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
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
|
|
{
"S": "/lectio/203/stamdata/stamdata_edit_student.aspx?id=666\u0026prevurl=studieplan%2fuvb_hold_off.aspx%3fholdid%3d64420093564",
"T": "/lectio/203/stamdata/stamdata_edit_teacher.aspx?teacherid=666\u0026prevurl=studieplan%2fuvb_hold_off.aspx%3fholdid%3d64420093564",
"H": "/lectio/203/stamdata/stamdata_edit_hold.aspx?id=666\u0026prevurl=studieplan%2fuvb_hold_off.aspx%3fholdid%3d64420093564"
}