Head Quarters Syllabus Projects
International Baccalaureate Math Studies:
- Overview of IB Math Studies
- The Internal Assessment: The Project
- Assessment Criteria
CURRICULUM
This course is designed to prepare students for the IB Math Studies exam. Topics studied will include: numbers and algebra, geometry and trigonometry, sets and logic,probability, statistics, functions, financial math, and a review for the exam. The prerequisites for this course are Geometry and IB diploma candidate.
Learning Objectives
The student will:
Demonstrate the following skills.
Numbers and Algebra
The student will understand and be able to use:
Sets and their notation, natural, integers, rational, and real numbers
Exponential expressions
Scientific notation
Estimation
Systeme International (SI) and other basic units of measurement
Arithmetic sequences and series and their formulae
Geometric sequences and series and their formulae
Inequalities; solutions in one variable, number line graphs
Solutions of quadratic equations by factoring and graphing
Sets and logic
The student will understand and be able to use:
Basic concepts of set theory, subsets
Venn diagrams and simple applications
Basic concepts of symbolic logic; definition of a proposition; symbolic notation of propositions
Compound statements,: implication, negation, "and", "or"
Truth tables to provide proof
Definition of implication, converse, inverse, contrapositive; logical equivalence
Testing validity of simple arguments through truth tables an, contradiction and tautology
Geometry and Trigonometry
The student will understand and be able to use:
The Sine Rule, Cosine rule, Area of a triangle
Coordinates in 2 and 3 dimensions, points, lines, midpoints, angles
Distance between points, angle size, identification of right angles
Equation of a line in 2 dimensions, slope-intercept form and standard form
Gradients, intercepts, points of intersection, parallel lines, perpendicular lines
Geometry of 3-D shapes, cuboid, prism, pyramid
Vectors: displacements, components in column form, sum, difference, zero vectors, scalar multiplication, magnitude of vectors, position vectors.
Functions
The student will understand and be able to use:
Concept of a function as a mapping.
Domain and range of a function
Linear functions and their graphs, f(x)=mx + b
Piecewise linear functions; continuous functions; step functions
Linear inequalities and their graphs
The graph of the quadratic functions 7 = ax^2 + bx + c
Properties of symmetry; axis of symmetry; x= -b/2a; intercepts
Graphs and properties of the sine and cosine functions, amplitude and period.
Graphs and properties of exponential functions
Growth and decay; basic concepts of asymptotic behavior.
Statistics
The student will understand:
The student will understand and be able to use:
Classification of discrete and continuous data
Scatter diagrams and best line of fit by eye
simple discrete data; frequency tables; frequency polygons
Grouped data, discrete or continuous; frequency tables, mid-interval values, interval width, upper and lower boundaries.
Cumulative frequency for grouped data and their curves, percentiles, quartiles
Histograms
Mean
Standard deviation
Variance
Cumulative frequency curves
Median and interquartile range
Probability
The student will understand and be able to use:
Concept of population and sample
Sample space; event A and its complement
Equally likely events, probability of an event
Combined events, mutually exclusive events, independent events
Conditional probability
Venn diagrams; tree diagrams; tables of outcomes
Solutions with and without replacement
Normal distribution
The student will understand and be able to use:
Standard normal variable
The student will:
Apply statistical formulas to calculate the mean, variance, and standard deviation.
Construct frequency diagrams to illustrate probabilities.
Construct histograms to illustrate probabilities.
Interpret frequency diagrams and histograms to solve problems.
Apply the Normal distribution to real world situations to solve statistical problems.
Financial Math
The student will understand and be able to use:
Currency conversions
Simple interest formulae
Compound interest formulae
Construction and use of tables, loan and repayment schemes, investment and saving schemes, inflation
Linear programming
Internal Assessment Criteria:
IB Math Studies Web Sites
Internal Assessment Criteria:
1 Introduction
The project is internally assessed by the teacher and externally moderated by the IBO using assessment criteria which relate to the objectives for group 5 aims.
Group 5 Aims:
The aims of all courses in group 5 are to enable the candidates to:
*appreciate the international dimensions of the mathematic and the multiplicity of its cultural and historical perspectives.
*develop logical, critical, and creative thinking in mathematics.
*develop mathematical knowledge, concepts and principles.
*employ and refine the powers of abstraction and generalization.
*develop patience and persistence in problem-solving.
*communicate mathematically, both clearly and confidently, in a variety of contexts.
*have an enhanced awareness of technological developments in a variety of mathematical concepts.
*develop an appreciation of the beauty, power, and usefulness of mathematics.
2 Forms of the assessment criteria
Each project should be assessed against the following six criteria:
A-Statement of Task
B-Data Collection
C-Analysis
D-Evaluation
E-Structure and communication
F-Commitment
3 Applying the assessment criteria
Each project is judged individually and not against other projects. Projects are judged against the six criteria in A to F (listed above)
4 The final mark is is reached by adding the scores in each of the areas of criteria. The maximum mak is 25.
