Undervisningsbeskrivelse
Stamoplysninger til brug ved prøver til gymnasiale uddannelser
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Termin(er)
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2025/26
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Institution
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Z - NAB KHS
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Fag og niveau
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Matematik B
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Lærer(e)
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Merethe Nørgaard
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Hold
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2024 1f24 Ma EN (2f25 Ma EN)
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Oversigt over gennemførte undervisningsforløb
Beskrivelse af de enkelte undervisningsforløb (1 skema for hvert forløb)
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Titel
1
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Differential Calculus
All chapters are refferring to the Plus 2 book unless otherwise is stated.
Monotonicity and extrema
How to find extrema using differential calculus
Finding monotonicity using differential calculus
Tangents and secants chapter 4.1
How the slope of the secant is used to find the slope of the tangent.
Formula of the slope of the secant
∆x→0
Relation between f and f’ chapter 4.2
Rules chapter 4.3
Coefficient rule
Rule of sums and differences
product rule
Functions
How to find the derivative of:
Polynomial chapter 3.3
Exponential function chapter 5.2
Other function in formula collection
f' as the instantanious growth rate
Proofs chapter 4.4
Proof that f' (x)=a if f(x)=ax
Proof that f' (x)=2x if f(x)=x^2
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Indhold
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Kernestof:
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
9 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
2
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Chi squared distribution
Χ^2-test chapter 7.3
Zero and alternative Hypothesis’ chapter 7.3
Observed Values chapter 7.3.1
Expected Values chapter 7.3.1
Degrees of freedom chapter 7.3.3
Test size chapter 7.3.2
Test probability p chapter 7.3.3
Based on Χ^2- distribution
Level of significance chapter 7.3.4
Critical value chapter 7.3.4
Based on Χ^2- distribution
Grounds for confirming or denying the hypothesis’. chapter 7.3.4
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Indhold
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Omfang
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Estimeret:
6,00 moduler
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
3
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Finance
All chapters are refferring to the Plus 1 book unless otherwise is stated.
Interest chapter 6.1
Interest per period
Effective Interest
Average Interest
ÅOP
Compond Interest chapter 6.2
Annuity chapter 6.3
Savings
Debt
Amortization schedule chapter 6.4
Remaining debt + formula
Proofs chapter 9.4
Compound interest
K_0,r, n
Annuity Savings
A_n, y, n
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Indhold
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
4
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Lineære funktioner
Kernestof:
• Definition af en lineær funktion
• Parametrene a og b's betydning for grafens udseende
• Løsning af ligninger med en ubekendt dels ved beregning og dels ved grafisk betragtning (Herunder beregning af skæringspunkter mellem to funktioner)
• Indtegne lineære funktioner ud fra forskrift manuelt og vha. værktøjer
• Aflæse lineære funktioner ud fra grafisk illustration
• Beregning af forskrift ud fra 2 kendte punkter på grafen for funktionen
• Beregning af forskrift ud fra 1 kendt punkt og 1 hældning
• Arbejdet med realistiske eksempler, der udvikler sig lineært
• Stykkevise lineære funktioner (gaffelforskrifter)
• Funktionsanalyse
• Inverse funktioner
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Indhold
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
5
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Exponential Functions
All chapters are refferring to the Plus 1 or Plus 2 book unless otherwise is stated.
General equation (f(x)=a∙b^x ) plus 1 chapter 4.2
Doubling and halving plus 1 chapter 4.2.1
b and a given two points plus 1 chapter 4.2.2
Equations using logarithms and using graphs Plus 1 chapter 4.2.5 and Plus 2 chapter 5.3.2
Finding x given y
Finding y given x
Regression analysis plus 1 chapter 4.1
Proofs:
Proof of formula for a and b plus 2 chapter 8.2
Proof of the doubling constant plus 2 chapter 8.2
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Indhold
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
6
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Descriptive Statistics
All chapters are refferring to the Plus 1 book unless otherwise is stated.
Types of data
Continuous chapter 5.5
Discrete chapter 5.4
Representative sample chapter 5.1
Observations, frequencies, cumulative frequencies, relative frequencies, cumulative relative frequencies chapter 5.3
Graphs and charts
Discrete chapter 5.4.2
Barchart
Cumulative relative frequency graph
Continuous chapter 5.5.2
Histogram
Cumulative relative frequency graph
Descriptors chapter 5.7
Mean
Formula
Mode/Modal class
Median
Quartiles
Quartile Range
Percentiles
Standard Deviation
Explanation of the mean and standard deviation formulas chapter 5.7.3 and 5.7.4
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Indhold
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
7
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2nd degree functions
All chapters are refferring to the Plus 1 book unless otherwise is stated.
General equation (f(x)=ax^2+bx+c) chapter 7.1
Graph based on a, b, c and d chapter 7.1 and 7.2.1
2nd degree Equations chapter 7.3
Finding x given y
Point of intersection
finding y given x
inequalities chapter 7.4
Zero/roots
Using the quadratic formula chapter 7.2.1
If b=0, using square roots
If factorized chapter 7.3.2
Extrema
Using the top point formula chapter 7.2.1
Economics chapter 7.6
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Indhold
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Omfang
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Estimeret:
Ikke angivet
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
8
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Probabilities
All chapters are refferring to the Plus 2 book unless otherwise is stated.
General knowledge chapter 7.1
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Indhold
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Omfang
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Estimeret:
8,00 moduler
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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Titel
9
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Distributions and confidence intervals
All chapters are refferring to the Plus 2 book unless otherwise is stated.
The Binomial Distribution chapter 7.2
Notation chapter 7.2.1
Probabilities chapter 7.2.2
P(X=r)
Using a probability tree
Using the binomial formula
Using Geogebra
P(X≤r) , P(X<r), P(X>r), P(X≥r)
Confidence interval of p chapter 7.2.3
The Normal distribution chapter 7.4
General overview
Approximation to the binomial distribution chapter 7.2.4
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Indhold
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Omfang
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Estimeret:
8,00 moduler
Dækker over:
0 moduler
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Særlige fokuspunkter
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Væsentligste arbejdsformer
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