sach day toan tieng anh (1)

7/30/2019 Sach Day Toan Tieng Anh (1)

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Ti liu tp hun ging dy mn Ton bngting Anh

1. Mathematical English Thut ng ton hc ting Anh

Chu Thu Hon - Trng PT Chuyn ngoi ng , i hcngoi ng,HQG H ni

2. Mt s vn trong vic son bi v ging dy mn Tonbng ting Anh

Nhm bin son ti liu tp hun mn Ton

3. The sine rule and the cosine rule Cc cng thc sin vcos

T Ngc Tr B gio dc

Loi bi ging: bi ging trung hc ph thng

4. Trig Derivative o hm hm lng gic

T Ngc Tr B gio dc


5. Equation of Circle Phng trnh ng trn

Nguyn c Thng Trng PT Amsterdam H Ni


6. Parametric equation of a line Phng trnh tham s cang thng (chuyn th bi ging ting Vit sang ting Anh)

Nguyn c Thng Trng PT Amsterdam H Ni



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7. Geometric Sequences Dy cp s nhn

Trn Thanh Tun i hc Khoa hc T nhin H Ni

Loi bi ging: A-level8. Application of Differentiat ion: Related Rates ng dng

ca php tnh vi phn: Cc tc bin thin ph thuc nhau

Trn Thanh Tun i hc Khoa hc T nhin H Ni

Loi bi ging: A-level

9. Permutations and Combinations - Hon v v T hp

Chu Thu Hon - Trng PT Chuyn ngoi ng , i hcngoi ng,HQG H ni

Loi bi ging: SAT


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LI NI U

Vi mc ch l trong khong 8 bui tp hun, cc thy c s sonc bi ging, v bc u c th ging bi c bng ting Anh,

nn b ti liu tp hun ny s trnh by nhng hng dn ht sc cbn vi cc bi son mu c ni dung khng kh a s cc thy cs khng gp vn kh khn g trong ni dung, m ch tp trung vocc phng php son bi ging v cch thc ging bi trn lp. cth ging bi trn lp, u tin cc thy c s phi son gio n biging . Cng vic ny kh l tng t vi vic son bi ging bngting Vit, ch khc l cc thy c s phi son bng ting Anh. V

vy, bi vit u tin trong ti liu tp hun l mt bng lit k ccthut ng Ton hc bng ting Anh kh l c bn v y . Nhngthut ng ny s l nhng t vng chuyn mn Ton cn thit chocng vic ging dy ca cc thy c. Tip theo , bi vit th hai,nhm bin son trnh by nhng hng dn c bn v cn thit ccthy c c th son mt bi ging v cc bc trnh by bi ging trn lp. Bi vit ny s cung cp cho cc thy c nhng hng dn

kh l chi tit cc thy c c th p dng v thc hnh c ngay.Phn cn li ca ti liu gm by bi son mu, trong bn bi cson theo cch chuyn th t bi son ting Vit sang ting Anh, haibi c son theo gio trnh ging dy A-level, v mt bi c sontheo gio trnh ging dy SAT. By bi son mu ny s cung cp chocc thy c nhng v d cc thy c bc u c th thc hnhson nhng bi ging ca mnh.

Nhm bin son hy vng nhng ti liu ny s gip ch c cc thyc mt phn trong vic ging dy Ton bng ting Anh. Ti liu cbin son trong mt thi gian khng di nn s c khng t thiu st,rt mong cc thy c gp nhm bin son c th chnh sa thnhmt ti liu tt hn.

Nhm bin son ti liu tp hun mn Ton.


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MATHEMATICAL ENGLISH

By CHU THU HON

GV Trng PT Chuyn ngoi ng, i hcngoi ng, HQG H ni

Arithmetic

0 zero 10 Ten 20 twenty1 one 11 Eleven 30 thirty2 two 12 Twelve 40 forty

3 three 13 thirteen 50 fifty4 four 14 fourteen 60 sixty5 five 15 fifteen 70 seventy6 six 16 sixteen 80 eighty7 seven 17 seventeen 90 ninety8 eight 18 eighteen 100 one hundred9 nine 19 nineteen 1000 one thousand

-245 minus two hundred and forty-five22 731 twenty-two thousand seven hundred and

thirty-one1 000 000 one million

56 000 000 fifty-six million1 000 000 000 one billion [US usage, now universal]7 000 000 000 seven billion [US usage, now universal]

1 000 000 000 000 one trillion [US usage, now universal]3 000 000 000 000 three trillion [US usage, now universal]

Fractions [= Rational Numbers]

12

one half38

three eighths

1

3 one third

26

9 twenty-six ninths


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14

one quarter [= onefourth]

534

minus five thirty-fourths

15

one fifth3

27

two and three sevenths

117

minus oneseventeenth

Real Numbers

-0.067 minus nought point zero six seven81.59 eighty-one point five nine

62.3 10 minus two point three times ten to the six[= -2 300 000 minus two million three hundred thousand]

34 10 four times ten to the minus three[ = 0.004=4/1000 four thousandths

[ 3.14159...] pi [pronounced as pie][ 2.71828...]e e [base of the natural logarithm]

Complex Numbers

i I3 4i three plus four i1 2i one minus two i

1 2 1 2i i the complex conjugate of one minus two i equals one plu

The real part and the imaginary part of 3 4i are equal, respectively,to 3 and 4.

Basic arithmetic operations

Addition: 3 5 8 three plus five equals [ = is equalto] eight

Subtraction: 3 5 2 three minus five equals [ = ]minus two

Multiplication: 3 5 15 three times five equals [ = ]


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fifteenDivision: 3 / 5 0.6 three divided by five equals [ =

] zero point six

2 3 6 1 5 Two minus three in brackets times six plus oneequals minus five

1 3 12 4 3

One minus three over two plus four equals minus

one third4! [ 1 2 3 4] four factorial

Exponentiation, Roots

25 5 5 25 five squared35 5 5 5 125 five cubed45 5 5 5 5 625 five to the (power of) four

15 1 5 0.2 five to the minus one25 21 5 0.04 five to the minus two

3 1.73205... the square root of three3 64 4 the cube root of sixty four5 32 2 the fifth root of thirty two

In the complex domain the notation n a is ambiguous, since any non-

zero complex number has n -th roots. For example, 4 4 has fourpossible values: 1 i (with all possible combinations of signs).

2 2

1 2

one plus two, all to the power of two plus two

1ie e to the (power of) pi i equals minus one


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Divisibility

The multiples of a positive integer a are the numbers , 2 ,3 , 4 ,...a a a a . If

b is a multiple of a , we also say that a divides b , or that a is a

divisor of b (notation: |a b ). This is equivalent tob

abeing an integer.

Division with remainder

If ,a b are arbitrary positive integers, we can divide b by a , in general,

only with a remainder. For example, 7 lies between the following twoconseentive multiples of 3:

7 12 3 6 7 3 3 9. 7 2 3 1 2

3 3

In general, if qa is the largest multiple of a which is less than or

equal to b , then

, 0,1,..., 1b qa r r a

The integer .,q resp r is the quotient(resp the remainder) of thedivision of b by a .

Euclids algorithm

The algorithm computes the greatest common divisor (notation:

,a b = gcd ,a b ) of two positive integers ,a b

It proceeds by replacing the pair ,a b (say, with a b ) byr ; a whereris the remainder of the division of b by a . This procedure, which

preserves the gcd, is repeated until we arrive at 0r .

Example. Compute gcd(12, 44).

44 3 12 8

12 1 8 4

8 2 4 0

gcd(12,44) = gcd(8,12) = gcd(0,4) = 4.


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This calculation allows us to write the fraction4412

in its lowest terms,

and also as a continued fraction:

44 44 4 11 13112 12 4 3 12

If gcd ,a b =1, we say that a and b are relatively prime.

add (v) /d/ cng

algorithm (n)

Euclids algorithm

/lrm/

/jukld/

thut ton

thut ton Euclid

bracket (n) /brkt/ du ngoc

Left bracket

right bracket

curly bracket

/left/

/rat/

/kli/

du ngoc tri

du ngoc phi

du ngoc {}

denominator (n) /dnmnet(r)/ mu s

difference (n) /dfrns/ hiu

divide (v) /dvad/ chia

divisibility (n) /dvz blti/ tnh chia ht

Divisor (n) /dvaz(r)/ s chia

exponent (n ) /kspnnt/ s mfactorial (n) /fktril/ giai tha

fraction (n)

continued fraction

/frkn/

/kntnjud /

phn s

phn s lin tc

gcd [= greatest

common divisor]

c s chung lnnht


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lcm [= least common

multiple]

bi s chung nhnht

infinity (n) /nfnti/ v cc, v tn

Iterate (v) /tret/ lynguyn hm

iteration (n) /tren/ nguyn hm

multiple (n) /mltpl/ bi s

multiply (v) /mltpla/ nhn

number (n)

even number (n)

odd number (n)

/nmb(r) /

/ivn/

/d/

s

s chn

s l

numerator (n) /njumret(r)/ t s

pair (n)

pairwise

/pe(r)/

/pe(r) waz/

cp

tng i, tng cp

power (n) /pa(r)/ ly thaproduct (n) /prdkt/ tch

quotient (n) /kwnt/ thng s

ratio (n) /rei/ t s

rational

irrational (a)

/rnl/

/r

nl/

hu t

v trelatively prime (n) /reltvli/ - /pram/ s nguyn t cng nhau

remainder (n) /rmend(r)/ d, s d

root (n) /rut/ cn, nghim

sum (n) /sm/ tng s

subtract (v) /sbtrkt/ tr


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Algebra

Algebraic Expressions

2

A a Capital a equals small a squareda x y a equals plus y b x y b equals minus y

c x y z c equals times y times z c x y z c equals y z

y z xy x plus y in brackets z plus y 2 3 5x y z x squared plus y cubed plus z to the (power of)

fiven n nx y z x to the n plus y to the n equals z to the n

3m

x y x minus y in brackets to the (power of) three m x minus y , all to the (power of) three m

2 3x y Two to the times three to they 2ax bx c a squared plus b plus c

3 y The square root ofx plus the cube root ofy

n y The n -th root ofx plus y a b

c d

a plus b over c minus d

n

m

(the binomial coefficient ) n over m

Indices

0x zero; x nought

1 ix y one plus y i

i jR (capital) R (subscript) i j ; (capital) R lower i j ;

k

i jM (capital) M upper k lower i j;


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(capital) M superscript k subscript i j

0

n i

iia x

sum of a I x to the i for i from nought [= zero] to nsum over i (ranging) from zero to n of a i (times) xto the i

1 mmb

product of b m for m from one to infinity;product over m (ranging) from one to infinity of bm

1

n

i j j k ja b

sum of a I j times b j k for j from one to n;sum over j (ranging) from one to n of a i j times bj k

0

n i n i

i

nx y

i

sum of n over i x to the i y to the n minus i for ifrom nought [= zero] to n.

Matrices

column (n)

column vector

/klm/

/vekt(r)/

ct

vect ct

determinant (n) /dtmnnt/ nh thc

index (n)

(pl. indices)

/ndeks/

(/ndsiz/)

s m

Matrix (n)

matrix entry (pl.entries)

m n matrix [ m by n

matrix]

/metrks/

/entri/

ma trn

h s ma trnma trn m n

row (n)

row vector

/r/

/vekt(r)/

hng

vect hng


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Inequalities

x y is greater than y x y is greater (than) or equal to y x y is smaller than y x y is smaller (than) or equal to y

0x is positive0x is positive or zero; is non-negative0x is negative0x is negative or zero

Polynomial equations

A polynomial equation of degree 1n with complex coefficients

10 1 0... 0 0n n

nf x a x a x a a

has n complex solutions (= roots), provided that they are counted withmultiplicities.

For example, a quadratic equation

2ax 0 ( 0)bx c a

can be solved by completing the square , i.e. , by rewriting the L.H.Sas

2

onstana x c t another constant.

This leads to an equivalent equation

2 2 4,

2 4b b ac

a xa a

whose solutions are

1,2

2

bx

a


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where 22 2 1 24b ac a x x is the discriminant of the originalequation. More precisely,

2

1 2ax .bx c a x x x x If all coefficients , ,a b c are real, then the sign of plays a crucial role

If 0 , then 1 2 2x b a is a double root;

If 0 , then 1 2x x are both real;

If 0 , then 1 2x x are complex conjugates of each other (and

non-real).

coefficient (n) /kfnt/ h s

Degree (n) /dri / , cp bc

discriminant bit s, bit thcEquation /kwen/ phng trnh

L.H.S. [= left hand

side]R.H.S. [= right hand

side]

v tri

v phi

polynomial (adj) /plinomil/ a thc

polynomial (n) phng trnh i sProvided that /prvadd/ ga s

root (n) /smpl/ cn, nghim

simple root /dbl/ nghim ndouble root /trpl/ nghim kp

Triple root /mltpl/ nghim bi ba

multiple root nghim bisolution(n) /slun/ nghim, li gii,

php giisolve (v) /slv/ gii


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Congruences

Two integers ,a b are congruent modulo a positive integer m if they

have the same remainder when divided by m (equivaqlently, if their

difference a b is a multiple of m ).

(mod )a b m a is congruent to b modulo m

( )a b m

Some people use the following, slightly horrible, notation:

.a b m

Fermats Little Theorem. Ifp is a prime number and a is an

integer, then modpa a p . In other words, pa a is always divisible

by p .

Chinese Remainder Theorem.If 1 2, ,..., km m m are pairwise relatively

prime integers, then the system of congruences

1 1mod ... modk kx a m x a m

has a unique solution modulo 1 2, ,..., km m m , for any integers 1 2, ,..., ka a a .

Geometry

Lines and angles

line AB (n) /lain/ ng thng AB

ray AB (n) /rei/ tia AB

line segment AB (n) /lain 'segmnt/ on thng AB

length of segment

AB (n)

/lev 'segmnt/ chiu di onthng AB


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AB XY means the

same thing as AB =

XY

/mi:nz seim iz/

ng ngha vi,tng t nh

angle(n) /'gl/ gc

vertex(n) /v:teks/ nh

acute angle /'kju:t 'gl/ gc nhn

right angle /'rait 'gl/ gc vung

obtuse angle /b'tju:s 'gl/ gc t

straight angle /stret 'gl/ gc bt

m A = m B we can

write A B:

congruent

/kgrunt/ tng ng,bng

supplementary (a) /splmntri/ ph

complementary(a) /,kmpli'mentri/ b

vertical angle(n) /'v:tikl 'gl/ gc i nh

bisect(v) /baisekt/ chia i

midpoint(n) /midpint/ trung im

perpendicular(a) /p:pn'dikjul/ vung gcparallel(a) /'prlel/ song song

transversal(n)(a) /trnzv:sl/ ngngang,ngang


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Triangle

exterior angle(n) /eks'tiri 'gl/ gc ngoi

scalene triangle(n) /skeili:n traigl/ tam gic thng

isosceles triangle(n) /aissili:z traigl/ tam gic cn

equilateral

triangle(n)

/i:kwiltrl

traigl/

tam gic u

acute triangle(n) /'kju:t traigl/ tam gic nhn

Obtuse triangle (n) /b'tju:s traigl/ tam gic t

right triangle(n) /'rait traigl/ tam gic vung

hypotenuse(n) /hai'ptinju:z/ cnh huyn

leg(n) /leg/ cnh gc vung

Pythagorean

theorem and

corollaries

/paigrin 'irm

nd k'rlris/

nh l pythagore v

h qu

perimeter (n) /primit/ chu vi

triangle inequality(n) /traigl ,ini:'kwliti/ bt ng thc tam gic

height(n) /hait/ chiu cao

altitude(n) /ltitju:d/ chiu cao

Similar triangles(n) /simil traigls/ tam gic ng dng

ratio of similitude(n) /reiiou v

similitju:d/

t s ng dng


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Quadrilaterals and other polygons

/kwdriltrls nd r pligns/ t gic v cc agic khc

polygon(n) /plign/ a gic

side (n) /said/ Cnh

vertex (n) /v:teks/ nh

vertices s nhiu ca vertex

diagonal(n) /daignl/ ng cho

quadrilateral(n) /kwdriltrl/ t gic

regular polygon (n) /'rgjul plign/ a gic u

exterior angle

(n)

/eks'tiri 'gl/ gc ngoi

parallelogram(n) /prlelgrm/ hnh bnh hnh

base (n) /beis/ y

height (n) /hait/ chiu cao

opposite sides are

parallel: AB//CD

and AD //BC

/'pzit saids :'prlel/

cc cnh i dinsong song

opposite sides are

congruent: AB CD

and AD BC

/'pzit saids :kgrunt/

cc cnh i dintng ng/bngnhau


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opposite angles are

congruent: A

C and B D

/'pzit 'gls:kgrunt/

cc gc i dintng ng

/bng nhau

two congruenttriangles: ABC

ACD

/tu: kgrunttraigls/:

hai tam gic tngng/bng nhau

rectangle (n) /rektgl/ hnh ch nht

length (n) /le/ chiu di

width (n) /wd/ chiu rng

rhombus (n) /rmbs/ hnh thoi

Square (n) /skwe/ hnh vung

trapezoid(n) /trpizid/ hnh thang

isosceles trapezoid(n)

/aissili:z trpizid/ hnh thang cn

perimeter (n) /primit/ chu vi

Circles

circle (n) /'s:kl/ ng trn

center (n) /'sent/ tm

radius (n) /reidis/ bn knhdiameter(n) /dai'mit/ ng knh

chord (n) /krd/ dy cung

circumference(n) /s:kmfrns/ chu vi ng trn

semicircle(n) /semis:kl/ na ng trn,bn nguyt

arc (n) /rk/ cung


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intercept (v) /'intsept/ chn

central angle (n) /sentrl 'gl/ gc tm

Solid and coordinate geometry

rectangular solid =

box(n)

/rek'tgjul/ /'slid/ Hnh hp ch nht

face (n) /feis/ mt, b mt

edge (n) /ed/ Cnh

length (n) /le/ Chiu di, di

width (n) /wid / Chiu rng

height (n) /hait/ Chiu cao

cube (n) /kju:b/ Hnh lp phng

volume (n) /'vljum/ Khi, th tch

cubic unit (n) /'kju:bik/ /'ju:nit/ n v lp phng

surface area (n) /'s:fis/ /'eri/ Din tch b mt

diagonal (n) /dai'gnl/ ng chocylinder(n) /'silind/ Hnh tr

circle (n) /'s:kl/ ng trn

prism (n) /prism/ Lng tr

two congruent

parallel bases

/kgrunt//'prlel/

hai y song song


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right prism (n) /rait/ /prism/ Lng trng

cone (n) /koun/ Hnh nn

slant height (n) /sl:nt/ /hait/ ng sinh

circumference(n) /s'kmfrns/ Chu vi

Lateral surface area

(n)

/'ltrl/ /'s:fis/

/'eri/

Din tch xung

quang

pyramid(n) /'pirmid/ Hnh chp

polygon(n) /'plign/ a gic

Square(n) /skwe/ Bnh phng, hnhvung

triangle (n) /traigl/ Hnh tam gic

Sphere(n) /sfi/ Hnh cu, mt cu

Radius(n) /reidis/ Bn knh

radii(n) /'reidjai/ S nhiu ca bnknh

x-axis(n) /eks/ /'ksis/ Trc honh

y-axis (n) /wai/ /'ksis/ Trc tung

origin(n) /'ridin/ Gc ta

quadrant(n) /'kwdrnt/ Gc phn t, cung

phn t

x-coordinate (n) /eks/ /kou':dnit/ Honh

y-coordinate (n) /wait/ /kou':dnit/ Tung

horizontal line (n) /,hri'zntl/ /lain/ ng thng song

song trc honh


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vertical line (n) /'v:tikl/ /lain/ ng thng song

song trc tung

midpoint of a

segment (n)

/'segmnt/ Trung im ca

on thng

slope (n)=gradient /sloup/ H s gc

equation of line (n) /i'kwein/ /v, v/

/lain/

Phng trnh

ng thng

y-intercept (n) /'intsept/ Giao vi trc tung

parabola /p'rbl/ Parabolaxis of symmetry /'ksis/ /v, v/

/'simitri/

Trc i xng

vertex or turning

point

/'v:teks/ - /'t:ni/

/pint/

nh

y = ax

2

+ bx + c, a >0

The parabola opens

upward and the

vertex is the lowest

point on the

parabola

y = ax

2

+ bx + c, a

sach day toan tieng anh (1)

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