Holdet 2024 maSL1/i - Undervisningsbeskrivelse

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Undervisningsbeskrivelse

Stamoplysninger til brug ved prøver til gymnasiale uddannelser
Termin(er) 2024/25 - 2025/26
Institution Kolding Gymnasium
Fag og niveau Matematik -
Lærer(e) Thor Ferslev Langgård
Hold 2024 maSL1/i (2i ma SL/1, DP2 ma SL/1)

Oversigt over gennemførte undervisningsforløb
Titel 1 DP1 maSL/1 24/25 Sequences & Series
Titel 2 DP1 maSL/1 24/25 Straight lines & Simultaneous eq.
Titel 3 DP1 maSL/1 24/25 Measurement: Circles & Solids
Titel 4 DP1 maSL/1 24/25 Trigonometry
Titel 5 DP1 maSL/1 24/25 Sets, Venn Diagrams & Probability
Titel 6 DP1 maSL/1 24/25 Statistics & Linear regression
Titel 7 DP1 maSL/1 24/25 Hypothesis testing
Titel 8 DP1 maSL/1 24/25 Financial mathematics
Titel 9 DP1 maSL/1 24/25 Random Variables
Titel 10 DP2 maSL/1 25/26 Functions & Models
Titel 11 DP2 maSL/1 25/26 Calculus (Derivatives & Integral)
Titel 12 DP2 maSL/1 25/26 Voronoi diagrams
Titel 13 DP2 maSL/1 25/26 Trigonometric functions

Beskrivelse af de enkelte undervisningsforløb (1 skema for hvert forløb)
Titel 1 DP1 maSL/1 24/25 Sequences & Series

Sequences: An ordered list of numbers defined by a rule
Sequence notation & Terminology
Arithmetic & Geometric sequences
   General term formulas

Series: Sum of the terms of a sequence
Series notation & Terminology
Sigma notation
Arithmetric & Geometric series
   Formulas for sums of finite number of terms
Indhold
Kernestof:

Supplerende stof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 1 27-08-2024
Omfang Estimeret: Ikke angivet
Dækker over: 8 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 2 DP1 maSL/1 24/25 Straight lines & Simultaneous eq.

Gradient
x- & y-intercept
Parallel & Perpendicular lines
Equation of a line
   Gradient-intercept form
   General form
Graphing lines
Perpendicular bisectors

Simultaneous equations
Indhold
Kernestof:

Supplerende stof:
Omfang Estimeret: Ikke angivet
Dækker over: 3 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 3 DP1 maSL/1 24/25 Measurement: Circles & Solids

Circles
Arc lenght
Sector area & perimeter

Solids
Surface area & Volume
Indhold
Kernestof:
Omfang Estimeret: Ikke angivet
Dækker over: 3 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 4 DP1 maSL/1 24/25 Trigonometry

Right angled Triangles
   Trigonometric ratios (SOH-CAH-TOA)
   Angle of elevation / depression
   True bearings
   Angle between a line and a plane

Unit circle
   Definition & Equation x² + y² = 1
   Angle measurement (positive anti-clockwise)
   Definition of trigonometric ratios via the unit circle
   Supplementary angles
   cos²θ + sin²θ = 1

Non-right angled Triangles
   Area formulas
   Cosine rule
   Sine rule

Points in space
   Distance and midpoint formulas
   Measurements (surface area & volume)
   Trigonometry
Indhold
Kernestof:

Supplerende stof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 3 08-10-2024
Assignment 4 05-11-2024
Omfang Estimeret: Ikke angivet
Dækker over: 6 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 5 DP1 maSL/1 24/25 Sets, Venn Diagrams & Probability

Sets
Notation and Terminology
   Finite and infinite sets
   Subsets
   Empty set ∅ = { }
   Intersection A∩B (both in A and B)
   Disjoint sets A∩B = ∅
   Union A∪B (either in A or B or both)
   Universal set U
   Complement A' (not in A)
Special number sets (ℕ, ℤ, ℚ, ℝ)

Venn diagrams
Regions and Numbers in regions

Probabilities
Notation and Terminology
   Impossible and certain events
Experimental probabilities
Two-way tables
Sample space & Events
   List, 2D-grid, Tree diagrams & Venn diagrams
Theoretical probability
   P(A) = n(A) / n(U)
   0 ≤ P(A) ≤ 1
   P(A) + P(A') = 1
Addition law of probability
   P(A∪B) = P(A) + P(B) - P(A∩B)
Independent events
   P(A∩B) = P(A)·P(B)
Dependent events
   P(A∩B) = P(A)·P(B given that A has occurred)
Conditional probability
   P(A|B) = P(A∩B) / P(B)
Indhold
Kernestof:
Omfang Estimeret: Ikke angivet
Dækker over: 8 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 6 DP1 maSL/1 24/25 Statistics & Linear regression

Descriptive statistics intro
Terminology for statistics:
   Data
   Population and Census
   Sample and Survey
   Parameter & Statistic
Errors in sampling and Sampling methods
Types of data:
   Categorical variables
   Quantitative variables (Discrete vs. Continuous)

Discrete data (ungrouped data)
Frequency and Relative frequency
Column graphs
Distribution (symmetric / negatively skewed / positively skewed)
The centre of data: Mode, Mean and Median
Lower and upper quartiles
   Range and Interquartile range (IQR)
   Box-and-Whisker-plots (5-number summary)
   Outliers
Variance and Standard deviation

Continuous data (grouped data)
Class intervals
Frequency histograms
Modal class
Mid-interval values as best estimate of data values
Cumulative frequency graphs
   Percentiles
   Median, Lower and upper quartiles
   Range and Interquartile range (IQR)
Variance and Standard deviation


Linear regression - Bivariate statistics
Correlation: Direction, Linearity, Strength, Outliers & Causality
Pearson's product-moment correlation coefficient rₚ
   Properties
Interpolation & Extrapolation
The least squares regression line
Spearman's Rank correlation coefficient rₛ
   Ranks and Tied ranks
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 7 - Kognity assignment 29-01-2025
Assignment 8 26-02-2025
Omfang Estimeret: Ikke angivet
Dækker over: 9 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 7 DP1 maSL/1 24/25 Hypothesis testing

Statistical hypotheses in general
Null hypothesis H₀
Alternative hypothesis H₁
Significance level α
p-value
Reject H₀ if p ≤ α

Four types of hypothesis tests using a TI-84+
Student's t-test
Two-sample t-test   (Pooled tests!)
χ² (chi-squared) goodness of fit test
   Expected frequencies = Number of trials · Theoretical probability
   Degrees of freedom df = Number of categories - 1
χ² (chi-squared) test for independence
   Expected frequency tables
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 9 12-03-2025
Omfang Estimeret: Ikke angivet
Dækker over: 4 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 8 DP1 maSL/1 24/25 Financial mathematics

Growt and decay (geometric sequences)

Compound interest
   Inflation
   Real value of investments
   Depreciation

Financial models using TI-84+

Loans and annuities
Indhold
Kernestof:
Omfang Estimeret: Ikke angivet
Dækker over: 3 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 9 DP1 maSL/1 24/25 Random Variables

Discrete random variables
Random variables
   Discrete vs. Continuous
Discrete probability distributions
   Uniform discrete random variables
   Mode & Median
   Probability mass function
Expectation
   Fair games
Binomial distribution
   Binomial experiments
   Pascal's triangle
   Binomial distribution
   Mean & standard deviation

Continuous random variables
Probability density functions
Normal distribution curve
   Geometric significance of μ & σ
Quantiles
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 11 08-05-2025
Omfang Estimeret: Ikke angivet
Dækker over: 5 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 10 DP2 maSL/1 25/26 Functions & Models

Functions
Relations & Functions
   Algebraic test
   Vertical line test
Function notation
Domain & Range
Graphs of functions
Sign diagrams
Inverse functions

Modelling
The modelling cycle
Linear models
   Exact vs. Approximate models
Piecewise linear models

Quadratic functions
Terminology regarding quadratic functions and their graphs
General form: f(x) = a⋅x² + b⋅x + c
   Parabolas and the graphical meaning of a
Axes intercepts   (where x = 0   &    where y = 0)
Axis of symmetry x = -b / (2a)   & Vertex
Graph → Quadratic function

Direct and inverse variation
Two Directly proportional variables
Two Inversely proportional variables
Variation models: Direct variation vs. Inverse variation

Exponentials & Logarithms
Exponents & Laws of exponents
Exponential functions
   Graphs of y = k⋅aˣ + c and y = k⋅a⁻ˣ + c
Growth and Decay
Exponential equations
   Logarithms in base 10
   Natural logarithms
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
Assignment 1 27-08-2025
Assignment 2 08-10-2025
Omfang Estimeret: Ikke angivet
Dækker over: 12 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 11 DP2 maSL/1 25/26 Calculus (Derivatives & Integral)

Differentiation
Rates of change
   Constant rates of change
   Average rates of change
   Instantaneous rates of change
Limits
Gradients of tangents: Derivative function
Rules of differentiation
   Lone Constants
   Constants multiplied with a function
   Addition/subtraction rule
   Power rule (xⁿ)
Tangents & Normals
Monotonicity
   Increasing & Decreasing
   Sign diagrams
   Stationary points
   Points of inflection
Rates of change
Optimisation

Integration
Approximating the area under a curve using the trapezoidal rule
Antiderivatives & Indefinite integrals
   Rules of integration
   Particular values
Definite integrals = Areas under curves
Indhold
Kernestof:

Skriftligt arbejde:
Titel Afleveringsdato
maSL/1 Exploration - Idea(s) (in ManageBac) 05-11-2025
maSL/1 Exploration - Outline (in ManageBac) 20-11-2025
maSL/1 Exploration - 1st draft (in ManageBac) 21-12-2025
Omfang Estimeret: Ikke angivet
Dækker over: 14 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 12 DP2 maSL/1 25/26 Voronoi diagrams

Voronoi diagrams
   Sites, Cells, Edges, Vertices
Constructing Voronoi diagrams
   Rep: Perpendicular bisector
   Calculating vs. Drawing diagrams
Completing unfinished Voronoi diagrams
   Missing edges
   Missing sites
Adding a site to a Voronoi diagram
Nearest neighbour interpolation
The largest empty circle problem
Indhold
Kernestof:
Omfang Estimeret: Ikke angivet
Dækker over: 3 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer

Titel 13 DP2 maSL/1 25/26 Trigonometric functions

Unit circle
Definition
Circle equation (Pythagoras) x² + y² = r²
Angle measurement (positive anti-clockwise)
Definition of trigonometric ratios via the unit circle
cos²θ + sin²θ = 1
Periodicity of trigonometric ratios

Trigonometric functions
Periodic functions
Waves
   Period
   Principal axis y = (max + min)/2
   Amplitude = (max - min)/2
Basic Sine & Cosine functions
   y = sin θ
   y = cos θ
General Sine & Cosine functions
   y = a · sin(b·x) + d
   y = a · cos(b·x) + d
Indhold
Kernestof:
Omfang Estimeret: Ikke angivet
Dækker over: 2 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer