COURSE CURRICULUM
S.A.T. Math
Total duration (199 hours) or (9 months, 4 hours per week).
Arithmetic. (26 h)
1.1. Number theory. (12 h)
1.1.1. Natural, whole and negative numbers.
1.1.2. Fractions
1.1.3. Decimals.
1.1.4. Addition, subtraction, multiplication and division.
1.1.5. Properties of operations.
1.1.6. Division with a remainder.
1.1.7. Divisibility rules.
1.1.8. Greatest Common Factor and Least Common Multiple.
1.1.9. Exponents and properties.
1.1.10. Roots.
1.1.11. Exponents with fractional degrees.
1.1.12. Scientific notation.
1.1.13. Order of operations and applications. PEMDAS
1.1.14. Rational numbers.
1.1.15. Irrational numbers.
1.1.16. Real numbers.
1.1.17. Imaginary numbers.
1.1.18. Numbers on a number line
1.1.19. Absolute value and distance on a number line
1.1.20. Roman numerals.
1.2. Proportions. (4 h)
1.2.1. Ratio and rates. Unit rate.
1.2.2. Proportions and applications.
1.2.3. Word problems with proportions.
1.3. Percent. (4 h)
1.3.1. Relation percent, fraction and decimals.
1.3.2. Percent of change.
1.3.3. Mark Up and Mark Down.
1.3.4. Interest.
1.3.5. Compound interest.
1.4. Measurement. (4 h)
1.4.1. Metric units of measurement
1.4.2. Customary units of measurement.
1.5. Operations with time. (2 h)
Algebra (113 h)
2.1. Definitions. (1 h)
2.1.1. Variable
2.1.2. Coefficient.
2.1.3. Monomial.
2.1.4. Polynomial.
2.2. Operations with monomials. (1 h)
2.3. Properties of polynomials. (1 h)
2.4. Combining like terms. (1 h)
2.5. Algebraic addition and subtraction of polynomials. (1 h)
2.6. Operations with parentheses. (1 h)
2.7. Algebraic multiplication. (6 h)
2.7.1. Multiplication of monomials.
2.7.2. Raising a term to a power.
2.7.3. Multiplication polynomial by term
2.7.4. Multiplication polynomial by polynomial.
2.7.5. Ordered polynomials
2.7.6. Multiplication of ordered polynomials.
2.7.7. Formulas of multiplication
2.8. Algebraic division. (6 h)
2.8.1. Division of monomials.
2.8.2. Division of polynomial by monomial.
2.8.3. Division polynomial by polynomial. Long division.
2.8.4. Factorization of algebraic expressions
2.8.5. Method of auxiliary term.
2.9. Algebraic fractions. (6 h)
2.9.1. Convert denominator and numerator to an integer form.
2.9.2. Changing sign of an algebraic fraction.
2.9.3. Fraction reducing.
2.9.4. Least common denominator. Addition and subtracting fractions.
2.9.5. Operations with algebraic fractions.
2.10. Equations. (4 h)
2.10.1. Equality, Identity, Equation.
2.10.2. Properties of equations.
2.10.3. Solving a linear equation.
2.10.4. Equation with parameters.
2.10.5. Equations in word problems.
2.11. Coordinate plane. (2 h)
2.11.1. Distance on a coordinate plane.
2.12. Linear function. (6 h)
2.12.1. Properties of a linear function.
2.12.2. Midpoint, slope, intercepts, distance.
2.12.3. Parallel and perpendicular lines on a coordinate plane.
2.12.4. Word problems with linear functions.
2.12.5. Proportional relationship.
2.13. Transformation and Symmetry. (6 h)
2.14. Quadratic equations. (12 h)
2.14.1. General form of quadratic equation.
2.14.2. Incomplete quadratic equation.
2.14.3. Viet Theorem.
2.14.4. Factorization of quadratic trinomial.
2.15. Quadratic function. (4 h)
2.15.1. Graph of a quadratic function.
2.15.2. Explore of a quadratic function. Completing square.
2.15.3. Problems with quadratic function.
2.16. Inequalities. (12 h)
2.16.1. Verbal expressions with inequalities.
2.16.2. Properties of inequality.
2.16.3. Solving of inequalities.
2.16.4. Numeric and point sets using inequalities.
2.16.5. Word problems with inequalities.
2.16.6. Absolute value of real number(magnitude).
2.16.7. Method of intervals for solving an inequality.
2.16.8. Inequalities with absolute value.
2.17. Systems of a linear equations. (2 h)
2.18. Roots. (6 h)
2.18.1. Values of root. Principal root.
2.18.2. Properties of roots.
2.18.3. Transform irrational expressions.
2.18.4. Operations with roots.
2.18.5. Operations with irrational expressions. Like roots.
2.19. Irrational equations (2 h)
2.19.1. Extra roots of equation
2.19.2. Equation with two radicals.
2.20. Exponent and properties. (1 h)
2.21. Exponential function. (2 h)
2.22. Logarithms. (2 h)
2.23. Exponential and logarithmic equations. (4 h)
2.24. Functions and graphs. (12 h)
2.24.1. Definitions.
2.24.2. Increasing and decreasing functions.
2.24.3. Asymptote.
2.24.4. Extremum, minimum and maximum.
2.24.5. Convexity and concavity of functions.
2.24.6. Inverse function.
2.24.7. Odd and Even function.
2.24.8. Function transformation.
2.25. Binomial theorem. (2 h)
2.26. Arrangements. (4 h)
2.27. Divisibility. (6 h)
Geometry. (18) h
3.1. Plane geometry. (12 h)
3.1.1. Definitions.
3.1.2. Lines and properties.
3.1.2.1. Perpendicular lines
3.1.2.2. Parallel lines.
3.1.2.3. Transversal.
3.1.3. Angles and properties.
3.1.3.1. Measurement of an angle.
3.1.3.2. Supplementary, complementary and adjacent angles.
3.1.3.3. Problems.
3.1.4. Polygons.
3.1.4.1. Area and perimeter.
3.1.4.2. Angles in polygons.
3.1.4.3. Regular polygons.
3.1.4.4. Congruent and similar polygons.
3.1.5. Triangles and properties
3.1.6. Quadrilaterals.
3.1.6.1. Trapezoid
3.1.6.2. Parallelogram.
3.1.6.3. Rectangle.
3.1.7. Compound shapes.
3.1.8. Circle and its parts.
3.2. Solid geometry. (6 h)
3.2.1. Classify 3D figures.
3.2.2. Volume and Net.
3.2.3. Prizm.
3.2.4. Pyramid.
3.2.5. Sphere.
3.2.6. Cylinder.
Trigonometry (24 h)
4.1. Angles and measures.
4.2. Relations in a triangle.
4.3. Trigonometric function of special angles.
4.4. Main trigonometric identity
4.5. Trigonometric function of the special angles, involving regular polygons.
4.6. Reciprocals of trigonometric functions.
4.7. Trigonometric function of any angle.
4.8. Reference angle.
4.9. Trigonometric function of real number.
4.10. Trigonometric identities.
4.11. Trigonometric functions and graphs.
4.12. Trigonometric equalities.
4.13. Solving of triangles.
Probability theory and statistics. (6 h)
Scientific calculator, GeoGebra and CAS. (12 h)
WHAT YOU WILL LEARN
After completing this course you will be able to pass any test according to current requirements to your age, skills, and expertise.
