. For example, we can translate a shape, then rotate it, and then enlarge it.

Unit 20: Quadratic equations

Subtopic	Description
Quadratic equations	A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Equations of the form x^2=k	Equations of the form x^2 = k can be solved by taking the square root of both sides.
The null factor law	The null factor law states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
Solution by factorisation	To solve a quadratic equation by factorisation, we first try to factor the expression on the left-hand side of the equation. If we can factor the expression into two linear factors, then we can solve the equation by setting each factor equal to zero.
Problem solving	Quadratic equations can be used to solve a variety of real-world problems. For example, we can use quadratic equations to find the distance travelled by a projectile, the area of a triangle, or the volume of a sphere.
Completing the square	Completing the square is a method that can be used to solve any quadratic equation. It involves adding a constant term to both sides of the equation in order to create a perfect square trinomial on the left-hand side of the equation. Once we have created a perfect square trinomial, we can solve the equation by taking the square root of both sides.

Unit 21: Quadratic Functions

Subtopic	Description
Quadratic functions	A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Graphs of quadratic functions	The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that is symmetrical about its axis of symmetry. Subtopic: Using transformations to graph quadratics
Using transformations to graph quadratics	Transformations can be used to graph quadratic functions. For example, we can translate a parabola up, down, left, or right. We can also stretch or compress a parabola vertically or horizontally.
Axes intercepts	The x-intercepts of a quadratic function are the points where the graph of the function crosses the x-axis. The y-intercept of a quadratic function is the point where the graph of the function crosses the y-axis.
Using axes intercepts to graph quadratics	We can use the axes intercepts to graph a quadratic function. To do this, we plot the axes intercepts on the graph and then sketch the parabola so that it passes through the axes intercepts.
Projectile motion	Projectile motion is the motion of an object that is thrown or launched into the air. The path of a projectile is a parabola.

Unit 22: Congruence and Similarity

Subtopic	Description
Congruence	Congruence is a relationship between two shapes that are exactly the same size and shape.
Congruent triangles	Two triangles are congruent if they satisfy any of the following conditions: Side-Side-Side (SSS): If all three corresponding sides of the two triangles are equal, then the two triangles are congruent. Side-Angle-Side (SAS): If two corresponding sides of the two triangles are equal and the angle between the two sides is equal, then the two triangles are congruent. Angle-Side-Angle (ASA): If two corresponding angles of the two triangles are equal and the side between the two angles is equal, then the two triangles are congruent. Right Angle-Hypotenuse-Side (RHS): If two right triangles have equal hypotenuses and one side of each triangle is equal, then the two triangles are congruent.
Similarity	Similarity is a relationship between two shapes that have the same shape but not necessarily the same size.
Similar triangles	Two triangles are similar if they satisfy any of the following conditions: Angle-Angle (AA): If two corresponding angles of the two triangles are equal, then the two triangles are similar. Side-Side-Side (SSS): If all three corresponding sides of the two triangles are proportional, then the two triangles are similar. Side-Angle-Side (SAS): If two corresponding sides of the two triangles are proportional and the angle between the two sides is equal, then the two triangles are similar. E. Areas of similar figures
Area of similar triangles	The areas of two similar figures are proportional to the square of any corresponding side lengths.
Volume of similar solids	The volumes of two similar solids are proportional to the cube of any corresponding side lengths.

Unit 23: Trigonometry

Subtopic	Description
Scale diagrams in geometry	Mathematical diagrams that are similar to real objects and its accurate enlarged visuals with scaled lengths.
Labelling right-angled triangles	Applying trigonometric ratios to find missing angles and sides.
The trigonometric ratios	Introduction to sine, cosine, and tangent ratios in a right-angled triangle.
Finding side lengths	Solving problems involving length of sides.
Finding angles	Solving problems involving angles.
Problem solving	Problem solving using basic rules of trigonometry and ratios.
Bearings	Understanding and using bearings in navigation.

Unit 24: Deductive Geometry

Subtopic	Description
Deductive geometry	Deductive geometry is a type of mathematics that uses logic to prove theorems. A theorem is a statement that can be proven to be true using the definitions, axioms, and postulates of geometry.
Midpoint theorem	The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half of the length of the third side.
Angle in a semicircle theorem	A semicircle is half of a circle. The angle in a semi-circle theorem states that an angle inscribed in a semicircle is a right angle.
Chords of a circle theorem	A chord of a circle is a line segment that has both of its endpoints on the circle. The chords of a circle theorem states that two chords of a circle that intersect inside the circle intersect at right angles.
Radius-tangent theorem	A tangent to a circle is a line that intersects the circle at exactly one point. The radius-tangent theorem states that a radius drawn to a point of tangency is perpendicular to the tangent at that point.
Tangents from an external point theorem	An external point is a point that is not on the circle. The tangents from an external point theorem states that from any external point to a circle, there are exactly two tangents.

Unit 25: Proportion

Subtopic	Detailed Description
Direct proportion	Two quantities are said to be in direct proportion if they increase or decrease at the same rate.
Powers in direct proportion	If two quantities are in direct proportion and one of the quantities is raised to a power, then the other quantity is also raised to the same power.
Inverse proportion	Two quantities are said to be in inverse proportion if one quantity increases as the other decreases and vice versa.
Powers in inverse proportion	If two quantities are in inverse proportion and one of the quantities is raised to a power, then the other quantity is raised to the negative of the same power.

Unit 26: Probability

Subtopic	Detailed Description
Sample space and events	A sample space is the set of all possible outcomes of an experiment. An event is a subset of the sample space.
Theoretical probability	Theoretical probability is the probability of an event happening based on the number of possible outcomes in the sample space and the number of favourable outcomes.
Probabilities from Venn diagrams	A Venn diagram is a diagram that can be used to represent the relationships between different events.
Independent events	Independent events are events that do not affect each other.
Dependent events	When the occurrence of one event affects the occurrence of another, they are said to be dependent.
Probabilities from tree diagrams	A tree diagram is a diagram that can be used to represent the different possible outcomes of an experiment.
Experimental probability	Based on the actual event and the number of times an experiment is repeated to calculate its probability.
Probabilities from tabled data	A table is used to showcase the values of the variables and their frequencies, which is in turn used to calculate probability of events.
Expectation	If an experiment has n number of trials and the probability of a single event is p, then the expected occurrence of the event is, number of trials*probability.

Unit 27: Statistics

Subtopic	Detailed Description
Types of data	Data can be classified into two main types: qualitative and quantitative. Qualitative data is data that describes something, such as eye colour or hair colour. Quantitative data is data that measures something, such as height or weight.
Discrete numerical data	Discrete numerical data is data that can only take on certain values. For example, the number of students in a class is discrete numerical data, because there can only be a whole number of students in a class.
Continuous numerical data	Continuous numerical data is data that can take on any value within a range. For example, the height of a student is continuous numerical data, because there can be any height between 0 cm and 200 cm.
Describing the distribution of data	The distribution of data is how the data is spread out. There are several ways to describe the distribution of data, such as using histograms, cumulative frequency graphs, and box plots.
Measures of centre	Measures of centre are used to describe the central tendency of a data set. There are several measures of centre, such as the mean, median, and mode.
Cumulative frequency graphs	A cumulative frequency graph is a graph that shows the number of data points that are less than or equal to a certain value.
Measures of spread	Measures of spread are used to describe how spread out the data is. There are several measures of spread, such as the range, interquartile range, and standard deviation.
Box plots	A box plot is a graph that shows the median, quartiles, and outliers of a data set.
Comparing numerical data	There are several ways to compare numerical data, such as using scatter plots and box plots.

Unit 28: Networks

Subtopic	Detailed Description
Networks	A network is a set of objects that are connected to each other in some way. The objects in a network are called nodes, and the connections between the objects are called edges.
Routes on networks	A route on a network is a path that starts at one node and ends at another node.
Shortest route problems	A shortest route problem is the problem of finding the shortest route between two nodes in a network.
Eulerian networks	An Eulerian network is a network in which it is possible to trace a route that visits every edge exactly once.

Unit 29: Non-right angled trigonometry

Subtopic	Description
Trigonometry with obtuse angles	Trigonometry can also be used to solve non-right angled triangles. In a non-right angled triangle, one of the angles is greater than 90 degrees.
Area of a triangle	The area of a triangle can be calculated using the following formula: Area of a triangle = 1/2 * base * height
Sine rule	The sine rule is a rule that can be used to solve any triangle, given the length of one side and the measure of two angles.
Cosine rule	The cosine rule is a rule that can be used to solve any triangle, given the lengths of two sides and the measure of the angle between them.
Problem solving	Trigonometry can be used to solve a variety of real-world problems. For example, trigonometry can be used to find the distance to an object, the height of a building, or the angle of elevation of the sun.

Unit 30: Mathematical logic

Subtopic	Description
Propositions	A proposition is a statement that is either true or false.
Compound propositions	A compound proposition is a proposition that is formed by combining two or more propositions using logical connectives.
Implication	An implication is a compound proposition of the form “If P, then Q.” It is true if Q is true whenever P is true.
Equivalence	An equivalence is a compound proposition of the form “P if and only if Q.” It is true if P and Q are both true or both false.
Constructing truth tables	A truth table is a table that shows the truth value of a compound proposition for all possible combinations of truth values of the simple propositions that make up the compound proposition.
Tautology and logical contradiction	A tautology is a compound proposition that is always true, regardless of the truth values of the simple propositions that make up the compound proposition. A logical contradiction is a compound proposition that is always false, regardless of the truth values of the simple propositions that make up the compound proposition.
Logical equivalence	Two compound propositions are logically equivalent if they have the same truth value for all possible combinations of truth values of the simple propositions that make up the compound propositions.

Also Read: Comprehensive IB English SL & HL Syllabus

MYP 5

There are a total of 27 units under mathematics MYP 5.

Unit 1: Exponents

Subtopic	Description
Exponent laws	Rules governing manipulation of expressions with exponents.
Standard form (scientific notation)	Representing large/small numbers using powers of 10.

Unit 2: Algebra: Expansion

Subtopic	Description
The distributive law	Property stating the product of a sum and another expression.
The product (a+b)(c+d)	Expanding the product of two binomials.
The difference between two squares	Factoring the difference between two squares.
The perfect squares expansion	Factoring perfect squares.
Further expansion	Expanding more complex expressions.
Binomial expansion	Explains how a binomial’s powers expand algebraically.

Unit 3: Algebra: Factorisation

Subtopic	Description
Common factors	Factorising by common factors involves finding the greatest common factor (GCD) of all the terms in the expression and then factoring it out. The greatest common factor (GCD) of two or more numbers is the largest number that is a factor of all the numbers.
Difference between two squares factorisation	Factorising the difference between two squares using a^2 – b^2 = (a + b)(a – b)
Perfect squares factorisation	Two phrases, like (a + b)^2, are used to represent the perfect square formula. The perfect square formula can be expanded as follows: (a + b)^2 = a^2 + 2ab + b^2.
Factorising x^2+bx+c	Factorising using (a + b)^2 = a^2 + 2ab + b^2
Miscellaneous factorisation	To factorise an expression of the form ax^2 + bx + c, where a ̸= 1, we can use the following steps: Divide the expression by a. Factor the resulting expression using the methods described above. Multiply the factored expression by a.
Factoring ax^2+bx+c, a is not equal to 1	Factorising using (a + b)^2 = a^2 + 2ab + b^2

Unit 4: Sets

Subtopic	Description
Sets	A collection of well-defined objects.
Complement of a set	The set of all elements not in A.
Intersection and union	Combining elements of two sets.
Special number sets	Commonly used number sets like natural numbers, integers, and real numbers.
Interval notation	Representing sets of numbers on a number line.

Unit 5: Linear equations and inequalities

Subtopic	Description
Linear equations	Equation of the form ax + b = 0, where a and b are constants, and a is not equal to 0.
Problem solving with equations	Solving problems by setting up and solving linear equations.
Linear inequalities	Inequality of the form ax + b < 0, ax + b > 0, ax + b ≤ 0, or ax + b ≥ 0, where a and b are constants, a is not equal to 0.
Problem solving with linear inequalities	Solving linear equations and linear inequalities in two variables can be done in the same way.

Unit 6: Venn diagrams

Subtopic	Description
Venn diagrams	A Venn diagram uses overlapping circles to depict relationships between sets.
Venn diagram regions	Venn diagram regions illustrate different combinations of sets. The number of regions is 2^n, where n is the number of sets.
Numbers in regions	Counting rules for elements in Venn diagram regions: elements in a region = sum of elements in constituent sets, overlap = common elements in both sets, empty region always has 0 elements.
Problem solving with Venn diagrams	Venn diagrams can solve counting, probability, and logic problems.

Unit 7: Surds and other radicals

Subtopic	Description
Radicals	An expression containing a square root.
Properties of radicals	Properties for simplifying and manipulating radical expressions.
Simplest surd form	Expressing surd expressions in simplest form by removing perfect squares.
Power equations	Solving equations involving powers of numbers, such as quadratic equations.
Operations with radicals	Performing addition, subtraction, multiplication, and division with radicals.
Division with surds	Dividing surds using steps like rationalising the denominator.

Unit 8: Pythagoras’ Theorem

Subtopic	Description
Pythagoras’ theorem	Fundamental principle in geometry stating that in a right-angled triangle, sum of square of altitude and square of base is equal to square of hypotenuse.
Pythagorean triples	Identifying sets of three positive integers satisfying Pythagoras’ theorem.
Problem solving	Applying Pythagoras’ theorem to find missing side lengths or solve real-world problems involving right-angled triangles.
Converse of pythagoras’ theorem	When the sum of square of altitude and square of base is equal to square of hypotenuse, the triangle is considered to be right-angled.

Unit 9: Algebraic fractions

Subtopic	Description
Evaluating algebraic fractions	Evaluating an algebraic fraction involves substituting values for the variables in the fraction and then simplifying.
Simplifying algebraic fractions	Simplifying an algebraic fraction involves finding the greatest common factor (GCD) of the numerator and denominator and then factoring it out.
Multiplying algebraic fractions	Multiplying algebraic fractions involves multiplying the numerators and the denominators.
Dividing algebraic fractions	Dividing algebraic fractions involves inverting the divisor and then multiplying.

Unit 10: Formulae

Subtopic	Description
Formula construction	Understanding and creating mathematical expressions (formulae).
Substituting into formulae	Replacing variables in formulae with known values.
Rearranging formulae	Solving problems by rearranging and substituting in formulae.
Rearrangement and substitution	Replacing variables in formulae with known values and solving problems by rearranging and substituting in formulae.

Unit 11: Measurement

Subtopic	Description
Length and perimeter	Units of length are used to measure the distance between two points. The perimeter of a shape is the total length of all the sides of the shape.
Area	Area of a flat figure, is the amount of space it encloses within.
Surface area	Total surface area of a solid is the total area of all faces of the solid, top, bottom sides etc.
Volume	Volume is the amount of a space a 3d object encloses within it.
Capacity	Capacity is the amount of liquid that a container can hold.

Unit 12: Quadratic Equations

Subtopic	Description
Equations of the form x^2=k	Equations of the form x^2 = k can be solved by taking the square root of both sides.
The null factor law	The null factor law states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
Solution by factorisation	To solve a quadratic equation by factorisation, we first try to factor the expression on the left-hand side of the equation. If we can factor the expression into two linear factors, then we can solve the equation by setting each factor equal to zero.
Completing the square	Completing the square is a method that can be used to solve any quadratic equation. It involves adding a constant term to both sides of the equation in order to create a perfect square trinomial on the left-hand side of the equation. Once we have created a perfect square trinomial, we can solve the equation by taking the square root of both sides.
The quadratic formula	In some questions where it is difficult or time-consuming to use the method of factoring or completing the square, one can use the quadratic formula to find the solution of a quadratic equation. The quadratic formula,
Problem solving	Quadratic equations can be used to solve a variety of real-world problems. For example, we can use quadratic equations to find the distance travelled by a projectile, the area of a triangle, or the volume of a sphere.

Unit 13: Coordinate Geometry

Subtopic	Detailed Description
The distance between two points	Calculating the distance between two points using the distance formula.
Midpoints	Finding the midpoint of a line segment using the midpoint formula.
Gradient	Understanding the concept of the gradient (slope) of a line.
Parallel and perpendicular lines	Identifying relationships between lines.
Using coordinate geometry	Graphical representations showing the relationship between two continuous variables over time or another continuous range.
The equation of a line	The common relationship between the x and y coordinates of a point on the line is referred to as the equation of a line. The equation of a line can be either written in gradient-intercept form or general form.
Graphing straight lines	Using graphs to show straight lines.
Finding the equation of a line	There are a few different ways to find the equation of a line, depending on the information that is given.
Perpendicular bisectors	When one line intersects another line at an angle of 90 degrees and bisects it into two equal parts, it is known as the perpendicular bisector.
3-dimensional coordinate geometry	Cartesian geometry.

Unit 18: Simultaneous equations

Subtopic	Description
Graphical solution	The graphical solution method involves plotting the graphs of both equations and finding the point of intersection of the two graphs. The point of intersection is the solution to the simultaneous equations.
Solution by substitution	The solution by substitution method involves solving one of the equations for one of the variables and then substituting the expression for the variable into the other equation. The solution to the simultaneous equations is the value of the other variable.
Solution by elimination	The solution by elimination method involves eliminating one of the variables from the two equations and then solving the remaining equation for the other variable. The solution to the simultaneous equations is the value of the variable that satisfies both equations.
Problem solving	Simultaneous equations can be used to solve a variety of real-world problems. For example, we can use simultaneous equations to find the distance between two points, the price of two items, or the number of people in two groups.
Non-linear simultaneous equations	Two or more equations that are being solved simultaneously, at least one of which is not linear, are referred to as a system of nonlinear equations.

Unit 15: Congruence and Similarity

Subtopic	Description
Congruent triangles	Congruence is a relationship between two shapes that are exactly the same size and shape. Two triangles are congruent when they are completely same in size and shape.
Proof using congruence	Two triangles are congruent if they satisfy any of the following conditions: Side-Side-Side (SSS): If all three corresponding sides of the two triangles are equal, then the two triangles are congruent. Side-Angle-Side (SAS): If two corresponding sides of the two triangles are equal and the angle between the two sides is equal, then the two triangles are congruent. Angle-Side-Angle (ASA): If two corresponding angles of the two triangles are equal and the side between the two angles is equal, then the two triangles are congruent. Right Angle-Hypotenuse-Side (RHS): If two right triangles have equal hypotenuses and one side of each triangle is equal, then the two triangles are congruent.
Similar triangles	Two triangles are similar if they satisfy any of the following conditions: Angle-Angle (AA): If two corresponding angles of the two triangles are equal, then the two triangles are similar. Side-Side-Side (SSS): If all three corresponding sides of the two triangles are proportional, then the two triangles are similar. Side-Angle-Side (SAS): If two corresponding sides of the two triangles are proportional and the angle between the two sides is equal, then the two triangles are similar. E. Areas of similar figures
Areas and volumes of similar triangles	The areas of two similar figures are proportional to the square of any corresponding side lengths. The volumes of two similar solids are proportional to the cube of any corresponding side lengths.

Unit 16: Circle geometry

Subtopic	Description
Angle in a semicircle theorem	A semicircle is half of a circle. The angle in a semi-circle theorem states that an angle inscribed in a semicircle is a right angle.
Chords of a circle theorem	A chord of a circle is a line segment that has both of its endpoints on the circle. The chords of a circle theorem states that two chords of a circle that intersect inside the circle intersect at right angles.
Radius-tangent theorem	A tangent to a circle is a line that intersects the circle at exactly one point. The radius-tangent theorem states that a radius drawn to a point of tangency is perpendicular to the tangent at that point.
Tangents from an external point theorem	An external point is a point that is not on the circle. The tangents from an external point theorem states that from any external point to a circle, there are exactly two tangents.
Angle between a tangent and a chord theorem	Among the circle theorems is the alternate segment theorem. According to the theorem, “For any circle, the angle formed by the chord in the alternate segment is equal to the angle formed between the tangent and the chord through the point of contact of the tangent.”
Angle at the centre theorem	A circle’s center angle is twice that of its circumference angle.
Angles subtended by the same arc theorem	The angle at a circle’s center is twice that of its circumference when two angles are subtended by the same arc.
Cyclic quadrilaterals	A four-sided shape that may be engraved into a circle is called a cyclic quadrilateral.
Tests for cyclic quadrilaterals	Opposite angles are supplementary.

Unit 17: Trigonometry

Subtopic	Description
Labelling right-angled triangles	Applying trigonometric ratios to find missing angles and sides.
The trigonometric ratios	Introduction to sine, cosine, and tangent ratios in a right-angled triangle.
Finding side lengths	Solving problems involving length of sides.
Finding angles	Solving problems involving angles.
Problem solving	Problem solving using basic rules of trigonometry and ratios.
True Bearings	Understanding and using bearings in navigation.

Unit 18: Non-right angled trigonometry

Subtopic	Description
Trigonometry with obtuse angles	Trigonometry can also be used to solve non-right angled triangles. In a non-right angled triangle, one of the angles is greater than 90 degrees.
Area of a triangle	The area of a triangle can be calculated using the following formula: Area of a triangle = 1/2 * base * height
Sine rule	The sine rule is a rule that can be used to solve any triangle, given the length of one side and the measure of two angles.
Cosine rule	The cosine rule is a rule that can be used to solve any triangle, given the lengths of two sides and the measure of the angle between them.
Problem solving	Trigonometry can be used to solve a variety of real-world problems. For example, trigonometry can be used to find the distance to an object, the height of a building, or the angle of elevation of the sun.

Unit 19: Probability

Subtopic	Detailed Description
Sample space and events	A sample space is the set of all possible outcomes of an experiment. An event is a subset of the sample space.
Theoretical probability	Theoretical probability is the probability of an event happening based on the number of possible outcomes in the sample space and the number of favourable outcomes.
The addition law of probability	It is easy to determine the likelihood of either of the two occurrences happening by summing the probabilities of each event and then subtracting the probabilities of both events happening: P(A) + P(B) – P(A and B) equals P(A or B).
Independent events	Independent events are events that do not affect each other.
Dependent events	When the occurrence of one event affects the occurrence of another, they are said to be dependent.
Experimental probability	Based on the actual event and the number of times an experiment is repeated to calculate its probability.
Expectation	If an experiment has n number of trials and the probability of a single event is p, then the expected occurrence of the event is, number of trials*probability.
Conditional probability	The likelihood that an event (A) will occur in light of the occurrence of another event (B) is known as conditional probability.

Unit 20: Statistics

Subtopic	Detailed Description
Discrete numerical data	Discrete numerical data is data that can only take on certain values. For example, the number of students in a class is discrete numerical data, because there can only be a whole number of students in a class.
Continuous numerical data	Continuous numerical data is data that can take on any value within a range. For example, the height of a student is continuous numerical data, because there can be any height between 0 cm and 200 cm.
Describing the distribution of data	The distribution of data is how the data is spread out. There are several ways to describe the distribution of data, such as using histograms, cumulative frequency graphs, and box plots.
Measures of centre	Measures of centre are used to describe the central tendency of a data set. There are several measures of centre, such as the mean, median, and mode.
Box plots	A box plot is a graph that shows the median, quartiles, and outliers of a data set.
Cumulative frequency graphs	A cumulative frequency graph is a graph that shows the number of data points that are less than or equal to a certain value.

Unit 21: Bivariate Statistics

Subtopic	Detailed Description
Scatter graphs	Dots are used in scatter graphs to show the values of two distinct numerical variables. The values for each individual data point are indicated by the position of each dot on the horizontal and vertical axes. Relationships between variables are observed through the use of scatter plots.
Correlation	Dependence in a statistical relationship between two variables.
Pearson’s correlation coefficient r	A way to measure linear correlation.
Line of best fit by eye	In a scatter plot of various data points, a relationship is expressed by the line of best fit.
Linear regression	A variable’s value can be predicted using linear regression analysis based on the value of another variable.

Unit 22: Relations and Functions

Subtopic	Description
Relations and functions	The relationship between input and output is displayed by the relation. Whereas, a function is a relation which derives one output for each given input. Not every relation is a function, but every function is a relation.
Function notation	Defines function.
Domain and range	The domain of a graph is made up of all the input values displayed on the x-axis since the term “domain” refers to the set of possible input values. The collection of potential output values that are displayed on the y-axis is known as the range.
Sign diagrams	The intervals when a function produces positive or negative outputs are displayed on a sign diagram.
Transformation of graphs	The process of altering an existing graph, or graphed equation, to create a different graph from the one that came before it is known as graph transformation.

Unit 23: Quadratic functions

Subtopic	Description
Quadratic functions	A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Graphs of quadratic functions	The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that is symmetrical about its axis of symmetry. Subtopic: Using transformations to graph quadratics
Using transformations to graph quadratics	Transformations can be used to graph quadratic functions. For example, we can translate a parabola up, down, left, or right. We can also stretch or compress a parabola vertically or horizontally.
Axes intercepts	The x-intercepts of a quadratic function are the points where the graph of the function crosses the x-axis. The y-intercept of a quadratic function is the point where the graph of the function crosses the y-axis.
Axis of symmetry of a quadratic	The parabola and associated axis of symmetry that arise from graphing a quadratic function in the coordinate plane are vertical.
Vertex of a quadratic	Finding vertex.
Finding a quadratic function	Quadratic formula and other ways to find quadratic function.
Problem solving	Application based questions for quadratic function.

Unit 24: Number sequences

Subtopic	Detailed Description
Number sequences	A sequence is a list of numbers that follow a specific pattern.
Arithmetic sequences	In an arithmetic sequence, the terms have a common difference between them which can be either added or subtracted.
Geometric sequences	In a geometric sequence, the terms have a common ratio between them which can be either divided or multiplied.
Sequences in finance	The progression of the investment’s value over time.

Unit 25: Exponentials

Subtopic	Detailed Description
Exponential functions	An exponential function is a function in the form f (x) = a^x.
Graphs of exponential functions	Graphs representing function in the form f (x) = a^x.
Exponential equations	An equation with a variable in the exponent position is clearly identified as an exponential equation.
Exponential decay	When something depletes at a pace proportionate to its remaining quantity, it is said to be experiencing exponential decay.

Unit 26: Differential calculus

Subtopic	Detailed Description
Limits	The values at which a function approaches the output for a given set of input values are known as limits in mathematics.
Finding the gradient of a tangent	Finding gradient using gradient formula.
The derivative function	Represents the function’s rate of change.
Differentiation from first principles	Differentiation.
Rules for differentiation	Product rule Quotient rule
Finding the equation of a tangent	Equation of tangent.
Stationary points	Derivative of the function is 0.

Unit 27: Integration

Subtopic	Description
The area under a curve	Finding area under curve.
Integration	Calculating integral.
Rules for integration	Mathematical rules to solve integral problems.
The definite integral	Fixed value in a curve within two given limits.
The Riemann integral	Used for practical applications and functions. It is a definite integral.

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