This course is designed to prepare students for either IB Methods 12 or AP Calculus.  It will build upon existing knowledge and skills and introduce new topics such as polynomial functions, graphing, series and sequences, exponential and logarithmic functions, vectors, trigonometry, and matrices.  It is intended to provide a sound mathematical basis for those students planning to pursue further studies in such fields as chemistry, economics and business administration.  It is a demanding program since it contains a variety of topics and requires background knowledge.  Students will also learn to apply mathematics to other areas of their studies.  The prerequisite for this course is a minimum of a B average in Integrated Algebra II/Trigonometry.

Learning Objectives
    The student will:
        Demonstrate the following skills
 

Numbers

Computation
    The student will understand and be able to use:
        Decimal approximations
        Significant figures
        Absolute, relative and percentage errors
    The student will:
        Give answers to correct precision.
        Calculate margin of error in answers.

Logarithms
    The student will understand and be able to use:
        Laws of indices
        Use of positive indices
        Negative rational indices
        Concept of logarithms
        Logs to solve logarithmic equations.
        Do algebraic manipulation using log rules.

Sequences and Series
    The student will understand and be able to use:
        Arithmetic and finite geometric sequences
        Simple and compound interest
        Arithmetic and finite geometric series
        Binomial Theorem
    The student will:
        Find specific terms and sums of sequences and series.
        Calculate the principal or the interest rate using the interest formula.
        Find specific terms in a binomial expansion using the binomial theorem.

Algebra and Coordinate Geometry

Linear Equations and Inequalities
    The student will understand and be able to use:
        Simultaneous linear equations in two variables
        Simultaneous linear inequalities in two variables
        Solve and graph simultaneous equations in 2 variables.
        Solve and graph simultaneous inequalities in 2 variables.

Quadratic Functions and Equations
    The student will understand and be able to use:
        Quadratic functions with real coefficients
        Quadratic equations with real roots
        Simultaneous solution of a linear and a quadratic equation
        Solve and graph quadratic functions by hand and with a calculator.

Graphical Treatment
    The student will understand and be able to use:
        Equations of a straight line
        Parallel and perpendicular lines
        Distance between two points
        Mid-point of a line segment
        Graphing
    The student will:
        Calculate by hand and with a calculator, the distance and midpoint.
        Identify parallel and perpendicular lines.
        Calculate slope and y-intercept of lines.

Geometry and Trigonometry

Geometry
    The student will understand and be able to use:
        Similarity
        Lengths
        Areas
        Volumes
        Surface areas
        Arcs and sectors
    The student will:
        Calculate areas, lengths, volumes, surface areas, arcs, and sectors using a correct formula.

Trigonometry
    The student will understand and be able to use:
        Trigonometric ratios
        Sine and cosine rules
        Circular functions
        Graphs
        Solution of simple equations
    The student will:
        Solve equations using trigonometry.
        Solve triangles using the sine and cosine rules.
        Use both degrees and radians to solve trig equations.
        Graph the sine, cosine, and tangent functions.

Vectors and Matrices

Vectors
    The student will understand and be able to use:
        Addition and multiplication by a scalar
        Components of a vector
        Length of a vector
        Zero vector
        Negative of a vector
        Subtraction
        Unit vectors
        Calculation of a resultant
        Column vectors
        Scalar product of two vectors
        Angle between two vectors
    The student will:
        Use vector properties to add and subtract vectors.
        Find the length of a vector.
        Find the scalar and cross products.
        Find the angle between 2 vectors.
        Use vectors to represent and solve real-world problems.

Matrices

Matrix Operations
    The student will understand and be able to use:
        Addition and subtraction of matrices
        Multiplication of a matrix by a scalar
        The zero matrix
    The student will:
        Use matrix algebra to combine m x n matrices.

Square Matrices (2 x 2)
    The student will understand and be able to use:
        Unit matrix
        Determinant and inverse matrix
        Singular matrix
        Solution of simultaneous linear equations .
    The student will:
        Find the determinant of a matrix.
        Find the inverse of a non-singular 2x2 matrix.
        Solve simultaneous equations using matrix methods.

Probability
    The student will understand and be able to use:
        Mutually exclusive and independent events
        Probability tree diagrams
        Conditional probability
    The student will:
        Apply probability formulas to find unions and intersections.
        Construct tree diagrams to illustrate conditional probability.
        Construct Venn diagrams to illustrate conditional probability.
        Identify mutually exclusive events and apply probability formulas to them.
        Identify independent events and apply probability formulas to them.