This is a representative list of topics covered in our Grade 12 Math program - however all programs will be customized for the individual student.
Algebra I
- Linear equations/inequalities
- Monomials and polynomials
- Factoring second and third degree polynomials
- Rational expressions/functions
- Quadratic equations
- Quadratic functions
- Exponents, factors, variation, exponential growth/decay
- Hypothesis, counterexamples
- Correlation for data
- Patterns, relations, functions
- Changing parameters of given functions
- Graphs, matrices, sequences, series, recursive relations
- Radical equations/inequalities
- Limits and infinity
Geometry And Measurement
- Logical reasoning
- Geometric proofs
- Euclidean/non-Euclidean geometries
- Formal/informal proofs
- Conditional statements
- Pythagorean Theorem
- Intersection of a plane with 3-d figures
- Congruence, similarity, triangle inequality theorem
- Properties of quadrilaterals, circles, parallel lines cut by a transversal
- Angles of triangles and polygons
- Basic constructions
- Triangle congruence relationships
- Similarity properties and transformations, trigonometric ratios, Pythagorean triples
- Coordinate geometry
- Special right triangles
- Properties of inscribed/circumscribed polygons of circles
- Rotations, translations, reflections
- Planar cross-sections; perpendicular lines/planes
- Effect of rigid motions on figures, isosceles triangle theorem; polyhedra
- Parabolic functions (vertex, axis of symmetry)
- Compound loci in the coordinate plane
Probability And Statistics
- Types of events
- Measures of central tendency/dispersion, quartiles, interquartiles
- Permutations and combinations
- Methods of data representation
- Statistical experiments (more than one variable)
- Correlation and causation
AP Probability And Statistics
- Probability problems with finite sample spaces
- Conditional probability
- Discrete/continuous random variables
- Mean, variance of discrete random variable
- Standard distributions
- Mean, standard deviation of normally distributed random variable
- Central limit theorem
- Line of best fit - least squares regression
- Correlation coefficient
- Statistic of a distribution
- Mean, standard deviation of sampling distribution
- Mean, standard deviation of population distribution
- Confidence intervals
- P-value for a statistic
- Chi-square distribution/test
Algebra II
- Absolute value to solve equations/inequalities
- Systems of linear equations/inequalities
- Operations on polynomials
- Factoring polynomials/trinomials
- Operations on complex numbers
- Operations on rational expressions
- Graphing quadratic equations
- Quadratic equations in complex number system
- Quadratic functions
- Laws and properties of logarithms
- Fractional exponents, exponential functions
- Conic sections
- Ellipse, parabola, hyperbola
- Binomial theorem
- Types of series
- Composition of functions
- Continuous and discrete functions
- Complex numbers for solutions of quadratic equations
- Factoring, exponents
- Systems of equations/inequalities
- Estimation of solutions
- Standard functions
- Inverse of a function
- Solutions of function equations
- Slope, various forms of equation of line
TRIGONOMETRY
- Graphing functions
- Trigonometric functions
- Formulas for sines and cosiness
- Polar/rectangular coordinates
- Complex numbers in polar form
- DeMoivre's theorem
- Inverse trigonometric functions
- Area of triangle (one angle and 2 adjacent sides)
PRE-CALCULUS
- Limits of sequences, series
- Continuity, end behavior, asymptotes, limits
- Regression
- Law of Sines/Cosines, area formulas
- Parametric/rectangular forms of functions
- Vectors
- Even/odd functions, significant values
- Functions and operations
- Conic sections- applications
- Sequences and series
CALCULUS
- Limits- operations on functions
- Continuity of a function
- Intermediate value, extreme value theorem
- Derivatives, differentiability
- Derivatives of functions
- Chain rule
- Rolle's theorem, mean value theorem, and L'Hopital's rule
- Maxima, minima, inflection points, intervals
- Newton's method (approximating the zeros of a function)
- Differentiation to solve problems
- Definite/indefinite integrals
- Riemann sums
- Fundamental theorem of calculus
- Definite integrals problems
- Techniques of integration
- Inverse trigonometric functions
- Integrals of functions
- Simpson's rule, Newton's method
- Improper integrals (limits of definite integrals)
- Tests for convergence/divergence of sequences/series
- Power series, Taylor series/polynomials
- Elementary differential equations
Linear Algebra
- Types of linear systems
- Gauss-Jordan elimination, Gauss-Jordan method
- Vectors and vector addition
- Geometrical solution sets of systems of equations
- Rectangular matrices to row echelon form
- Matrix multiplication
- Inverse to a square matrix
- Determinants of 2 by 2 and 3 by 3 matrices
- Row reduction methods, Cramer's rule
- Scalar (dot) product
Mathematical Analysis
- Various forms of complex numbers
- Mathematical induction
- Roots and poles of rational functions
- Graphing rational functions - asymptotes
- Limits of sequence/function
Mathematical Models with Applications
- Theoretical/empirical probability
- Probability models
- Studying patterns and analyzing data
- Rates, linear functions, direct/inverse variation
- Problems related to personal income, credit, financial planning
- Transformations, symmetry
