Holdet 2024 MathApSL - Undervisningsbeskrivelse
menu

Undervisningsbeskrivelse

Stamoplysninger til brug ved prøver til gymnasiale uddannelser
Termin(er) 2024/25 - 2025/26
Institution Ikast-Brande Gymnasium
Fag og niveau Matematik -
Lærer(e) Anders Kristensen
Hold 2024 MathApSL (1i MathApSL, 2i MathApSL)

Oversigt over gennemførte undervisningsforløb
Titel 1 Topic 1: Intro
Titel 2 Topic 2: Sequences
Titel 3 Topic 3: Financial math
Titel 4 Topic 4: Geometry and Trigonometry
Titel 5 Topic 5: Sets & Probability
Titel 6 Topic 6: Statistics
Titel 7 Topic 7: Probability distributions
Titel 8 Topic 8: Functions
Titel 9 IA
Titel 10 Topic 9: Calculus

Beskrivelse af de enkelte undervisningsforløb (1 skema for hvert forløb)
Titel 1 Topic 1: Intro

Textbook References
Core SL 1: Chapters 1, 3, 4
Applications SL 2: Chapter 1

Key Concepts
- Equations of lines
- Graphing lines
- Perpendicular lines
- Simultaneous equations
- Surds and radicals
- Exponents
- Equations
- Solving equations on the GDC
- Significant figures
- Absolute and percentage error

TOK Connections
- Precision vs. Accuracy: How do mathematical conventions influence our understanding of error and measurement?
- Symbolic Representation: How do symbols and notation shape mathematical thinking and communication?

ATL Skills
- Thinking: Apply logic and reasoning to solve equations and interpret graphs.
- Communication: Use appropriate mathematical language and notation.
- Research: Explore real-world contexts where error estimation is critical (e.g., engineering, science).

TI-Nspire Calculator Skills
- Graphing linear equations and analyzing intersections
- Solving simultaneous equations using the 'Solve' and 'Graph' features
- Using 'Approximate' and 'Exact' modes for radicals and surds
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 1 - In-class 23-09-2024
Assignment 2 - Equations 29-10-2024
Omfang Estimeret: Ikke angivet
Dækker over: 11 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 2 Topic 2: Sequences

Textbook References
Core SL 1: Chapter 5

Key Concepts
- Number sequences
- Arithmetic sequences
- Geometric sequences
- Series

TOK Connections
- Patterns and Predictions: How do mathematical sequences help us understand and predict phenomena?
- Infinity and Convergence: What philosophical questions arise from infinite series?

ATL Skills
- Thinking: Recognize patterns and develop general rules.
- Communication: Represent sequences using appropriate notation.
- Self-management: Organize steps in solving sequence problems.

TI-Nspire Calculator Skills
- Summing series using sigma notation
Indhold
Kernestof:
Omfang Estimeret: Ikke angivet
Dækker over: 7 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 3 Topic 3: Financial math

b]Textbook References[/b]
Core SL 1: Chapter 5
Applications SL 2: Chapter 2

Key Concepts
- Compound interest
- Loans
- Annuities

TOK Connections
- Value and Time: How does mathematics help us understand the value of money over time?
- Ethics in Finance: What ethical considerations arise in financial modeling?

ATL Skills
- Thinking: Apply formulas to real-world financial problems.
- Research: Investigate financial products and their mathematical models.
- Communication: Explain financial decisions using mathematical reasoning.

TI-Nspire Calculator Skills
- Using finance solver for compound interest and loans
- Calculating annuities using built-in finance functions
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Test - Sequences + Finance 29-11-2024
Omfang Estimeret: Ikke angivet
Dækker over: 6 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 4 Topic 4: Geometry and Trigonometry

Textbook References
• Core SL 1: Chapters 6, 7, 8, 9
• Applications and Interpretations SL 2: Chapter 17

Key Concepts
• Circles, arcs, sectors
• Right-angled triangles, Pythagoras, SOHCAHTOA
• Non-right angled triangles, sine and cosine rule
• Trigonometry in 3D geometry
• Voronoi diagrams and interpolation

TOK Connections
• How do geometric models help us understand spatial relationships?
• What is the role of abstraction in mathematical representations of space?

ATL Skills
• Thinking: Apply geometric reasoning and spatial visualization
• Communication: Use diagrams and notation to explain solutions
• Research: Investigate real-world applications of trigonometry and geometry

TI-Nspire Calculator Skills
• Using TI-Nspire to solve triangles using cosine, sine and tangent
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Mid-term 17-01-2025
Assignment 3 - In class 07-02-2025
Assignment 4 - Voronoi 28-02-2025
Omfang Estimeret: Ikke angivet
Dækker over: 22 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 5 Topic 5: Sets & Probability

Textbook References
• Core SL 1: Chapters 2, 10

Key Concepts
• Set notation, Venn diagrams
• Experimental and theoretical probability
• Tree diagrams, conditional probability

TOK Connections
• How does probability influence decision-making under uncertainty?
• To what extent can randomness be modeled mathematically?

ATL Skills
• Thinking: Analyze probabilistic models and outcomes
• Communication: Represent events using set notation and diagrams
• Research: Explore probability in games, genetics, and risk analysis

TI-Nspire Calculator Skills
• Using TI-Nspire to simulate probability experiments
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Test - Sets and probability 25-03-2025
Omfang Estimeret: Ikke angivet
Dækker over: 16 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 6 Topic 6: Statistics

Book: Core SL 1
Chapters: 11 + 12

Book: Applications and Interpretations SL 2
Chapters: 5 + 16

- Sampling
- Data
- Frequency tables
- Mean, median, mode
- Range and interquartile range
- Box plots (box and whisker diagrams)
- Cumulative frequency graphs
- Standard deviation and variance
- Pearson's product-moment correlation coefficient
- Line of best fit by eye
- Line of best fit by regression
- Spearman's rank correlation coefficient
- t-test
- Two sample t-test
- Chi-squared goodness of fit test
- Chi-squared 2-way test of independence
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 5 - In class 29-04-2025
End-of-year exam 27-05-2025
Omfang Estimeret: Ikke angivet
Dækker over: 25 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 7 Topic 7: Probability distributions

Textbook References
• Applications and Interpretations SL 2: Chapters 14, 15

Key Concepts
• Random variables and distributions
• Binomial and normal distributions

TOK Connections
• How do probability distributions model uncertainty in the real world?
• What assumptions underlie statistical models?

ATL Skills
• Thinking: Analyze and interpret probability distributions
• Communication: Use notation and graphs to describe distributions
• Research: Apply distributions to real-world contexts (e.g., quality control)

TI-Nspire Calculator Skills
• Using TI-Nspire to calculate binomial and normal probabilities
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
In-class: Probability distributions 11-09-2025
Omfang Estimeret: Ikke angivet
Dækker over: 11 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 8 Topic 8: Functions

Book: Applications and Interpretations SL 2
Chapter: 3, 4, 6, 7, 8, 9

- Function notation
- Domain and range
- Graphs of functions
- Sign diagrams
- Tranformation of functions
- Inverse functions
- Modeling
- Linear model
- Simultaneous equations
- Quadratic functions
- Axes intercepts (roots)
- Axis of symmetry
- Vertex
- Intersection of graphs
- Power equations
- Using GDC to find models
- Exponential functions
- Logartithmic functions
- Periodic functions (sine + cosine)
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
In-class: Quadratic models 30-10-2025
Omfang Estimeret: Ikke angivet
Dækker over: 26 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 9 IA

Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
IA proposal 18-12-2025
End of Writing Day 1 19-01-2026
End of Writing Day 2 23-01-2026
IA Complete version 26-01-2026
IA Polished version 04-03-2026
Omfang Estimeret: Ikke angivet
Dækker over: 12 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 10 Topic 9: Calculus

Book: Applications and Interpretations SL 2
Chapter: 10, 11, 12, 13

- Rate of change
- Limits
- Gradient of a tangent
- The derivative functions
- Differentation
- Rules for differentation
- Equations of tangents
- Equations of normals
- Increasing and decreasig
- Stationary points (turning points or point of inflection)
- Optimizations problems
- Area under a curve using the trapezodial rule
- The Fundamental Theorem of Calculus
- Antidifferentation to fin the antiderivative
- Rules for integrations
- Finding the integration constant "c"
- Finding the area under a curve
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Voluntary: Calculus 27-03-2026
Omfang Estimeret: Ikke angivet
Dækker over: 27 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer