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  • Welcome to the CP Subject Centre
  • Faria Education Group
  • Core
    • Service Learning
    • Language Development
    • Reflective Project
    • Personal and Professional Skills
  • Career-related Study
  • Studies in language and literature
    • Language and Literature
      • Aims & Objectives
      • Syllabus
        • Area of Exploration - Readers, Writers and Texts
        • Area of Exploration - Time and Space
        • Area of Exploration - Intertextuality: Connecting Texts
        • Development of Linguistic Skills
        • Conceptual Understanding
        • Non-Literary Texts
      • Assessment
    • Literature
      • Aims and Objectives
      • Syllabus
        • Areas of Exploration
        • Development of Linguistic Skills
        • Conceptual Understanding
      • Assessment
    • Classical Languages (Last Assessment 2023)
      • Aims & Objectives
      • Syllabus
        • Part 1: Study of Language
        • Part 2: Study of Literature
        • Part 3: Individual study
      • Assessment
    • Classical Languages (First Assessment 2024)
    • Literature and Performance (First Assessment 2024)
  • Language acquisition
    • Language Ab Initio
      • Aims & Objectives
      • Syllabus
        • Identities
        • Experiences
        • Human Ingenuity
        • Social Organization
        • Sharing the Planet
        • Texts
      • Assessment
    • Language B
      • Aims & Objectives
      • Syllabus
        • Identities
        • Experiences
        • Human Ingenuitiy
        • Social Organization
        • Sharing the Planet
        • Texts
      • Assessment
  • Individuals and societies
    • Business Management (Last Assessment 2023)
      • Aims & Objectives
      • Syllabus
        • Unit 1: Business Organization and Environment
        • Unit 2: Human Resource Management
        • Unit 3: Finance and Accounts
        • Unit 4: Marketing
        • Unit 5: Operations Management
      • Assessment
    • Business Management (First Assessment 2024)
    • Digital Society
    • Economics
      • Aims & Objectives
      • Syllabus
        • Unit 1: Introduction to Economics
        • Unit 2: Microeconomics
          • Real-world issue 1
          • Real-world issue 2
        • Unit 3: Macroeconomics
          • Real-world issue 1
          • Real-world issue 2
        • Unit 4: The Global Economy
          • Real-world issue 1
          • Real-world issue 2
      • Assessment
    • Geography
      • Aims & Objectives
      • Syllabus
        • Part one: Geographic themes (SL and HL options)
          • Option A: Freshwater
          • Option B: Oceans and coastal margins
          • Option C: Extreme environments
          • Option D: Geophysical hazards
          • Option E: Leisure, tourism and sport
          • Option F: Food and health
          • Option G: Urban environments
        • Part two: Geographic perspectives - global change (SL and HL core)
          • Unit 1: Changing population
          • Unit 2: Global climate - vulnerability and resilience
          • Unit 3: Global resource consumption and security
        • Part two: Geographic perspectives - global change (HL core extension)
          • Unit 4: Power, places and networks
          • Unit 5: Human development and diversity
          • Unit 6: Global risks and resilience
      • Assessment
    • Global Politics
      • Aims & Objectives
      • Syllabus
        • Engagement Activity
        • Core
        • Additional Higher Level
      • Assessment
    • History
      • Aims & Objectives
      • Syllabus
        • Prescribed Subjects
        • World History Topics
        • HL Options: Depth Studies - History of Africa and the Middle East
        • HL Options: Depth Studies - History of the Americas
        • HL Options: Depth Studies - History of Asia and Oceania
        • HL Options: Depth Studies - History of Europe
      • Assessment
    • Information Technology in a Global Society
      • Aims & Objectives
      • Syllabus
        • Strand 1: Social and Ethical Significance
        • Strand 2: Application to Specific Scenarios
        • Strand 3: IT Systems
        • The Project (practical application of IT skills)
      • Assessment
    • Philosophy
      • Aims & Objectives
      • Syllabus
        • Prescribed Texts
        • Core
        • Additional Higher Level
        • Options
      • Assessment
    • Psychology
      • Aims & Objectives
      • Syllabus
        • Core
          • Biological approach to understanding behaviour
          • Cognitive approach to understanding behaviour
          • Sociocultural approach to understanding behaviour
          • Approaches to researching behaviour
        • Options
          • Abnormal psychology
          • Developmental psychology
          • Health psychology
          • Psychology of human relationships
      • Assessment
    • Social and Cultural Anthropology
      • Aims & Objectives
      • Syllabus
        • Part 1: Engaging with Anthropology
          • The language of anthropology
          • The practice of anthropology
          • Anthropological thinking
        • Part 2: Engaging with Ethnography
          • Group 1
          • Group 2
          • Group 3
        • Part 3: Engaging with Anthropological Practice
      • Assessment
    • World Religions
      • Aims & Objectives
      • Syllabus
        • Part 1: Introduction to World Religions
        • Part 2: In-depth Studies
        • Part 3: Internal Assessment
      • Assessment
  • Sciences
    • Biology (FA 2025)
    • Biology (LA 2024)
      • Aims & Objectives
      • Syllabus
        • Core
          • 1. Cell biology
          • 2. Molecular biology
          • 3. Genetics
          • 4. Ecology
          • 5. Evolution and biodiversity
          • 6. Human physiology
        • Additional Higher Level
          • 7. Nucleic acids
          • 8. Metabolism, cell respiration and photosynthesis
          • 9. Plant biology
          • 10. Genetics and evolution
          • 11. Animal physiology
        • Options
          • Option A: Neurobiology and behaviour
          • Option B: Biotechnology and bioinformatics
          • Option C: Ecology and conservation
          • Option D: Human physiology
      • Assessment
    • Chemistry (FA 2025)
    • Chemistry (LA 2024)
      • Aims & Objectives
      • Syllabus
        • Core
          • 1. Stoichiometric relationships
          • 2. Atomic structure
          • 3. Periodicity
          • 4. Chemical bonding and structure
          • 5. Energetics/thermochemistry
          • 6. Chemical kinetics
          • 7. Equilibrium
          • 8. Acids and bases
          • 9. Redox processes
          • 10. Organic chemistry
          • 11. Measurement and data processing
        • Additional Higher Level
          • 12. Atomic structure
          • 13. The periodic table - the transition metals
          • 14. Chemical bonding and structure
          • 15. Energetics/thermochemistry
          • 16. Chemical kinetics
          • 17. Equilibrium
          • 18. Acids and bases
          • 19. Redox processes
          • 20. Organic chemistry
          • 21. Measurement and analysis
        • Options
          • A. Materials
          • B. Biochemistry
          • C. Energy
          • D. Medicinal chemistry
      • Assessment
    • Computer Science (FA 2025)
    • Computer Science (LA 2024)
      • Aims & Objectives
      • Syllabus
        • Core
          • Topic 1 - System fundamentals
          • Topic 2 - Computer organization
          • Topic 3 - Networks
          • Topic 4 - Computational thinking, problem-solving and programming
        • Additional Higher Level
          • Topic 5 - Abstract data structures
          • Topic 6 - Resource management
          • Topic 7 - Control
        • Options
          • A - Databases
          • B - Modelling and simulation
          • C - Web science
          • D - Object-oriented programming
      • Assessment
    • Design Technology
      • Aims & Objectives
      • Syllabus
        • Core
          • 1. Human factors and ergonomics
          • 2. Resource management and sustainable production
          • 3. Modelling
          • 4. Final production
          • 5. Innovation and design
          • 6. Classic design
        • Additional Higher Level
          • 7. User-centred design (UCD)
          • 8. Sustainability
          • 9. Innovation and markets
          • 10. Commercial production
      • Assessment
    • Nature of Science
      • Aims & Objectives
      • Syllabus
        • Introduction
        • Part A - Concepts
        • Part B - The Quest for Understanding
        • Part C - The Impact of Science
        • Part D - Challenges and the Future
      • Assessment
    • Physics (FA 2025)
    • Physics (LA 2024)
      • Aims & Objectives
      • Syllabus
        • Core
          • 1. Measurements and uncertainties
          • 2. Mechanics
          • 3. Thermal physics
          • 4. Waves
          • 5. Electricity and magnetism
          • 6. Circular motion and gravitation
          • 7. Atomic, nuclear and particle physics
          • 8. Energy production
        • Additional Higher Level
          • 9. Wave phenomena
          • 10. Fields
          • 11. Electromagnetic induction
          • 12. Quantum and nuclear physics
        • Options
          • A. Relativity
          • B. Engineering physics
          • C. Imaging
          • D. Astrophysics
      • Assessment
    • Sports, Exercise and Health Science
      • Aims & Objectives
      • Syllabus
        • Core
          • Topic 1: Anatomy
          • Topic 2: Exercise physiology
          • Topic 3: Energy systems
          • Topic 4: Movement analysis
          • Topic 5: Skill in sports
          • Topic 6: Measurement and evaluation of human performance
        • Additional Higher Level
          • Topic 7: Further anatomy
          • Topic 8: The endocrine system
          • Topic 9: Fatigue
          • Topic 10: Friction and drag
          • Topic 11: Skill acquisition and analysis
          • Topic 12: Genetics and athletic performance
          • Topic 13: Exercise and immunity
        • Options
          • Option A: Optimizing physiological performance
          • Option B: Psychology of sports
          • Option C: Physical activity and health
          • Option D: Nutrition for sports, exercise and health
      • Assessment
  • Mathematics
    • Mathematics: analysis and approaches
      • Aims & Objectives
      • Syllabus
        • Topic 1: Numbers and Algebra
        • Topic 2: Functions
        • Topic 3: Geometry and Trigonometry
        • Topic 4: Statistics and Probability
        • Topic 5: Calculus
      • Assessment
    • Mathematics: applications and interpretation
      • Aims & Objectives
      • Syllabus
        • Topic 1: Number and Algebra
        • Topic 2: Functions
        • Topic 3: Geometry and Trigonometry
        • Topic 4: Statistics and Probability
        • Topic 5: Calculus
      • Assessment
  • The arts
    • Dance
      • Aims & Objectives
      • Syllabus
        • Composition and Analysis
        • World Dance Studies
        • Performance
      • Assessment
    • Film
      • Aims & Objectives
      • Syllabus
        • Reading Film
        • Contextualizing Film
        • Exploring Film Production Roles
        • Collaboratively Producing Film (HL only)
      • Assessment
    • Music
      • Aims & Objectives
      • Syllabus
        • Areas of Inquiry
        • Contexts
        • Musical Processes
        • Musical Roles
        • Exploring Music in Context
        • Experimenting with Music
        • Presenting Music
      • Assessment
    • Theatre (Last Assessment 2023)
      • Aims & Objectives
      • Syllabus
        • Theatre in Context
        • Theatre Processes
        • Presenting Theatre
      • Assessment
    • Theatre (First assessment 2024)
    • Visual Arts
      • Aims & Objectives
      • Syllabus
        • Visual Arts in Context
        • Visual Arts Methods
        • Communicating Visual Arts
        • The Visual Arts Journal
        • Art-making Forms
        • Research
      • Assessment
  • Interdisciplinary courses
    • Literature and Performance
      • Aims and Objectives
      • Syllabus
        • Part 1: Critical Study of Texts
        • Part 2: Exploration of the Chose Approach to the Text
        • Part 3: Realization of Texts in Performance
        • Prescribed Literature in Translation
      • Assessment
    • Environmental Systems & Societies
      • Aims & Objectives
      • Syllabus
        • Topic 1: Foundations of environmental systems and societies
        • Topic 2: Ecosystems and ecology
        • Topic 3: Biodiversity and conservation
        • Topic 4: Water and aquatic food production systems and societies
        • Topic 5: Soil systems and terrestrial food production systems and societies
        • Topic 6: Atmospheric systems and societies
        • Topic 7: Climate change and energy production
        • Topic 8: Human systems and resource use
      • Assessment
  • School-based syllabuses
    • Art History
      • Aims & Objectives
      • Syllabus
        • Topic 1: The Art and Architecture of Ancient Greece
        • Topic 2: Rome - Republic and Empire
        • Topic 3: The Middle Ages
        • Topic 4: Romanesque and Gothic Art and Architecture
        • Topic 5: The Art of the Renaissance
        • Topic 6: The Baroque Age - Art and the Architecture of 17th-century Europe
        • Topic 7: The 'Age of Reason' to 'Romanticism'
        • Topic 8: Experiments in the 19th- and 20th-century Art
      • Assessment
    • Astronomy
      • Aims & Objectives
      • Syllabus
        • Topic 1: The Stars
        • Topic 2: The Planets
        • Topic 3: Galaxies
        • Topic 4: Cosmology
      • Assessment
    • Brazilian Social Studies
      • Aims & Objectives
      • Syllabus
        • Topic 1: The Construction of Brazilian Geographical Space
        • Topic 2: Brazil in the Globalization Era - Core Topic
        • Topic 3: The Demographic and Urban Dynamics of Contemporary Brazil
        • Topic 4: Environment and Society
        • Topic 5: From Discovery to the End of the Colonial Era (1500-1822)
        • Topic 6: The Monarchical Experience (1822-1889)
        • Topic 7: Early Republican Brazil (1889-1945) - Core Topic
        • Topic 8: Contemporary Brazil (1945 - )
      • Assessment
    • Classical Greek and Roman Studies
      • Aims & Objectives
      • Syllabus
        • Part A - Two Topics from the Following Four Options
        • Part B - Two Topics from the Following Four Options
      • Assessment
    • Food Science and Technology
      • Aims & Objectives
      • Syllabus
        • 1. Nutrition
        • 2. Materials, Component and Their Application
        • 3. Food Quality and Safety
        • 4. Food Process Engineering
      • Assessment
    • Marine Science
      • Aims & Objectives
      • Syllabus
        • Core
          • Topic 1 Origin and Structure of Oceans
          • Topic 2 Dynamics of Earth's Crust
          • Topic 3 Patterns of Water Movement
          • Topic 4 Properties of Ocean Water
          • Topic 5 Life in Oceans
        • Options
          • A. Marine ecosystems and conservation
          • B. Atmosphere, ocean and climate
          • C. Geology of ocean basins
      • Assessment
    • Modern History of Kazakhstan
      • Aims & Objectives
      • Syllabus
        • Topic 1. Kazakhstan at the Beginning of the 20th Century
        • Topic 2. Kazakhstan During the Civil Confrontation (1917-1920)
        • Topic 3. The Formation of the Soviet Union and Kazakhstan (1920-1940)
        • Topic 4. The Great Patriotic War and Kazakhstan (1941-1945)
        • Topic 5. Kazakhstan and the Socialism (1946-1985)
        • Topic 6. Kazakhstan: from Perestroika to independence
      • Assessment
    • Political Thought
      • Aims & Objectives
      • Syllabus
        • Topic 1: Political Thinkers
        • Topic 2: Political Concepts
      • Assessment
    • Turkey in the 20th Century
      • Aims & Objectives
      • Syllabus
        • Turkey at the Beginning of the 20th Century
        • Topic 2: The Foundations of the Turkish Republic 1923-1945
        • Topic 3: The Global Changes Between the World Wars and Their Effect on Turkey 1918-1939
        • Topic 4: Turkey under pressure during World War II
        • Topic 5: Reconstruction, democracy and developments in the region 1945-1985
        • Topic 6: The Effects of Globalization and the Dialogue with Europe 1985-2000
      • Assessment
    • World Arts and Cultures
      • Aims & Objectives
      • Syllabus
        • Part 1: Prescribed Topics
        • Part 2: Intercultural Studies
        • Part 3: Regional Study
      • Assessment
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On this page
  • Concepts
  • SL Content
  • AHL Content
  1. Mathematics
  2. Mathematics: analysis and approaches
  3. Syllabus

Topic 3: Geometry and Trigonometry

Concepts

  • Essential understandings

    • Geometry and trigonometry allows us to quantify the physical world, enhancing our spatial awareness in two and three dimensions. This topic provides us with the tools for analysis, measurement and transformation of quantities, movements and relationships.

  • Suggested concepts embedded in this topic

    • Generalization, space, relationships, equivalence, representation,

    • AHL: Quantity, Modelling.

  • Content-specific conceptual understandings:

    • The properties of shapes depend on the dimension they occupy in space.

    • Volume and surface area of shapes are determined by formulae, or general mathematical relationships or rules expressed using symbols or variables.

    • The relationships between the length of the sides and the size of the angles in a triangle can be used to solve many problems involving position, distance, angles and area.

    • Equivalent measurement systems, such as degrees and radians, can be used for angles to facilitate ease of calculation.

    • Different representations of the values of trigonometric relationships, such as exact or approximate, may not be equivalent to one another.

    • The trigonometric functions of angles may be defined on the unit circle, which can visually and algebraically represent the periodic or symmetric nature of their values.

    • AHL: Position and movement can be modelled in three-dimensional space using vectors.

    • AHL: The relationships between algebraic, geometric and vector methods can help us to solve problems and quantify those positions and movements.

SL Content

  • SL 3.1

    • The distance between two points in three- dimensional space, and their midpoint.

    • Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids.

    • The size of an angle between two intersecting lines or between a line and a plane.

  • SL 3.2

    • Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles.

    • The sine rule: asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}sinAa​=sinBb​=sinCc​

    • The cosine rule: cos⁡C=a2+b2−c22ab\cos C=\frac{a^2+b^2-c^2}{2ab}cosC=2aba2+b2−c2​ ; f(x)=ax+bcx2+dx+e′f(x)=\frac{ax+b}{cx^2+dx+e'}f(x)=cx2+dx+e′ax+b​ , and f(x)=ax2+bx+cdx+f(x)=\frac{ax^2+bx+c}{dx+}f(x)=dx+ax2+bx+c​

    • Area of a triangle as 12absin⁡C\frac{1}{2} ab \sin C21​absinC

  • SL 3.3

    • Applications of right and non-right angled trigonometry, including Pythagoras’ theorem.

    • Angles of elevation and depression.

    • Construction of labelled diagrams from written statements.

  • SL 3.4

    • The circle: radian measure of angles; length of an arc; area of a sector.

  • SL 3.5

    • Definition of cos⁡θ,sin⁡θ\cos \theta, \sin \thetacosθ,sinθ in terms of the unit circle.

    • Definition of tan⁡θ\tan \thetatanθ as sin⁡θcos⁡θ\frac{\sin \theta}{\cos \theta}cosθsinθ​ .

    • Exact values of trigonometric ratios of 0,pi6,pi4,pi3,pi20, \frac{pi}{6}, \frac{pi}{4}, \frac{pi}{3}, \frac{pi}{2}0,6pi​,4pi​,3pi​,2pi​ and their multiples.

    • Extension of the sine rule to the ambiguous case.

  • SL 3.6

    • The Pythagorean identity cos⁡2θ+sin⁡2θ=1\cos^2 \theta + \sin^2 \theta=1cos2θ+sin2θ=1 . Double angle identities for sine and cosine.

    • The relationship between trigonometric ratios.

  • SL 3.7

    • The circular functions sin⁡x\sin xsinx , cos⁡x\cos xcosx , and tan⁡x\tan xtanx ; amplitude, their periodic nature, and their graphs

    • Composite functions of the form f(x)=asin⁡(b(x+c))+df(x)=a \sin (b(x+c))+df(x)=asin(b(x+c))+d

    • Transformations.

    • Real-life contexts.

  • SL 3.8

    • Solving trigonometric equations in a finite interval, both graphically and analytically.

    • Equations leading to quadratic equations in sin⁡x\sin xsinx , cos⁡x\cos xcosx or tan⁡x\tan xtanx

AHL Content

  • AHL 3.9

    • Definition of the reciprocal trigonometric ratios sec⁡θ\sec \thetasecθ , csc⁡θ\csc \thetacscθ and cot⁡θ\cot \thetacotθ

    • Pythagorean identities: 1+tan⁡2θ=sec⁡2θ1 + \tan^2 \theta = \sec^2 \theta1+tan2θ=sec2θ , 1+cot⁡2θ=csc⁡2θ1 + \cot^2 \theta = \csc^2 \theta1+cot2θ=csc2θ

    • The inverse functions f(x)=arcsin⁡x,f(x)=arccos⁡x,f(x)=arctan⁡xf(x)=\arcsin x, f(x) = \arccos x, f(x) = \arctan xf(x)=arcsinx,f(x)=arccosx,f(x)=arctanx ; their domains and ranges; their graphs.

  • AHL 3.10

    • Compound angle identities.

    • Double angle identity for tantantan .

  • AHL 3.11

    • Relationships between trigonometric functions and the symmetry properties of their graphs.

  • AHL 3.12

    • Concept of a vector; position vectors; displacement vectors.

    • Representation of vectors using directed line segments.

    • Base vectors i,j,ki, j, ki,j,k

    • Components of a vector: v=v1i+v2j+v3kv=v_1 i + v_2 j + v_3 kv=v1​i+v2​j+v3​k

    • Algebraic and geometric approaches to the following:

      • the sum and difference of two vectors

      • the zero vector 0\mathbf{0}0 , the vector −v-\mathbf{v}−v

      • multiplication by a scalar, kvk \mathbf{v}kv , parallel vectors

      • magnitude of a vector, ∣v∣| \mathbf{v} |∣v∣ ; unit vectors, v∣v∣\frac{\mathbf{v}}{|\mathbf{v}|}∣v∣v​

      • position vectors OA→=a,OB→=b\overrightarrow{OA}=\mathbf{a}, \overrightarrow{OB}=\mathbf{b}OA=a,OB=b

      • displacement vector AB→=b−a\overrightarrow{AB}=\mathbf{b}-\mathbf{a}AB=b−a

    • Proofs of geometrical properties using vectors.

  • AHL 3.13

    • The definition of the scalar product of two vectors.

    • The angle between two vectors.

    • Perpendicular vectors; parallel vectors.

  • AHL 3.14

    • Vector equation of a line in two and three dimensions: r=a+λbr=a + \lambda br=a+λb

    • The angle between two lines.

    • Simple applications to kinematics.

  • AHL 3.15

    • Coincident, parallel, intersecting and skew lines, distinguishing between these cases.

    • Points of intersection.

  • AHL 3.16

    • The definition of the vector product of two vectors.

    • Properties of the vector product.

    • Geometric interpretation of ∣v×w∣|\mathbf{v} \times \mathbf{w}|∣v×w∣

  • AHL 3.17

    • Vector equations of a plane: r=a+λb+μc\mathbf{r} = \mathbf{a} + \lambda \mathbf{b} + \mu \mathbf{c}r=a+λb+μc , where b\mathbf{b}b and c\mathbf{c}c are non-parallel vectors within the plane.

    • r⋅n=a⋅n\mathbf{r} \cdot \mathbf{n} = \mathbf{a} \cdot \mathbf{n}r⋅n=a⋅n , where n\mathbf{n}n is a normal to the plane and a is the position vector of a point on the plane.

    • Cartesian equation of a plane ax+by+cz=dax + by + cz = dax+by+cz=d .

  • AHL 3.18

    • Intersections of: a line with a plane; two planes; three planes.

    • Angle between: a line and a plane; two planes.

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Last updated 2 years ago