Holdet 2024 Math/i - Undervisningsbeskrivelse

Undervisningsbeskrivelse

Stamoplysninger til brug ved prøver til gymnasiale uddannelser
Termin(er) 2024/25
Institution Esbjerg Gymnasium
Fag og niveau Matematik -
Lærer(e) Niels Brage
Hold 2024 Math/i (1i Math)
Oversigt over gennemførte undervisningsforløb
Titel 1 Course outline for PreIB math
Titel 2 Algebra 1
Titel 3 Graph and functions
Titel 4 Numbers
Titel 5 Algebra2
Titel 6 Geometry and trigonometri
Titel 7 Probability and statistics
Titel 8 Preparation for Mock exam

Beskrivelse af de enkelte undervisningsforløb (1 skema for hvert forløb)
Titel 1 Course outline for PreIB math

Cambridge IGCSE: Mathematics: Core and Extended - 3rd edition by Ric Pimentel and Terry Wall

Topics included in the course:
Algebra 1: Chapter 3 and 11.
Graphs and functions: Chapters 28, 17, 18 and 19.
Numbers: Chapters 1, 2, 4, 5, 7, 8 and 10.
Algebra 2: Chapters 12 and 13.
Geometry and trigonometry: Chapters 20, 22, 27, 30 and 31.
Probability and statistics: Chapters 35, 36, 37, 38 and 39.

Indhold
Kernestof:
Omfang Estimeret: 1,00 modul
Dækker over: 1 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer
Titel 2 Algebra 1

Chapter 3: Calculations and order

Ordering: (Signs for ordering e.g: equal to, not equal to, greater than, less
than, greater than or equal to, less than or equal to)
The Number line
The order of operations: (1) Brackets, (2) Powers/roots, (3) Multiplication/division (4) Addition/subtraction

Chapter 11:  Algebraic representation and manipulation
Expanding a bracket
Expanding a pair of brackets
Simple factorising
Substitution
Transformation of formulae
Further expansion
Further factorization
Evaluation
Factorising quadratic expressions
Transformation of complex formulae
Algebraic fractions
Simplifying complex algebraic fractions
Indhold
Kernestof:
Omfang Estimeret: 6,00 moduler
Dækker over: 5 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer
Titel 3 Graph and functions

Chapter 17 - Graphs in practical situations
- Conversion graphs
- Speed, distance and time
- Gradient(speed) = distance / time
- Travel graphs (distance as a function of time)
- Speed-time graphs (Speed as a function of time), gradient on this graph is the acceleration / decelereation
- Area under speed-time graphs (it gives the distance)

Chapter 18 - Graphs of functions
- Quadratic functions (parabola)
- Graphical solution of a quadratic equation
- Reciprocal function (hyperbola)
- Types of graph (linear (straight line), quadratic (parabola), cubic (cubic curve), reciprocal (hyperbola)
- Cubic functions (cubic curve)
- Exponential functions
- Gradients of tangents to different curves (by using the two point-formula)
- Solving equations by graphical methods

Chapter 19 - Functions
- Notation f(x)
- Inverse functions
- Composite functions

Chapter 28 - Straight-line graphs
- The gradient of a straight line
- The equation of a straight line
- The general equation of a straight line
- Parallel lines and their equations
- Drawing straight line graphs
- Graphical solutions of simultaneous equations
- Calculating the length of a line segment
- The midpoint of a line segment
- The equation of a line through two points
- Perpendicular lines
Indhold
Kernestof:
Omfang Estimeret: 16,00 moduler
Dækker over: 16 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer
Titel 4 Numbers

Chapter 1 -  Number and language
The set of Natural numbers(N), Integers(Z), Rational numbers(Q) and Real numbers(R)
Rational and irrational numbers

Prime numbers, Square numbers, Cube numbers
Factors, Highest common factor, roots

Chapter 2 - Accuracy
Approximation, Rounding, Lower/Upper bound and Significant figures

Chapter 4 - Integers, fractions, decimals and percentages
Fractions and different rules, Fraction to decimal, Decimal to fraction and Recurring decimal to fraction

Chapter 5 - Further percentages
Percentage, Increase/decrease (and multipliers, ex 5% increase is equivalent to a multiplier of 1.05)

Chapter 7 - Indices and standard form
Laws of indices, the zero index, negative indices, Exponential equation (and logarithms) and Standard form

Chapter 8 - Money and finance
Interest and Compound interest

Chapter 10 - Set notation and Venn diagrams
Sets, Subsets, Universal set, Complement, Empty set, Set notation (intersection and union) and Venn diagrams

Chapter 6 - Ratio and proportion
Direct proportion, Divide a ratio into a given ratio, Inverse proportion, Increase and decrease by a given proportion.
Indhold
Kernestof:
Omfang Estimeret: 18,00 moduler
Dækker over: 19 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer
Titel 5 Algebra2

Algebra and graphs

Chapter 12
Algebraic indices

Chapter 13
Equations (simple, advanced and use of the quadratic formula) and inequalities
Indhold
Kernestof:
Omfang Estimeret: 5,00 moduler
Dækker over: 5 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer
Titel 7 Probability and statistics

Probability
Chapter 35 - Probability
Chapter 36 - Further probability

Statistics
Chapter 37 - Mean, median, mode and range
Chapter 38 - Collecting and displaying data - Not including histograms
Chapter 39 - Cumulative frequency
Indhold
Kernestof:
Omfang Estimeret: 12,00 moduler
Dækker over: 13 moduler
Særlige fokuspunkter
Væsentligste arbejdsformer