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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

S A T Math Prep

Brain Groomer

s a t math topics
S A T Math Topics
  • Number Theory
  • Rate problems
  • Geometry I
  • Algebra I
  • Geometry II
  • Algebra II
  • Geometry III
  • Set Theory
number theory4
Number Theory
  • Fractions
  • Decimals
  • Scientific Form
  • Percentages
  • Ratios
  • Proportions
  • Variations
fractions decimals etc
Fractions, Decimals, etc.
  • Have an eye on the answer.
  • Simplify fractions to the extent needed
  • Decimal and Percentage
  • Decimal and scientific form
proportions
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 problems8
Rate Problems
  • Word problem setup
  • Distance and time
  • Work
  • Cost
geometry i10
Geometry I
  • Area
  • Perimeter
  • Volume
slide11
Area
  • Area
    • Triangle, Square, Rectangle, Triangle, Parallelogram, Trapezoid, Circle, Sector
  • Surface area
    • Cubes, Cuboids, Prism, Sphere, Cylinder, Cone
algebra i13
Algebra I
  • Properties
  • Equations
  • Graphs
  • Inequalities
  • Exponents
geometry ii15
Geometry II
  • Triangles
  • Quadrilaterals
  • Polygons
  • Circles
geometry topics
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
Pythagoras Theorem
  • A**2 + B**2 = C**2
  • Common Ratios
    • 45 degree triangle
    • 30 / 60 degree Triangle
  • Area of right angle Triangle
triangles
Triangles
  • Isosceles, Equilateral, Scalene
  • Sum of the angles in aTriangle
  • Two sides of a triangle
  • Exterior angle
  • Similar
  • Congruent
circles
Circles
  • Area
  • Circumference
  • Sector area
  • Sector perimeter
polygons
Polygons
  • Regular
  • Sum of interior angles
  • Sum of exterior angles
  • Pentagon, Hexagon, Octagon
  • Quadrilateral
    • Square; Rectangle;
    • Trapezoid, Parallelogram, Rhombus
volume and surface area
Volume and Surface Area
  • Cube
  • Cuboid
  • Sphere
  • Cylinder
  • Cone
  • Pyramid
parallel lines
Parallel Lines
  • Properties
major topics
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
Functions
  • Domain
  • Range
  • Function value
    • Substitution
  • Function of a function
  • Zeros of a function
  • Y intercept
  • X intercept
general functions ctd
General Functions ctd.
  • X shift: y = f(x-h)
  • Y shift: y = f(x) + h
  • Linear
  • Quadratic
  • Polynomial
  • Slope
properties of exponent
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
Quadratic Functions
  • Parabola
  • Roots
number theory29
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
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
Sequence
  • Arithmetic
    • 1 , 5 , 9, 13, …
  • Geometric
    • 2, 12, 72, 432
  • Alternating
    • -2, 7, -12, 17, -22, 27, -32
data analysis
Data Analysis
  • Data interpretation (tables and graphs)
  • Descriptive statistics (mean, median, and mode)
average etc
Average etc..
  • Average
    • Average age
    • Average speed, distance
  • Mean
  • Mode
geometry iii36
Geometry III
  • Tables
  • Charts
  • Graphs
set theory and misc
Set Theory and Misc.
  • Sets
  • Relations
  • Domain
  • Range
slide39
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)