Grade 3-4 curriculum

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Natural numbers:

•     Operations with natural numbers
•     Common factor
•     Perfect squares, perfect cubes
•     Visual methods of solving problems
•     Prime numbers, decomposition of numbers in prime factors

Fractions:

•     Least Common Multiple, Greatest Common Divisors
•     Operations with fractions
•     Fractions in their lowest terms
•     Simplifying expressions involving fractions

Contest problems:

•     Preparation for Math Kangaroo 
•     Introduction to AMC8

Grade 5-6 curriculum

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Natural numbers:

•     Exponents and their properties
•     Gauss sums
•     Averages: mean, mode, median, range of a set of numbers

Fractions:

•     More complicated expressions involving fractions
•     Percentages

Equations:

•     Introduction to linear equations
•     Solving percentage problems using equations
•     Writing math for problems

Geometry:

•     Angles, lines, measurements
•     Most important geometrical shapes: triangles, rectangles, parallelograms, circles
•     Areas and perimeters

Math contest:

•     More advanced method for contest like Math Kangaroo, AMC8 and Gray Jay 

Grade 8 curriculum

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Algebra:

•     Radicals
•     Rates and proportions: word problems
•     Sequences
•     Functions and operators
•     Word problems and systems of equations
•     Time, travel, work

Geometry:

•     Angles
•     Congruence and similarity
•     The Pythagorean Theorem and special triangles
•     Analytic geometry
•     Basic 3D geometry   

Number theory:

•     Gauss sums
•     Number of divisors
•     Sum of divisors
•     Factoring techniques
•     Introduction to modular arithmetic

Counting:

•     Counting sets
•     Complementary counting 
•     Pascal’s triangle
•     Counting paths
•     Counting with digits
•     Probability

Grade 9 curriculum

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Algebra:

•     The Quadratic equation – introduction
•     Sequences: arithmetic and geometry progressions
•     Word problems and systems of equations
•     Time, travel, work

Geometry:

•     Coordinate geometry: lines, circles, parabolas 
•     Coordinate geometry: intersections of lines, circles, conditions for tangent lines
•     Similar triangles
•     3D geometry: areas and volumes 

Number theory:

•     Number bases – introduction
•     Factoring techniques – introduction
•     Introduction to Diophantine equations

Counting:

•     Stars and Bars
•     The Binomial Theorem and Pascal’s Triangle 
•     Overcounting
•     Casework
•     Counting with digits
•     Probability

Grade 10 curriculum

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Algebra:

•     The Quadratic equation
•     Polynomials and factorization, more advanced techniques
•     Sequences
•     Functions and operators
•     Word problems and systems of equations
•     Time, travel, work

Geometry:

•     Important lines in triangles and their intersections
•     Similar triangles
•     Circles, angles in circles, quadrilateral inscribed in circles, Power of a Point
•     Trigonometry: the unit circle, The Cosine Law, The Sine Law
•     3D geometry: angles and computations in 3D, lines perpendicular on planes   

Number theory:

•     Number bases
•     Fermat’s Little Theorem
•     Factoring techniques
•     Introduction to Diophantine equations

Counting:

•     Stars and Bars
•     The Binomial Theorem and Pascal’s Triangle 
•     Overcounting
•     Casework
•     Counting with digits
•     Probability

Grade 11 curriculum

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Algebra:

•     The Quadratic function, quadratics with parameters
•     Polynomial division, The Rational Theorem, new factorization techniques
•     Sequences: arithmetic and geometry sequences, recursive sequences
•     Word problems and systems of equations
•     Logarithms

Geometry:

•     Important lines in triangles, computations of lengths
•     Circles, angles in circles, quadrilateral inscribed in circles, Power of a Point
•     Trigonometrical identities and equations, periodicity of trigonometric functions
•      Areas and computational geometry using trigonometry
•     3D geometry: computations in 3D using trigonometry and coordinate geometry  

Number theory:

•     Number bases
•     Fermat’s Little Theorem and Euler’s Theorem
•     Factoring techniques
•     Diophantine equations

Counting:

•     Stars and Bars
•     Counting with Recursion
•     Probability
•     Expected Value

Grade 12 curriculum

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Advanced functions 12:

•     Transformations of functions
•     Functions: asymptotes, domain of definition, 
•     Financial mathematics

Calculus:

•     Continuous functions and limits
•     The tangent line
•     First derivatives and its use, intervals of monotonicity
•     Second derivative and its use, concavity of functions
•     Graphing functions, putting it all together
•     Rolle Theorem and Mean Value Theorem
•     L’Hospital Rule
•     Integrals, introduction
•     Vectors and their applications

Euclid preparation: putting together our previous work to prepare students for the Euclid Contest