Program of our Math classes

Math pre-K -- Math 3

Please see the attached document: Curriculum PreK-3

Math 4

Main topics studied in Math 4

  • Order of operations
  • Prime numbers, divisibility tests
  • Simple fractions
  • Negative numbers
  • Geometrical symmetries
  • Angles
  • Special quadrilaterals

Math 5

Main topics studied in Math 5

  • Overview of prime factorization
  • LCM and GCD
  • Fractions with large denominators
  • Algebraic laws. Distributivity (opening parentheses)
  • Negative numbers. Multiplication. Absolute value
  • Equations and word problems (big topic!)
  • Powers of 2 and binary numbers
  • Parallel lines, transversal lines, corresponding angles etc.
  • Congruence tests for triangles
  • Pythagorean theorem

Math 6

Main topics studied in Math 6

  • Basic logic (knights and knaves, logic operations)
  • Set theory basics (basic operations and Venn diagrams)
  • Linear equations continued. Simple inequalities (Review)
  • Powers: an am=an+m . Multiplication and division by powers of 10 (Review)
  • Square roots. Rational and irrational numbers
  • Arithmetic and Geometric Progressions
  • Probability. Basic combinatorics: permutations
  • Similarity; relation with areas and volumes
  • Constructions with ruler and compass
  • Coordinate plane and graphs of simple functions

Math 7

Main topics studied in Math 7

  • Combinatorics: choosing with and without repetitions. Pascal triangle; formual for nCk (no proof, and no binomial theorem)
  • Vectors and operations with them (in coordinates).
  • Basic trigonometry (definition of sin, cos). Law of sines.
  • Transformation of the plane. Reflections, rotations, and their compositions.
  • Quadratic equation. Quadratic formula, Vieta formula. Parabola.
  • Solving inequalities using interval method.
  • Fibonacci numbers

    • Optional topics

    • Plane patterns and symmetries.

    Math 8

    Main topics studied in Math 8

    • Overview of combinatorics. Pascal triangle and binomial formula.
    • Divisibility, Euclid's algorithm, arithmetic of remainders, congruences. Application: check digits
      Fundamental theorem of arithmetic
    • Euclidean geometry (following Kiselev). First postulates, congruence tests for triangles, alternate interior angle theorem, properties of sepcial quadrialterals, similar triangles, Thales theorem, inscribed angles.

    Math 9

    Main topics studied in Math 9

    • Elements of mathematical logic and set theory. Quantifiers. Bijection and injection. Infinite sets and cardinality.
    • Functions and graphs. Even, odd, periodic, monotonic functions. Graphs of basic functions (power function, roots, sin, cos,) and their transformations. Inverse function.
    • Equations of ellipse, hyperbola, parabola. Conic sections
    • Exponential function. Logarithm. Equations and inequalities with exponents and logarithms.
    • Polynomials; division of polynomials. Vieta formulas
    • Complex numbers
    • Mathematical induction

    Optional topics

    • Trigonometry. Trigonometric equations and formulas.
    • Advanced geometry with vectors: Ceva theorem, Ptolemey theorem, nine point circle.

    Math 10

    Main topics studied in Math 10

    • Sets and functions. Bijections
    • Infinite sets and cardinality
    • Equivalence relations.Zn
    • Solving equivalences, invertible elements in Zn, Chinese remainder theorem
    • Euler function and Public Key cryptography

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