SAT2数学知识汇总整理

　　为了帮助大家高效备考SAT，新东方在线SAT频道为大家带来SAT2数学知识汇总整理，希望对大家SAT备考有所帮助。更多精彩尽请关注新东方在线SAT频道!

　　I. ARITHMETIC

　　A. Whole numbers

　　1. Operations—addition, subtraction, multiplication, division

　　2. Prime and composite numbers

　　3. Factors and divisors

　　B. Fractions

　　1 Types—proper, improper, mixed numbers

　　2 Operations

　　C. Decimals

　　1 Operations

　　2 Conversions

　　a) Decimals to fractions 0) Fractions to decimals

　　3 Rounding and approximation

　　4 Powers of 10 a) Multiplication 0) Division

　　c) Scientific notation

　　D. Percent

　　1 Conversions

　　a) Percent to decimal 0) Decimal to percent

　　2 Percent problems

　　E Ratio and proportion

　　F Square roots

　　G. Averages

　　H Metric measurement

　　II ALGEBRA

　　A Signed numbers

　　1 absolute value

　　2 Inequality and order of signed numbers

　　3 Addition, subtraction, multiplication, division

　　4 Order of operations

　　5 Grouping symbols

　　6 Evaluating algebraic expressions and formulas

　　B. Properties of operations

　　1 Commutative properties

　　2 Associative properties

　　3 Distributive properties

　　4 Special properties of zero

　　5 Special properties of one

　　6 Additive and multiplicative inverses

　　C Operations with polynomials

　　1 Exponents and coefficients

　　2 Addition and subtraction

　　3 Multiplication

　　4 Division

　　D Equations in one variable

　　1 Methods of solution

　　2 Literal equations

　　E Inequalities in one variable

　　F Systems of equations and inequalities in two variables

　　G. verbal problems

　　1 number

　　2 Consecutive integer

　　3 Motion

　　4 Coin

　　5 Mixture

　　6 Age

　　7 Work

　　3 Variation—direct and inverse

　　H. Special products and factoring

　　1 Common monomial factors

　　2 Trinomials of the form ax2 + bx + c

　　3 Difference of two squares

　　4 Complete factoring

　　I Algebraic fractions

　　1 Simplifying fractions

　　2 Multiplication

　　3 Division

　　4. Addition and subtraction

　　a) Same denominators

　　b) Different denominators

　　5 Complex fractions

　　6 Equations involving fractions

　　J Radicals and irrational numbers

　　1 Simplifying radicals

　　2 Addition and subtraction of radicals

　　3 Multiplication and division of radicals

　　4 Rationalizing denominators

　　5 Radical equations

　　6 Fractional exponents

　　K. Solution of quadratic equations

　　1 Factoring

　　2 Completing the square

　　3 Formula

　　L. Graphing

　　1 Ordered pairs in the plane

　　2 Methods of graphing linear equations a) Pairs in the solution set

　　0) Intercepts

　　c) Slope and slope-intercept method

　　3 Parallel and perpendicular lines

　　4 Graphing inequalities

　　5 Graphical solution of systems of equations

　　M Solution of simple cubic equations

　　1 Factor theorem

　　2 Remainder theorem

　　3 Synthetic division

　　4 Irrational and complex roots

　　5 Solving simple cubic equations III. GEOMETRY

　　A Angles

　　1 Types—acute, right, obtuse

　　2 Complements and supplements

　　3 Vertical angles

　　B Lines

　　1 Parallel lines and their angles

　　2 Perpendicular lines

　　C. Triangles

　　1 Sum of the angles

　　2 Congruent triangles

　　3 Similar triangles

　　4 Special triangles a) Isosceles

　　0) Equilateral

　　c) Right (Pythagorean Theorem)

　　5 Vectors

　　D Polygons

　　1 Quadrilaterals a) Parallelogram 0) Rectangle

　　c) Square

　　d) rhombus

　　e) Trapezoid

　　f) Regular Polygons

　　E. Circles

　　1 Special lines and their related angles a) Radius and diameter

　　0) Chord

　　c) Tangent

　　d) Secant

　　2 Angle and arc measurement

　　3 Polygons inscribed in circles

　　F Perimeter and area

　　1 Triangles

　　2 Polygons

　　3 Circles

　　a) Circumference and arc length 0) Area of sectors and segments

　　G Volume

　　1 Pyramid

　　2 Prism

　　3 Cylinder

　　4 Cone

　　5 Sphere

　　6 cube

　　7 Rectangular solid

　　H Coordinate geometry

　　1 Coordinate representation of points

　　2 Distance between two points

　　3 Midpoint of a line segment

　　4 Slope of a line

　　5 Parallel and perpendicular lines

　　I Basic trigonometry

　　1 Definitions of sine, cosine, tangent

　　2 Trigonometry in special triangles a) 30°-60°-9u° triangle

　　0) Isosceles right triangle 3 Trigonometric problems a) Angle of elevation 0) Angle of depression

　　IV FUNCTIONS AND THEIR GRAPHS

　　A Relations and functions

　　1 Ordered pairs

　　2 Function notation

　　3 Domain and range

　　4 One-to-one functions

　　5 Inverse functions

　　6 combining functions

　　a) Addition, subtraction, multiplication, division 0) Composition

　　B Graphs

　　1 Linear a) Slope

　　0) Intercepts

　　2 Special functions

　　a) absolute value function 0) Step functions

　　3 Polynomial and rational functions a) Quadratic—parabola

　　i Axis of symmetry

　　n Vertex

　　0) cubics

　　c) hyperbola of the form xy = k

　　4 Related non-function graphs a) Circle

　　0) Ellipse

　　c) hyperbola of the form ax2 - 0y2 = c

　　5 Graphs of inverse functions

　　V REAL NUMBER SYSTEM

　　A sunsets of the real numbers

　　1 Natural numbers a) Primes

　　0) Composites—prime factorization

　　2 Integers

　　a) Multiples and divisors i Factors

　　n Divisibility

　　in Least common multiple iv Greatest common divisor v Perfect squares

　　b) Odd and even integers

　　3 Rational and irrational numbers

　　a) Decimal representations

　　b) Simplification of radicals and exponents

　　c) Identifying rational and irrational numbers

　　B Operations and properties

　　1 Properties of the binary operations

　　a) Closure

　　b) Commutative properties

　　c) Associative properties

　　d) Distributive properties

　　2 Absolute value

　　3 Real number line

　　a) Order

　　b) Density

　　c) Completeness

　　4 Properties of zero and one

　　a) Identity elements

　　b) Additive and multiplicative inverses

　　c) Division involving zero

　　d) Zero as an exponent

　　5 Nature of the roots of quadratic equations

　　6 Pythagorean triples

　　VI. LOGIC

　　A Propositions

　　1 Simple statements

　　a) Symbols

　　b) Quantifiers (all, some)

　　2 Negation

　　3 Compound statements

　　a) Conjunction

　　b) Disjunction

　　c) Implication (conditional statements)

　　i Necessary conditions

　　Sufficient conditions

　　in Equivalence (necessary and sufficient conditions)

　　d) Derived implications i Converse

　　Inverse in Contrapositive B Truth tables C Methods of proof

　　1 Valid arguments

　　a) Direct

　　b) Indirect—contradiction and counterexample

　　2 Invalid arguments—fallacies

　　VII SETS

　　A Meaning and symbols

　　1 Set notation

　　2 Set membership

　　3 Ordered pairs

　　4 Cardinality of a set

　　B Types of sets

　　1 Finite

　　2 Infinite

　　3 Empty

　　C. Relationships between sets

　　1 Equal sets

　　2 Equivalent sets

　　3 Subsets

　　4 Complements

　　D. Set Operations

　　1 Union

　　2 Intersection

　　3 Cartesian products

　　4 Laws of set operations

　　5 Closure

　　E Venn diagrams

　　VIII TRIGONOMETRY

　　A. Trigonometry of the right triangle

　　1 Definitions of the six functions

　　2 Relations of the functions of the complementary angles

　　3 Reciprocal relations among the functions

　　4 Variations in the functions of acute angles

　　5 Pythagorean and quotient relations

　　6 Functions of 30°, 45°, and 60°

　　7 Applications of the functions to right triangle problems

　　B. Trigonometric functions of the general angle

　　1 Generating an angle of any size

　　2 Radians and degrees

　　3 Using radians to determine arc length

　　4 Definitions of the functions of an angle

　　5 Signs of the functions in the four quadrants

　　6 Functions of the quadrantal angle

　　7 Finding the value of functions of any angle

　　C Identities and equations

　　1 Difference between identities in equations

　　2 Proving identities

　　3 Solving linear trigonometric functions

　　4 Solving trigonometric quadratic equations

　　D Generalized trigonometric relationships

　　1 Functions of the sum of two angles

　　2 Functions of the difference of two angles

　　3 Functions of the double angle

　　4 Functions of the half angle

　　E Graphs of trigonometric functions

　　1 Graphs of the sine, cosine, and tangent curves

　　2 Properties of the sine, cosine, and tangent curves

　　3 Definitions of amplitude, period, and frequency

　　4 Solving trigonometric equations graphically

　　F Solutions of oblique triangles

　　1 Law of sines

　　2 Law of cosines

　　3 Using logarithms to solve oblique triangle problems

　　4 Vector problems—parallelogram of forces

　　5 Navigation problems

　　IX MISCELLANEOUS TOPICS

　　A. Complex numbers

　　1 Meaning

　　2 Operations

　　a) Addition and subtraction

　　b) Multiplication and division i Powers of i

　　Complex conjugate

　　3 Complex roots of quadratic equations

　　B Number Bases

　　1 Converting from base 10 to other bases

　　2 Converting from other bases to base 10

　　3 Operations in other bases

　　C Exponents and logarithms

　　1 Meaning of logarithms

　　2 Computation with exponents and logarithms

　　3 Equations

　　4 Graphs of exponential and logarithmic functions

　　D Binary operations

　　1 Definition of binary operations

　　2 Properties of binary operations

　　3 Application to modular arithmetic

　　E Identity and inverse elements

　　1 Addition

　　2 Multiplication

　　3 Other operations

　　以上就是关于“SAT2数学知识汇总整理”的内容，更多精彩内容，请关注SAT频道!

SAT水平能力测试【0元免费测试】