Vadim Gritsyuk

Universal Adanced Math

1. Arithmetic (32 h)
   1.1. Whole numbers (6 h)
   1.1.1. Prime or composite
   1.1.2. Factors
   1.1.3. Divisibility
   1.1.3.1. Divisibility rules
   1.1.3.2. Proof of divisibility
   1.1.4. Prime factorization
   1.1.5. Greatest common factor. Least common multiple. Algorithms. Word problems
   1.2. Integers (6 h)
   1.2.1. Integers on number lines
   1.2.2. Points and their coordinates on a plane
   1.2.3. Opposite integer (Additive inverse) and absolute value. Geometric interpretation of an absolute value
   1.2.4. Compare and order integers
   1.2.5. Operations with integer
   1.2.6. Properties of addition
   1.2.7. Properties of multiplication
   1.2.8. Order of operations. PEMDAS. Parentheses rules
   1.3. Rational and irrational numbers (4 h)
   1.3.1. Definition. Identify of rational numbers
   1.3.2. Fractions and decimals
   1.3.3. Scientific notation
   1.3.3.1. Convert between standard and scientific notation
   1.3.3.2. Compare numbers written in scientific notation
   1.3.3.3. Operations with numbers written in scientific notation
   1.3.4. Convert fraction to decimal
   1.3.5. Terminating decimals. Nonterminating decimals. Identify of decimal’s type
   1.3.6. Rounding
   1.3.7. Convert terminating decimal to fraction
   1.3.8. Convert nonterminating decimal to fraction
   1.3.9. Compare rational numbers
   1.4. Fractions and mixed numbers (2h)
   1.4.1. Operation with fraction and mixed numbers
   1.4.2. Least common denominator
   1.4.3. Addition and subtraction
   1.4.4. Multiplication and division
   1.4.5. Reciprocals (Multiplicative inverse)
   1.5. Exponents and roots (4 h)
   1.5.1. Properties of exponents
   1.5.2. Operations with exponents
   1.5.3. Solve simple equations with exponents
   1.5.4. Exponent with negative bases
   1.5.5. Exponent with decimal bases
   1.5.6. Negative exponents
   1.5.7. Evaluate expressions using properties of exponents
   1.5.8. Roots and fractional exponents
   1.5.9. Square roots of perfect squares
   1.5.10. Arithmetic and algebraic value of a root of even degree
   1.5.11. Estimation of square roots
   1.5.12. Solve simple equations using square roots
   1.5.13. Cube roots of perfect cubes
   1.6. Ratio, rates and proportions (4 h)
   1.6.1. Equivalent ratios
   1.6.2. Compare ratios
   1.6.3. Solve proportions
   1.6.4. Estimate population size using proportions
   1.6.5. Scale drawings. Word problems
   1.6.6. Proportional division
   1.6.7. Additional rules of proportions
   1.7. Percent (4 h)
   1.7.1. Convert between percents, fractions, and decimals
   1.7.2. Find a percent of a number
   1.7.3. Find what percent one number is of another
   1.7.4. Find a whole by given part and percent
   1.7.5. Percent equation
   1.7.6. Percent of change
   1.7.7. Percent of change: find the original amount word problems
   1.7.8. Simple interest
   1.7.9. Compound interest
   1.8. Proportional relationship (2 h)
   1.8.1. Defining proportional relationship: table, equation, graph
   1.8.2. Identify proportional relationship: table, equation, graph
   1.8.3. Find the constant of proportionality from a graph, table
   1.8.4. Write equation from graph and table
   1.8.5. Graph proportional relationship
   1.8.6. Interpret graphs of proportional relationships
   1.9. Units of measurement
   1.10. Time
   1.11. Temperature
2. Algebra (44 h)
   2.1. Expression and properties (6 h)
   2.1.1. Write variable expressions
   2.1.2. Evaluate variable expressions
   2.1.3. Terms and coefficients
   2.1.4. Factors of variable expressions
   2.1.5. Properties of addition and multiplication
   2.1.6. Operation with distributive property. Factor out and expand
   2.1.7. Like terms. Combining like terms
   2.1.8. Identify equivalent linear expressions
   2.1.9. Identify equivalent linear expressions: word problems
   2.2. One variable linear equations (4)
   2.2.1. Properties of equalities
   2.2.2. Solving one variable linear equations
   2.2.3. Word problems
   2.3. One variable inequalities (4 h)
   2.3.1. Solutions to inequalities
   2.3.2. Graph inequalities on number line
   2.3.3. Write inequality from number line
   2.3.4. Properties of inequalities
   2.3.5. Solve inequality and graph solutions
   2.4. Functions (6 h)
   2.4.1. Identify function
   2.4.2. Independent and dependent variables
   2.4.3. Ways to setup a function: table, equation, graph
   2.4.4. Does (x, y) satisfy equation?
   2.4.5. Evaluate function
   2.4.6. Find values using function graphs
   2.4.7. Domain and range of functions
   2.5. Linear function (4 h)
   2.5.1. Equation of linear function
   2.5.2. Identify linear function from table
   2.5.3. Find a slope and shift form a graph
   2.5.4. Find a slope and shift form a table
   2.5.5. Find a missing coordinate using a slope
   2.5.6. Write a linear equation from a graph
   2.5.7. Write a linear equation from a slope and a point
   2.5.8. Write a linear equation from two points
   2.5.9. Linear equation in standard form and slope-intercept form
   2.5.10. Slopes of parallel and perpendicular lines
   2.5.11. Word problems
   2.5.12. Rate of change
   2.6. Systems of linear equations (4 h)
   2.6.1. Is (x, y) a solution to the system of equations?
   2.6.2. Solve a system of equations by graphing
   2.6.3. Find the number of solutions to a system of equations by graphing
   2.6.3.1. Consistent and independent with one solutions
   2.6.3.2. Consistent and dependent with infinitely many solutions
   2.6.3.3. Inconsistent with no solutions
   2.6.4. Solve a system of equations using substitution
   2.6.5. Solve a system of equations using elimination
   2.7. Monomials and polynomials (10)
   2.7.1. Operations with monomials
   2.7.1.1. Addition and subtraction like terms
   2.7.1.2. Multiplication
   2.7.1.3. Division
   2.7.1.4. Power of monomial
   2.7.1.5. Square and cube roots of monomials
   2.7.2. Operations with polynomials
   2.7.2.1. Addition and subtraction
   2.7.2.2. Multiplication
   2.7.2.3. Expand and factor out
   2.7.2.4. Special factoring rules
   2.7.2.4.1. Difference of squares
   2.7.2.4.2. Square of sum and difference
   2.7.2.4.3. Difference and sum of cubes
   2.7.2.4.4. Cube of sum and difference
   2.8. Coordinate plane (2)
   2.8.1. Review. Quadrants and axes
   2.8.2. Distance between two points
   2.8.3. Distance between two parallel lines
   2.8.4. Distance from point to line
   2.9. Number sequences (4 h)
   2.9.1. Arithmetic sequences
   2.9.2. Geometric sequences
   2.9.3. Identify arithmetic and geometric sequences
3. Geometry (38 h)
   3.1. Two-dimensional figures (2 h)
   3.2. Identify and classify polygons (10 h)
   3.2.1. Classify triangles
   3.2.2. Identify trapezoids
   3.2.3. Classify quadrilaterals
   3.2.4. Graph triangles and quadrilaterals
   3.2.5. Find missing angles in triangles
   3.2.6. Find missing angles in triangles using ratios
   3.2.7. Find missing angles in quadrilaterals
   3.2.8. Find missing angles in quadrilaterals
   3.2.9. Exterior Angle Theorem
   3.2.10. Interior angles of polygons
   3.2.11. Identify complementary, supplementary, vertical, adjacent, and congruent angles
   3.2.12. Find measures of complementary, supplementary, vertical, and adjacent angles
   3.2.13. Identify alternate interior and alternate exterior angles
   3.2.14. Transversals of parallel lines: name angle pairs
   3.2.15. Transversals of parallel lines: find angle measures
   3.2.16. Find lengths and measures of bisected line segments and angles
   3.2.17. Parts of a circle
   3.3. Transformations and congruence (6 h)
   3.3.1. Line symmetry
   3.3.2. Rotational symmetry
   3.3.3. Rotational symmetry: amount of rotation
   3.3.4. Identify reflections, rotations, and translations
   3.3.5. Describe a sequence of transformations
   3.3.6. Translations: graph the image
   3.3.7. Translations: find the coordinates
   3.3.8. Reflections over the x- and y-axes: graph the image
   3.3.9. Reflections over the x- and y-axes: find the coordinates
   3.3.10. Reflections: graph the image
   3.3.11. Reflections: find the coordinates
   3.3.12. Rotations: graph the image
   3.3.13. Rotations: find the coordinates
   3.3.14. Congruence statements and corresponding parts
   3.3.15. Side lengths and angle measures of congruent figures
   3.3.16. Congruent triangles: SSS, SAS, and ASA
   3.4. Transformations and similarity (2 h)
   3.4.1. Similar and congruent figures
   3.4.2. Dilations: graph the image
   3.4.3. Dilations: find the coordinates
   3.4.4. Dilations: scale factor and classification
   3.4.5. Side lengths and angle measures of similar figures
   3.5. Pythagorean theorem (4  h)
   3.5.1. Find the length of the hypotenuse
   3.5.2. Pythagorean theorem: find the missing leg length
   3.5.3. Pythagorean theorem: find the perimeter
   3.5.4. Pythagorean theorem: word problems
   3.5.5. Converse of the Pythagorean theorem: is it a right triangle?
   3.6. Three-dimensional figures (2 h)
   3.6.1. Parts of three-dimensional figures
   3.6.2. Nets of three-dimensional figures
   3.6.3. Front, side, and top view
   3.6.4. Base plans
   3.6.5. Similar solids
   3.7. Geometric measurement (12 h)
   3.7.1. Perimeter
   3.7.2. Area
   3.7.3. Area and perimeter: word problems
   3.7.4. Area between two shapes
   3.7.5. Area and circumference of circles
   3.7.6. Circles: word problems
   3.7.7. Area and perimeter of semicircles and quarter circles
   3.7.8. Volume of cubes, prisms, and pyramids
   3.7.9. Surface area of cubes, prisms, and pyramids
   3.7.10. Volume of cylinders
   3.7.11. Volume of cones
   3.7.12. Surface area of cylinders
   3.7.13. Surface area of cones
   3.7.14. Volume of spheres
   3.7.15. Surface area of spheres
   3.7.16. Volume and surface area of similar solids
   3.7.17. Perimeter and area: changes in scale
4. Probability and statistics (12 h)
   4.1. Probability of simple events
   4.2. Probability of opposite, mutually exclusive, and overlapping events
   4.3. Experimental probability
   4.4. Find probabilities using two-way frequency tables
   4.5. Make predictions
   4.6. Compound events: find the number of outcomes
   4.7. Compound events: find the number of sums
   4.8. Identify independent and dependent events
   4.9. Probability of independent and dependent events
   4.10. Factorials
   4.11. Permutations
   4.12. Counting principle
   4.13. Combination and permutation notation
   4.14. Calculate mean, median, mode, and range
   4.15. Interpret charts and graphs to find mean, median, mode, and range
   4.16. Mean, median, mode, and range: find the missing number
   4.17. Changes in mean, median, mode, and range
   4.18. Quartiles
   4.19. Identify an outlier
   4.20. Identify an outlier and describe the effect of removing it
   4.21. Outliers in scatter plots
   4.22. Scatter plots: line of best fit
   4.23. Identify representative, random, and biased samples