IB MATH STUDIES
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

Review for the IB Exam to be given in May.