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S A T Math Prep. Brain Groomer. S A T Math Topics. Number Theory Rate problems Geometry I Algebra I Geometry II Algebra II Geometry III Set Theory. Number Theory. Number Theory. Fractions Decimals Scientific Form Percentages Ratios Proportions Variations.

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## S A T Math Prep

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**S A T Math Prep**Brain Groomer**S A T Math Topics**• Number Theory • Rate problems • Geometry I • Algebra I • Geometry II • Algebra II • Geometry III • Set Theory**Number Theory**• Fractions • Decimals • Scientific Form • Percentages • Ratios • Proportions • Variations**Fractions, Decimals, etc.**• Have an eye on the answer. • Simplify fractions to the extent needed • Decimal and Percentage • Decimal and scientific form**Proportions**• Direct Proportions • If X and Y are directly proportional • X1 / X 2 = Y1 / Y2 ; or X1 / Y1 = X2 / Y2; or • X / Y = constant • Cost of items • Indirect Proportions • X1 * Y1 = X2 * Y2 ; or X*Y = constant • Number of workers and time to finish • Number of Taps and time to fill a bucket**Rate Problems**• Word problem setup • Distance and time • Work • Cost**Geometry I**• Area • Perimeter • Volume**Area**• Area • Triangle, Square, Rectangle, Triangle, Parallelogram, Trapezoid, Circle, Sector • Surface area • Cubes, Cuboids, Prism, Sphere, Cylinder, Cone**Algebra I**• Properties • Equations • Graphs • Inequalities • Exponents**Geometry II**• Triangles • Quadrilaterals • Polygons • Circles**Geometry Topics**• Pythagorean Theorem • special properties of isosceles, equilateral, and right triangles, Similarity • Area and circumference of a circle • Area and perimeter of a polygon • Volume of a box, cube, and cylinder • Properties of parallel and perpendicular lines • Coordinate geometry, Similarity, Transformations • Slope,**Pythagoras Theorem**• A**2 + B**2 = C**2 • Common Ratios • 45 degree triangle • 30 / 60 degree Triangle • Area of right angle Triangle**Triangles**• Isosceles, Equilateral, Scalene • Sum of the angles in aTriangle • Two sides of a triangle • Exterior angle • Similar • Congruent**Circles**• Area • Circumference • Sector area • Sector perimeter**Polygons**• Regular • Sum of interior angles • Sum of exterior angles • Pentagon, Hexagon, Octagon • Quadrilateral • Square; Rectangle; • Trapezoid, Parallelogram, Rhombus**Volume and Surface Area**• Cube • Cuboid • Sphere • Cylinder • Cone • Pyramid**Parallel Lines**• Properties**Major Topics**• Properties of exponents • Concepts of algebraic functions • Quadratic equations • Equations of lines • Absolute value • Algebraic word problems • Solutions of linear equations and inequalities • Systems of equations and inequalities • Direct and inverse variation • Newly defined symbols based on commonly used operations**Functions**• Domain • Range • Function value • Substitution • Function of a function • Zeros of a function • Y intercept • X intercept**General Functions ctd.**• X shift: y = f(x-h) • Y shift: y = f(x) + h • Linear • Quadratic • Polynomial • Slope**Properties of exponent**• (X ** m) * (X ** n) = (X ** (m + n)) • (X ** m) / (X ** n) = (X ** (m - n)) • (X ** m) ** n = (X ** mn) • X ** m ** n = X ** m ** n • (X ** 0) = 1 • (X ** (-m) ) = 1 / ( X ** m) • (X ** m) * ( Y ** m) = (X*Y) ** m • Roots or when exponent = ( 1 / m)**Quadratic Functions**• Parabola • Roots**Number Theory**• Integers: . . . , –4, –3, –2, –1, 0, 1, 2, 3, 4, . . . • (Note: zero is neither positive nor negative.) • Consecutive Integers: Integers that follow in sequence; for example, 22, 23, 24, 25. Consecutive integers can be more generally represented by n, n +1, n + 2, n + 3, . . . • Odd Integers: . . . , –7, –5, –3, –1, 1, 3, 5, 7, . . . , 2k + 1, . . . , where k is an integer • Even Integers: . . . , –6, –4, –2, 0, 2, 4, 6, . . . , 2k, . . . , where k is an integer • (Note: zero is an even integer.) • Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, . . . • (Note: 1 is not a prime and 2 is the only even prime.) • Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 • (Note: the units digit and the ones digit refer to the same digit in a number. For example, in the number 125, the 5 is called the units digit or the ones digit.)**Percentage**• Percent means hundredths, or number out of 100. For example, • 42 percent of X = 0.42 * X or (42/100) * X • Example: If the sales tax on a $30.00 item is $1.80, what is the sales tax rate? • Solution: 1.8 = (n / 100) * 30 ; n = 6 ; Tax is 6% • Percent Increase/Decrease • Example: If the price of a computer was decreased from $1,000 to $750, by what percent was the price decreased? • Solution: The price decrease is $250. The percent decrease is the value of n in the equation The value of n is 25, so the price was decreased by 25%.**Sequence**• Arithmetic • 1 , 5 , 9, 13, … • Geometric • 2, 12, 72, 432 • Alternating • -2, 7, -12, 17, -22, 27, -32**Data Analysis**• Data interpretation (tables and graphs) • Descriptive statistics (mean, median, and mode)**Average etc..**• Average • Average age • Average speed, distance • Mean • Mode**Geometry III**• Tables • Charts • Graphs**Set Theory and Misc.**• Sets • Relations • Domain • Range**Misc.**• Number Theory • Properties of integers (even, odd, prime numbers, divisibility, etc.) • Rational numbers • Arithmetic word problems (including percent, ratio, and proportion) • Sets (union, intersection, elements) • Counting techniques • Sequences and series (including exponential growth)

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