# 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

## 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.
• 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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