词汇->知识->读题->常错细节
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 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 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 P(X-2*sigma P(X-3*sigma 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