詞匯->知識->讀題->常錯細(xì)節(jié)
A.Arithmetic
a.odd & even
b.prime & composite
c.factor & multiple
? ? prime factorization ? ?(positive only: the definition of prime number)
? ? number of factors????(positive+negative)
d.gcd & lcm
? ? both calculated by factorization
e.consecutive numbers
f.remainder
? ? dividend=quotient*divisor+remainder ? ? ?0<=remainder<|divisor|
? ? be careful when dividend or divisor is negative
g.decimal
? ? digit:
? ? ? ? hundreds digit ? ?tens digit ? ?units(ones) digit . tenths digit ? ?hundredth digit
? ? ? ? cardinal number+s+digit ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ordinal number+s+digit
? ? terminating decimal/repeating decimal
h.fraction
? ? numerator/denominator
? ? proper fraction/improper fraction/mixed number
? ? reciprocal
i.
? ? x is divided by y; y divides x;
? ? ratio; ratio of a to b;
? ? there is twice as much A as B; there is twice A as much as B; A is twice as much as B;
? ? A is 20% more than B; B is 20% less than B;
? ? analyzed by preposition
B.Algebra
a.exponent operation
b.root
? ? square root, cube root, fourth root, ... , nth root
c.equation
? ? linear equation in one variable
? ? linear equation in two variables
? ? quadratic equation in one variable
d.inequality
? ? < less than?
? ? >greater than
? ? <=less than or equal to
? ? >=greater than or equal to
e.function
? ? coordinate geometry
? ? ? ? xy-cordinate system/xy-plane
? ? ? ? quadrant
? ? ? ? symmetric /reflection ? ?(perpendicular bisector)
? ? ? ? distance
? ? linear function y=kx+b
? ? ? ? slope k
? ? ? ? intercept b ? ?(x-intercept is specifically indicated)
? ? ? ? parallel
? ? ? ? perpendicular
? ? ? ? shift
? ? quadratic function
? ? ? ? parabola
? ? ? ? vertex
? ? ? ? Vieta's Theorem
? ? circle
? ? ? ? (x-a)^2+(x-b)^2=r^2 ? ? ? ?
f.sequence
? ? arithmetic sequence
? ? geometric sequence
C.Geometry
geometric figures are not necessarily drawn to scale
geometric objects are in the relative positions shown
a.2-D geometry
? ? line
? ? ? ? parallel
? ? ? ? cross
? ? ? ? perpendicular
? ? ? ? line segment
? ? angle
? ? ? ? opposite angle/vertical angle????
????????alternative angle????
? ? ? ? corresponding angle
? ? ? ? interior angle of the same side
? ? ? ? acute/right/obtuse angle
? ? ? ? complementary angle ? ?supplementary angle
? ? triangle
? ? ? ? alpha+beta+gemma=180 degree
? ? ? ? a+b>c????<-> ? ?c-b<a
? ? ? ? equilateral triangle ? ?isosceles triangle
? ? ? ? right triangle
? ? ? ? ? ? hypotenuse & leg
? ? ? ? ? ? Pythagorean Theorem ? ?a^2+b^2=c^2
? ? ? ? ? ? special right triangle
? ? ? ? acute triangle ? ? ? ? ? ? ? ? ? ? ? a^2+b^2>c^2
? ? ? ? obtuse triangle ? ? ? ? ? ? ? ? ? ? a^2+b^2<c^2
? ? ? ? congruent triangles
? ? ? ? similar triangles
? ? quadrilateral?
? ? ? ? parallelogram
? ? ? ? ? ? rectangle
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? square
? ? ? ? ? ? rhombus
? ? ? ? trapezoid
? ? polygon
? ? ? ? triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon
? ? ? ? n-sided polygon ? ?polygon with n sides ? ?polygon with n vertices
? ? ? ? interior angle/exterior angle ? ?diagonal ? ?regular polygon
????circle
? ? ? ? radius ? ?
????????diameter
? ? ? ? chord?
? ? ? ? circumference
? ? ? ? arc ? ? ? ? ? ? ? ? ? ? ? ? (major arc/minor arc)
? ? ? ? sector
? ? ? ? tangent ? ?
b.3-D geometry (solid geometry)
? ? rectangular solids
? ? ? ? vertex, edge, face
? ?cubes
? ?cylinders
? ? ? ? base, lateral surface
D.Data analysis
a.statics
? ? concepts
? ? ? ? Mean ? ?(Arithmetic Mean/Weighted Mean) ? ?Mean(a*x+b)=a*Mean(x)+b
? ? ? ? Median ? ?(odd elements/even elements) ? ?Median(a*x+b)=a*Median(x)+b
? ? ? ? Mode ? ?(more than one number-> all are)? ? ?Mode(a*x+b)=a*Mode(x)+b
? ? ? ? Range ? ?=max-min ? ?Range(a*x+b)=a*Range(x)
? ? ? ? Variance ? ?sigma^2 ? ?Variance(a*x+b)=a^2*Variance(x)
? ? ? ? Standard Deviation ? ?sigma=sqrt(Variance) ? ?SD(a*x+b)=a*SD(x)
? ? ? ? Quartile ? ? ? ?Q1, Q2, Q3
? ? ? ? IQR (interquartile range) ? ?=Q3-Q1
? ? ? ? Boxplot ? ?L-Q1-Q2(M)-Q3-G
? ? ? ? Percentile
? ??Graphs & Tables
? ? ? ? Frequency Distribution/Relative Frequency Distribution
? ? ? ? Bar Graph
? ? ? ? Circle Graph/Pie Graph
? ? ? ? Histogram
? ? ? ? Scatterplot
? ? ? ? Time Plot
? ? Normal Distribution
? ? ? ? 3-sigma principle:
? ? ? ? P(X-sigma<x<X+sigma)=68%
????????P(X-2*sigma<x<X+2*sigma)=95%
????????P(X-3*sigma<x<X+3*sigma)=99%
b.probability
? ? mutually exclusive
? ? independent ? ?P(A^B)=P(A)P(B)
? ? conditional probability ? ?P(A|B)=P(A^B)/P(B)
? ? Bayes' Rule ? ?P(A^B)=P(A|B)*P(B)
c.combination & permutation
d.set
? ? union
? ? intersection
? ? complementary/supplementary set
? ? universal set
? ? empty set
? ??
???
? ??????
